AUTO-ELECTROKINETIC FLOWS IN DEAD-END PORES FROM MIXED ION SYSTEMS

Transcription

1 The Pennsylvania State University The Graduate School Department of Chemical Engineering AUTO-ELECTROKINETIC FLOWS IN DEAD-END PORES FROM MIXED ION SYSTEMS A Thesis in Chemical Engineering by Abhishek Kar 2013 Abhishek Kar Submitted in Partial Fulfillment of the Requirements for the Degree of Master of Science May 2013

2 The thesis of Abhishek Kar was reviewed and approved* by the following: Darrell Velegol Distinguished Professor of Chemical Engineering Thesis Adviser Ayusman Sen Distinguished Professor of Chemistry Themis Matsoukas Professor of Chemical Engineering Robert Rioux Assistant Professor of Chemical Engineering Andrew L. Zydney Walter L. Robb Chair and Professor of Chemical Engineering Head of the Department of Chemical Engineering *Signatures are on file in the graduate school. ii

3 ABSTRACT In this dissertation, I demonstrate fluid flows using a mechanism called diffusiophoresis. Using modeling and experiments, I show that fluid flows and particle migration can occur over a distance of merely 1 millimeter phenomenon. Based on the physics behind diffusiophoresis, this thesis seeks to answer the following questions: a) What is the transport rate of particles by diffusiophoresis through a self-generated ion gradient especially from dissolving minerals? b) What are the transport and pumping rates in dead-end capillaries due to diffusiophoretic and diffusioosmotic flows from imposed gradients of simple monovalent salts (e.g. NaCl)? c) Can we control transport in dead-end capillaries in mixed ion mineral systems which have more complex diffusion patterns and shuttle changes in zeta potentials? Diffusiophoretic mechanism operates on the basis of spontaneous generation of electric field from an ion-gradient source which generates motion of charged mobile particles and diffuse layer across wall surfaces, creating flows similar to electrophoresis and electroosmosis respectively. It is an auto-electrokinetic mode of transport and fluid flow involving no external electric field in the system. Such flows are shown to occur even in dead-end capillaries which are inaccessible to any other form of fluid flow mechanism. Particle transport through diffusive processes have been studied before in relation with reaction-diffusion in biology and chemistry, Brownian ratchet processes, dispersion in microfluidics and even salt-fingering in ocean mixing. However, by establishment or selfgeneration of salt gradients, particle migration is shown to be boosted significantly. The novelty in my work comes in through experiments via various ion-gradient generation mechanisms iii

4 which show that diffusiophoresis can generate flows in capillaries with a dead-end where pressure-driven flows seize to operate. In this work, I show that the essential physics of diffusion-induced fluid flow could be used to generate pumping from calcium carbonate micropumps in microporous geologic systems, which could be further used for extraction of oil plugs entrapped inside dead-end pores of reservoir rocks. An understanding of the morphology of channels, and slip at the walls under extreme conditions of temperature and pressure, would give us a better understanding of the feasibility of diffusiophoresis in actual geological deposits. iv

5 TABLE OF CONTENTS LIST OF FIGURES... viii LIST OF TABLES... xv Chapter 1. Motivation and Research Goals The Motivation Overview of Thesis Research Objectives Experimental Strategy Summary of Results Applications of Diffusiophoresis Organization of the Dissertation Chapter 2. Auto-electrokinetic Flows: The Theory of Diffusiophoresis Charges on Entities Electrical Double Layer Zeta Potential Diffusiophoresis Theory Expression for Diffusiophoresis Electroosmosis: Electrophoresis: Ion Migration Electrokinetic Speed of tracers Chemiphoresis and Chemiosmosis Total Velocity Chapter 3. Experimental Methods Requirements of the Experiments Materials Zeta Potential Measurements Instrumentation Determining Speeds of Tracer Particles v

6 The vertical reservoir and sink set-up Predictions from Vertical capillaries Tracer particle tracking in CaCO 3 micropumps Preparation of emulsions and carbonated water Chapter 4. Diffusioosmotic Flows in Capillaries from Imposed Gradients of Monovalent Salts The Goal Experimental Design Experimental Results Modeling of diffusiophoresis for multiple ions in a closed tube Modeling Results Discussion Conclusion Chapter 5. Self-generated Diffusioosmotic Pumping from Calcium Carbonate Micropumps Introduction Materials and Experimental Methods Materials Calcium and Barium Carbonate Microparticle Synthesis Observation of Pumping Behavior of Carbonate Microparticles Observation of Pumping Behavior of Natural Rock Samples Zeta Potential measurements of particles and substrate Analysis of Pumping Behavior Results and Discussion Mechanism of flow Conclusion Chapter 6. Diffusioosmotic Pumping of Oil Emulsions from Dead-end Capillaries Mixed ion system: CaCO 3 with NaCl Diffusioosmotic pumping of oil emulsions Extraction of oil emulsions through carbonated water vi

7 Chapter 7. Conclusion and Future Work Summary of the thesis Future work Applications REFERENCES Appendix A.1. Calcium Carbonate Aqueous Equilibrium A.2. Concentration Profile and Diffusiophoretic Velocity Profile for a Calcium Carbonate Sphere Dissolving into an Infinite Bath vii

8 LIST OF FIGURES Figure 1-1: A schematic illustration of colloid-mediated transport in porous media. The sketch illustrates the transport of molecular solutes by colloidal particles. The extent of such transport and its importance are determined by a number of factors, such as the extent of adsorption of molecular solutes on the colloids and the grains, the deposition and retention of colloids in the pores, the influence of charges on the colloids and the pore walls, and so on. (Hiemenz, 1997).. 4 Figure 1-2: A schematic for extraction of oil plugs (dark region) trapped inside a dead-end microchannel and being pumped put through electroosmotic flow along the walls... 4 Figure 1-3: (a) Schematic of a velocity profile in streaming potential flow in a closed slit microcahnnel having a negative zeta potential. The flow profile is the same for a closed electrophoretic experiment with glass capillaries of negative zeta potential at the given salt and ph condition. (b) Schematic of vertical systems I have instead of the conventional electrophoretic cell with applied electric field across the cathode and the anode. Electric fileds are self-generated when ions from the reservoir diffuse in to the sink at different rates, and depending on whether the cation or the anion diffuses faster, the electric field is always pointed from the cation to the anion Figure 1-4: Schematic showing dissolution of calcium carbonate micropump placed on a negatively-charged substrate (silica, glass). In an aqueous medium, ions dissolve and diffuse at different rates in the solution. The anion diffusing faster than the cation, sets up an electric field normal to the surface of the pump, and pointing in the direction from the cation to the anion. The concentration gradient decays radially in space from the surface of the micropump Figure 1-5: Schematic showing oil plug extraction through diffusioosmotic flows induced by external salt gradients set-up in the confined system. The inner capillary, acting as the sink, has the lower salt concentration and oil plugs whereas the outer capillary, acting as the reservoir, has the higher salt concentration and nanoparticle tracers. The disparity in salt concentrations sets up diffusioosmotic flows along the walls of the inner capillary thereby driving particles in, and oil plugs out Figure 2-1: Schematic showing the electric double layer across a charged colloidal particle in an aqueous solution. The zeta potential of the particle is given by the charge at slipping plane of the colloidal particle. (Chapter 16, Malvern Zetasizer Manual) viii

9 Figure 2-2: Driving fluid movement by diffusioosmosis and diffusiophoresis. A schematic showing a salt gradient, with a low concentration on the left and high on the right. A spontaneous electric field arises, causing fluid flow on any charged surface, such as the particles and the wall below. The E field arises because the anion here (green circles) has a higher diffusion constant than the cation (yellow circles). The flow around the particle causes it to move ~10 m/s, and the flow at the wall which could be a pore wall is similar Figure 2-3: Directions of the particle velocity components and fluid flows that together constitute diffusiophoresis. This schematic assumes a system wherein both the particle and the underlying substrate are negatively charged, and the diffusion constant of the anion of the electrolyte is larger than the diffusion constant of the cation (i.e. the system laid out in Figure 1). Two constituent flows around the particle (due to chemiphoresis and electrophoresis) are shown, however, the same effect that creates these flows causes the particle to swim in the opposite direction (labeled Particle swim direction, note the corresponding black and red boarder on this arrow). If the diffusion constants were reversed from what is shown here, the electrophoretic and electroosmotic components in this schematic would reverse their directions, but the chemiosmotic and chemiphoretic components would be unaffected. Similarly, if the charge on the particle or substrate were reversed, the respective electrophoretic or electroosmotic components would reverse direction, but not the chemiphoretic or chemiosmotic components. 19 Figure 2-4: Electroosmotic flow in an open slit microchannel arising from an imposed salt gradient with higher salt concentration at the right and the lower salt concentration at the left. The walls are negatively charged and positive ions form the double layer around it Figure 2-5: Electrophoretic flow of a charged colloidal particle under electric fields generated from imposed salt gradients. Since the colloid is negatively charged, it moves against the electric field Figure 3-1: (a) Schematic of the vertical reservoir and sink system to study diffusiophoresis using colloidal particles and glass walls (b) Picture of the actual set-up showing two capillaries, the bigger at the bottom and the thinner at the top, sealed with the help of wax Figure 3-2: Set-up showing arrangement to make carbonated water. The needle going into the vial having water injects CO 2 at 25k Pa for 30 minutes. This forms carbonated water Figure 4-1: Microscope inclined on its hinge to a vertical position with gravity acting perpendicular to the normal of the sample base ix

10 Figure 4-2: Capillary set up of reservoir and sink with high salt concentration in the reservoir and lower salt concentration in the sink Figure 4-3: Movement of particles in a vertical capillary system. (a) A snapshot image of the vertical capillaries with DI and 3.0 µm spsl is in the outside capillary (reservoir) and 10 mm KCl in the inside capillary (sink). The inner capillary is sealed at the top to form a dead-end. Tracers are pulled in against gravity into the inner capillary (b) Similarly, a dead-end system with 10 mm KCl and 3.0 µm spsl in the outer capillary (reservoir) and DI in inner (sink). There is no flow against gravity into the inner capillary. Particles settle under gravity in outer capillary. (c) 3 time lapse shots of tracers (c.1, c.2, c.3) being pulled inwards by 10mM KCl rather than settling to the bottom. The inner capillary has 10mM KCl and 3.0 µm spsl and the outer capillary has DI. Particle under no salt gradient would have settled under gravity. However, due to chemiphoresis, they are pulled up against gravity Figure 4-4: A snapshot image of the vertical capillaries with salt as 10 mm NaCl in the inner capillary (reservoir) which has a closed end at the top and DI in the outer section acting as the sink. 3.0 µm spsl particles are dispersed in the inner capillary and are seen to move against gravity towards the dead end section. The flow profile of these tracers can be tracked and seen to be parabolic in nature, indicating minimum velocity at the wall surfaces (due to no-slip at boundary) and maximum velocity in the middle section. The speeds are roughly 3.5 ~ 4 µm/s up the inner capillary. The combination of all the 4 phenomena results in an increase in particle speed, with the dominant effect being electrokinetics Figure 4-5: Speeds of particles in capillaries, for diffusiophoresis in the presence of calcium carbonate. (a) The schematic of a vertical capillary immersed in the reservoir with salt solution. (b), (c), and (d): Particle speed at different distances from the reservoir with respect to time. (b) n 0 = 1 mm CaCO 3, ζp = -30 mv, ζw = -11 mv. (c) n 0 = 1 mm KCl, ζ p = -104 mv, ζ w = -70 mv. (d) n 0 = 1 mm NaCl, ζ p = -101 mv, ζ w = -65 mv Figure 4-6: The parabolic flow profile of tracers across the width of the capillary measured at height, h=0, from simulation and experimental data (a) Schematic of the set-up analyzed with 1 mm NaCl and 3 µm spsl at the top and DI water at the bottom. The electric field points into the outer capillary. (b) The parabolic flow profile for tracers at a distance of 200 µm from the mouth of the inner capillary. The simulation results were calculated for 100, 200 and 300 secs after the systems has been set-up. Interestingly, the speeds increase with time and then start decreasing. x

11 The dotted points show the experimental data for the particle velocities tracked at the same distance away from the mouth of the capillary. The speeds were couple of orders of magnitudes lesser than that obtained from simulation Figure 4-7: The parabolic flow profile of tracers across the width of the capillary measured at height, h=0, from simulation and experimental data (a) Schematic of the set-up analyzed with 1 mm NaCl at the bottom and DI water and 3 µm spsl at the top. The electric field points into the inner capillary. (b) The parabolic flow profile for tracers at a distance of 200 µm from the mouth of the inner capillary. The simulation results were calculated for 100, 200 and 300 secs after the systems has been set-up. Interestingly, the speeds increase with time and then start decreasing. The dotted points show the experimental data for the particle velocities tracked at the same distance away from the mouth of the capillary. The speeds were couple of orders of magnitudes lesser than that obtained from simulation Figure 5-1: Two calcium carbonate micropumps showing tracers getting pumped away on the glass surface after being pulled in from the bulk. These are 1.5 µm spsl particles and they are suspended in DI water along with the micropumps Figure 5-2: Schematic of microflows for one single CaCO 3 particle micropump and two images of the same micropump showing aggregation and exclusion region. These systems contained only calcium carbonate pumps (~ 5 µm) and 3 μm sulfate-functionalized polystyrene latex tracer particles (spsl) in DI water. Scale bars in these images are 10 μm. The videos (S1 and S2 respectively) were filmed on a bare glass substrate using an inverted microscope. (a) Tracers in the bulk get attracted towards the pump, some adhere, and the rest get pumped out in to the bulk radially. (b) The spsl tracers are adhered to the surface of the pump, but not permanently. (c) A clear exclusion region of tracers develops around the micropump on the glass surface. These tracers exhibit Brownian motion mostly and rise up in to the solution Figure 5-3: Schematic of microflows for one single CaCO 3 particle micropump and two interacting micropumps with no aggregation or exclusion region. These systems contained only calcium carbonate pumps (~10 µm) and 3.5 μm amidine-functionalized polystyrene latex tracer particles (spsl) in DI water. Scale bars in these images are 10 μm. The videos (S3 and S4 respectively) were filmed on a bare glass substrate using an inverted microscope. (a) Tracers settle on to the glass surface vertically around the calcite particle. The settling times are enhanced when the tracers are directly over head the pump. On reaching the surface, they get pumped out by the flow going out radially. (b) Very little aggregation of tracers around the micropump. (c) Two interacting micropumps with no stagnation region of flow xi

12 Figure 5-4: Microflows for one single CaCO 3 particle micropump and two interacting micropumps. These systems contained only calcium carbonate pumps and 1.4 μm sulfatefunctionalized polystyrene latex tracer particles (spsl) in DI water. (a,d) time-lapse images. The videos (S1 and S5 respectively) were filmed on a bare glass substrate using an inverted microscope. Optical microscopy time-lapse images were taken at 40 magnification with overlays every 0.2 s. Scale bars in these images are 10 μm. In the vector field plots, axes are distance in μm. (b, e) vector field. The black circles represent the location of the micropumps, and the vector arrows represent the tracer particle direction and speed in μm/s at the substrate surface. The plots were generated by tracking the movement of particles over 0.3 seconds. (c, f) radial speed plots. In (c), the radial speeds of all spsl tracers sampled in (b) are plotted against the distance of those tracers from the center of the lone calcium carbonate micropump. In (f), the radial speed of tracer particles within 6 microns of the line between the two micropumps in (e) (boxed area shown) is plotted against the distance of those tracers from the midpoint between the two pumps. In both cases, curves have been added to guide the eye. 70 Figure 5-5: Barium carbonate microparticle pumping 1.4 μm spsl tracer particles outward, overlays are 0.33 sec apart, scale bar is 20 μm Figure 5-6: Flows for one single gypsum rock particle and three time lapse images of flows for calcite rock particle. The rocks were rough less than 1 µm in size. The scale bars in the image is 40 µm. For Alabaster, the tracers got pumped out at the bottom surface, and as the rock was sandwiched in between two surfaces and closed at the edges, the flows reversed back mostly through the middle extending up to the top plate. The flows out at the top did not extend for more than 200 µms into the bulk, whereas flows at the bottom extended for more than a centimeter. For the calcite rock, similar flows were seen. However, in this case the calcite was taken in a capillary and sealed at all the ends. The tracers got pumped out at the bottom layer, and came back from the top Figure 6-1: A snapshot image of the vertical capillaries with 10 mm NaCl in the inner capillary which has a closed end at the top and 0.5 mm CaCO 3 in the outer capillary which is sealed too. 3.0 µm spsl particles are dispersed in the outer capillary and are seen to move against gravity towards the dead end section of the inner capillary. Particles in the bulk of the outer capillary seem to settle under gravity until they reach the mouth of the inner capillary where they are rapidly pulled inside. The velocities increase with increase in NaCl concentration. In this case, the direction of electric field produced from the leading and the lagging ions of each system act xii

13 opposite to each other. However in such mixed ion systems, there is not a simple prediction regarding the direction of field Figure 6-2: A schematic showing oil plug extraction through diffusioosmotic flows induced by external salt gradients set-up in the confined system. The inner capillary, acting as the sink, has the lower salt concentration and oil plugs whereas the outer capillary, acting as the reservoir, has the higher salt concentration and nanoparticle tracers. The disparity in salt concentrations sets up diffusioosmotic flows along the walls of the inner capillary thereby driving particles in, and oil plugs out Figure 6-3: (a) Extraction of oil droplets from a dead-end pore. A time lapse image showing oil plug extraction through diffusioosmotic flows induced by external salt gradients set-up in the confined system. The salt outside in the reservoir is 0.5 mm CaCO 3 with 3.0 µm spsl particles in it. The inner capillary has DI with roughly 10 ~ 20 µm (or even larger sized) oil emulsions formed through emulsification of hexadecane with 2% Tween-20 solution. Along the wall of the inner capillary, tracers are transported inside along with fluid flow due to chemiosmosis and electroosmosis, respectively. As it is a dead end capillary, the fluid comes back through the middle section of the inner capillary carrying with it the oil plugs and drains them off into the reservoir Figure 6-4: A time lapse image showing a hexadecane oil plug emulsified with oleic acid being pumped out of inner capillary having DI, and outer capillary having 0.5 mm CaCO Figure 6-5: (a) A similar vertical capillary set-up to visualize flows under carbonated water gradients with different solution in the other chambers. However, the set-up is inverted in comparison to the previous ones for a better visualization of flows (b) Snapshot images of the experiments with carbonated water. Inner capillary contained carbonated water and 3.0 µm spsl particles, while outer capillary was filled with: (a) DI water, (b) CaCO 3 solution (5mM), (c) NaCl solution and (d) carbonated water (control). In experiments (a), (b) and (c) particles showed movement against gravity, while in the control (d) particles move along the direction of gravity Figure 7-1: Tributary networks. a) Marble Canyon Section of the Grand Canyon. Small tributaries feed a larger stream of water. b) Our model experimental system. The larger horizontal tube will contain aqueous solution driven by pressure. The smaller tributaries will contain oil rich phase(s), which will be actively transported into the main channel by diffusio- xiii

14 osmosis. The tributaries could enter straight, or slanted (as shown). Both types will be built at the Penn State Nanofabrication Lab, which we have extensive experience using. c) The net effect of the extraction process Figure 7-2: Long cross-linked chains of colloidal spsl particles exposed to 0.5 mm CaCO 3 for 1 hour xiv

15 LIST OF TABLES Table 3-1: A list of salts used in my experiments with their specific molecular weights and diffusion coefficients of the ions produced on dissolution of these minerals in water Table 3-2: Protocol followed for tracking particles undergoing diffusiophoretic in a vertical configuration Table 4-1:Diffusivities of different ions produced from salts Table 4-2: Diffusivities of different ions produced from salts Table 5-1: Zeta potential values (mv) in various solutions xv

16 ACKNOWLEDGMENTS If the only prayer you said in your whole life was, thank you, that would suffice - Meister Eckhart, a famous German theologian during the Holy Roman Empire. Like most research projects, achieving my Masters has been a collaborative process, and I couldn t have done this without the support from the pillars of my life and the peers to whom I owe my utmost gratification. First of all, I would like to thank my scientific advisor: Darrell Velegol, who with his clarity of thinking, amazing motivational prowess and affection for students can make any individual realize the peak of his dreams. His reiteration of the words: A good scientific question is at the heart of any good research project served me well. I consider myself truly fortunate to have had the opportunity to work with him. I would like to thank my committee members: Ayusman Sen: who with has uncanny knack of asking the right scientific questions and the ability to put things in perspective, drove optimism and a refreshing outlook towards things I pursued; and Themis Matsoukas and Robert Rioux who provided valuable support and advice. I would also like to thank the Velegol lab group who helped me learn the skills and then explore in a very friendly environment where each one was treated as a family member. Neetu Chaturvedi (DuPont), Joe McDermott (postdoc, Harvard), Laura Mely Ramiréz (Sabic) and Tso- Yi Chiang Thank you guys! Finally, I would like to thank my family for their encouragement during hard times: Dad, Mom and my sister. My friends at Penn State, for making sure that I enjoy my graduate life; and last but not the least, my fiancé: Chandra, for being so far away (in India) but being at the heart of everything I do and everything I strive for. 1

17 Chapter 1 Motivation and Research Goals 1.1. The Motivation Colloidal transport plays an important role in industrial processes (Zhang 2002, Ferrigno 2002), waste water treatment (Yao 1971, Logan 2008) drug delivery applications (Langer 2000, Langer 1990), ground water mobilization (Ryan 1996), oil extraction etc. (Liu 2005). Many of the current industrial needs for colloidal particles stems from modern ways of oil recovery or Enhanced Oil Recovery (EOR) techniques that apply colloids as nanosensors for detecting oil deposits and oil-bore parameters. The petroleum industry needs micro/nano sensors that describe the : 1. Chemical and physical properties of reservoir fluids and rocks beyond the wellbore, 2. Three dimensional (3-D) distribution of reservoir fluids and rocks, and 3. Dynamic paths of fluids driving oil plugs in-or-out of closed confined spaces. Mobility being a major issue, a thorough understanding of transport of nanosensors through various pathways and mechanisms is a challenge to the entire geologic and chemical engineering community. My research in colloidal transport focuses on working at this cross-junction and exploring the relevant science in both the fields of engineering. A major challenge in engineering colloidal flows is in understanding the solution parameters and the geologic conditions, otherwise referred to as the reservoir and the sink (or the container) from chemical engineering perspective. With more than 60% of the oil deposit in earth entrapped inside the narrow, porous, dead-end structures of reservoir rocks, EOR techniques are focused at implementing modern strategies and pathways for oil recovery from these inaccessible resources. Convective flows induced from pressure gradients, according to Hagen-Poiseuille s equation (Bird 1960) 2

18 P 8 Q 4 L r require increasing pressure drops on shrinking channel diameters as r 4, where r being the radius of the channel to maintain the same flow rate. Moreover, in dead-end channels with just one inlet and no outlet, pressure driven flows seize to exist. This has been one of the major reasons behind the failure of existent EOR techniques like carbon dioxide sweeping, high-pressure steam injection and other expensive technologies like surfactant flooding and microbial injection based EOR processes. Electrokinetic flows is the only feasible way of non-destructive access to oil plugs entrapped inside tight, porous, dead-end rock systems. Their feasibility is enhanced in narrow channels as the flow rates vary as function of r 2 (Eqn.1) Q ek = v do (pr 2 ) where, v do represents the diffusioosmotic flow given by Smoluchwoski s equation which will be discussed later in this chapter. Electrokinetic pumps were first proposed by Osterle and Morrison (Ref 1965) almost 50 years ago as a means to generate large pressures using electric fields and have been amply applied and developed since (Reichmuth 2003, Yao 2003, Laser 2004, Terray 2002). The central idea is to exploit the fact that it is relatively easy to drive fluid flows through small spaces (e.g., small capillaries and porous rocks) electrokinetically as compared with pressure-driven flows. 3

19 Figure 1-1: A schematic illustration of colloid-mediated transport in porous media. The sketch illustrates the transport of molecular solutes by colloidal particles. The extent of such transport and its importance are determined by a number of factors, such as the extent of adsorption of molecular solutes on the colloids and the grains, the deposition and retention of colloids in the pores, the influence of charges on the colloids and the pore walls, and so on. (Hiemenz, 1997) Electrokinetic flows through a closed dead-end capillary leaves the fluid with nowhere to go, and conservation of mass then requires an equal and opposite (pressure-driven) fluid flux. The container, then, must establish whatever backpressure is required to drive the backflow - the smaller the pores, the higher the pressure (Squires 2008). Figure 1-2: A schematic for extraction of oil plugs (dark region) trapped inside a dead-end microchannel and being pumped put through electroosmotic flow along the walls Electrokinetic flows require an external power source for flows to happen. In dead channels and at depths of 15,000 ft. below the earth s crust, such a thing is not feasible. Thankfully though, seawater is saline. And this salinity can be used to create spontaneous 4

20 electric fields enabling electrokinetic flows in the porous spaces. The mechanism of it is called diffusiophoresis and diffusioosmosis (Anderson 1989). Such electric fields, roughly 1-10 V/cm, and related voltages called Spontaneous Potentials (Glover notes) are well-known to arise from stratification of salts into various concentration patterns. The mechanism of diffusiophoresis, though hasn t received much of attention compared to conventional electrokinetic flows, has several advantages: Its origin is purely physical in nature It requires no external power input It can convert energy coming from chemical reactions into a directed motion of fluid and particles It can assist transport in dead-end channels 1.2. Overview of Thesis The common theme of my thesis is dedicated towards understanding such diffusioosmotic flows generated from salinity gradients and their quantification in homogeneous and heterogeneous capillaries. Self-generated diffusioosmotic pumps are also analyzed for their flow fields and condition dependency. In order to quantify this phenomenon for a general case with multiple salts, I look at diffusion-driven flow patterns in mixed ion systems. I also look at applying these techniques of flow to drive fluid into-and-out of narrow, tight dead-end pores and transporting oil emulsions through the length of the capillary. 5

21 Research Objectives In this dissertation, I look at the process of diffusioosmotic flow in dead-end capillaries, especially in the context of mixed ion systems, and set forth the following goals: 1. self-generated diffusioosmotic pumping. What is the transport rate of particles by diffusiophoresis through a self-generated ion gradient especially from dissolving minerals? 2. dead-end pores. What are the transport and pumping rates in dead-end capillaries due to diffusiophoretic and diffusioosmotic flows from imposed gradients of simple monovalent salts (e.g. NaCl)? 3. multi-valent mixed ionic systems: Can we control transport in dead-end capillaries in mixed ion mineral systems which have more complex diffusion patterns and shuttle changes in zeta potentials? Along with these research goals, I also present my plans for future work oriented towards diffusioosmotic flows in porous anisotropic heterogeneous capillaries under extreme conditions of pressure and temperature. I propose a plan to understand the squeezing of oil droplets from dead-end channels under the pressures exerted from diffusioosmotic flows. This would involve a thorough experimental and modeling study and tested for varying wettability conditions and oilwater interaction under changing surfactant concentrations. Adsorption properties of multi-valent ionic species on particles and capillary wall affect zeta potentials and electrokinetic flows. I plan to encompass these effects in our study of pore clogging at extreme conditions. 6

22 Experimental Strategy Typically, Newtonian fluids are made to flow in channels, pipes, and porous media under the influence of pressure gradient. When channel dimensions are really high, such flows are very effective. When we go down in size to narrow channels with charged sidewalls, electrokinetic flows, or more specifically electroosmotic flows, tend to dominate over pressure driven flows. However, in case of dead-end channels, where applying an external electric field isn t feasible, diffusioosmosis is the only form of fluid flow possible inside these channels. As will be shown in Chapter 2, the physics behind diffusioosmotic flows is very similar to that of electroosmotic flows except that in electroosmotic flows an electric field is externally applied across the length of the channel whereas in diffusioosmotic flows, this electric field is self-generated in the solution media. Since the walls are charged in electrokinetic flows, the counter-ions from the solution close in around it due to coulombic forces that are attractive for oppositely charged specimens. This forms the Debye layer (κ -1 ) around the wall surface. On applying a tangential electric field, this mobile layer of charge drifts in response to the field forming the slip plane for fluidic flows. The high shear rates generated inside this slip plane makes the liquid in the bulk flow in a perfect plug flow fashion. Such an electrically driven flow is referred to as the electroosmotic flow of fluid (as shown in Figure 1-1) Diffusioosmotic flows are generated when a tangential concentration gradient of the electrolyte interacts with the charged wall. Same as in the case with electroosmotic flows, the range of flow is the Debye screening length κ -1. The self-generated electric field that interacts with the ions in the Debye layer can be generated from a concentration gradient of various salts like KCl, NaCl, CaCO 3, CaSO 4 etc. applied (or self-generated in some cases) across the length of a channel. Assuming, the concentration gradient to be uniform across the length of the whole 7

23 capillary, the diffusioosmotic flow profile looks exactly the same as electroosmotic flow profile i.e. a plug flow. However, when one end of the channel is sealed, there is no net flow within a given cross-section of the cell. This generates an equal and opposite flow along the center of the channels and the net flow looks parabolic in nature, with flows at the center in opposite direction to that at the walls (Figure 1-3). By tracking tracer particles at different distances from the horizontal axis of the capillary, I plot the velocity profile for flows in these dead-end capillary set-ups. The bedrock of my hypothesis is that under various salt gradients, the velocity flow profiles would look different, as it is also dependent on: 1. Zeta potentials of wall and tracer particles 2. Difference in diffusion coefficients of ions in the solution 3. Peclet Number, which is low for most micron sized particles moving at few µm/sec The primary experimental question to test here is: Can diffusioosmotic flows be quantified, experimentally, at various distances away from the source of ions, and the velocity flow profiles be obtained at each of these crosssections? How does presence of multi-valent ions along with mono-valent ions affect the diffusioosmotic flow patterns and velocities? More specifically, Can a self-generated salt gradient from dissolution of minerals have different flow profiles and velocities depending on the 3 parameters listed above for diffusioosmotic flows? 8

24 Electric Field Figure 1-3: (a) Schematic of a velocity profile in streaming potential flow in a closed slit microcahnnel having a negative zeta potential. The flow profile is the same for a closed electrophoretic experiment with glass capillaries of negative zeta potential at the given salt and ph condition. (b) Schematic of vertical systems I have instead of the conventional electrophoretic cell with applied electric field across the cathode and the anode. Electric fileds are self-generated when ions from the reservoir diffuse in to the sink at different rates, and depending on whether the cation or the anion diffuses faster, the electric field is always pointed from the cation to the anion. Imposing salt gradients across porous media is not a natural process of setting up diffusiophoretic flow of fluid as that would require an idealistic sink and reservoir kind of setup described in detail in Chapter 4. However, as in diffusiophoresis, the wall acts as the pump such flows can be set-up by a self-generated ionic gradient from the dissolution chemistry of components making up the wall. When the thermodynamic equilibrium of these closed geologic formations is disturbed, new surfaces become exposed, allowing further dissolution of the minerals into surrounding aqueous regions. This physical phenomenon produces local ion gradients originating at the rock surface which can then drive diffusioosmotic flows on the surface. We test this hypothesis with a dissolving calcium carbonate microparticle (Figure 1-4) which is found extensively in rocks and other geologic formations. 9

25 Figure 1-4: Schematic showing dissolution of calcium carbonate micropump placed on a negatively-charged substrate (silica, glass). In an aqueous medium, ions dissolve and diffuse at different rates in the solution. The anion diffusing faster than the cation, sets up an electric field normal to the surface of the pump, and pointing in the direction from the cation to the anion. The concentration gradient decays radially in space from the surface of the micropump. The primary experimental question to test here is: Through the process of dissolution, passivation, and reaction of geologic materials, selfgenerated ionic gradients can produce spontaneous phoretic microflows that are efficient, even in micro and nanochannels. Through various control experiments, we show that these flows are diffusiophoretic in nature. In pressure driven flows, the wall or the container is thought to be as the resistance to flow. Due to no slip at the walls (which are assumed stationary), the shear forces at different fluid layers is different and goes to zero at the surface of the wall. This gives rise to a parabolic flow profile of rather than a perfect plug flow provided the walls are not too far apart. However in case of diffusioosmotic flows, the wall acts as the pump driving flows on it s slip plane i.e. the Debye layer. As the flows scale by κ -1 (where κ -1 is of few orders of nanometers) the flows obtained are perfect plug flow in nature. In a closed container, the back-pressure drives a 10

26 parabolic flow in the opposite direction which can then drive immobile plugs of oil along the center into the reservoir having higher salt concentration (Figure 1-5). The primary question to test here is: Does diffusioosmotic flow along the wall surfaces enable fluid to flow from the reservoir into the sink and the oil plugs out of the sink into the reservoir? Dead-End Low conc. Capillary wall Salt (Reservoir) Oil emulsion Nanoparticle Oil Droplet Figure 1-5: Schematic showing oil plug extraction through diffusioosmotic flows induced by external salt gradients set-up in the confined system. The inner capillary, acting as the sink, has the lower salt concentration and oil plugs whereas the outer capillary, acting as the reservoir, has the higher salt concentration and nanoparticle tracers. The disparity in salt concentrations sets up diffusioosmotic flows along the walls of the inner capillary thereby driving particles in, and oil plugs out. Succinctly, the strategy I adopted for the above mentioned goals can be enumerated as: Through controlled experiments, show that on establishing a salt gradient across a capillary, we could move mobile charged latex particles against gravity towards the lower salt concentration regime (without an external pressure component). In a dead-end capillary set-up, these flows have to be circulated back because of the pressure developed at the dead-end junction, which pumps particles and emulsions out through the center. 11

27 Measuring particle speed at different distances from the high salt concentration zone and plotting them to obtain the spatial decay of speed. I match this result with our results from modeling standpoint and try to understand the degree of overlapping. Diffusiophoresis in case of multi-valent ionic species combined with normal Z:Z electrolytes like NaCl or KCl has not been explored before. This dissertation presents initial evidences of changes in flow patterns which can occur on conjugation of two competing effects i.e. from diffusion of multi-valent ionic species like Ca 2+ and monovalent species like Na + ; and non-unifrom concentration gradient in the system. Alteration of ζ spatially and dynamically on the particle and wall surface could significantly alter speeds and direction of flow. We propose a novel electroosmotic micropump, made of calcium carbonate, based on dissolution characteristics and difference is ionic diffusivities of different minerals which can pump liquid and tracer particles in narrow, porous and confined geologic systems Summary of Results To summarize my results from the hypothesis of diffusioosmotic flows due to imposed and self-generated salt gradients, I could show that diffusioosmotic flows come in handy when the channels are closed and confined at one end. On scaling down channel diameters, convective fluid flow from pressure gradients require a very large amount of pressure drop to be applied across the channels. These pressure driven flows, in fact, seize to exist in dead-end capillaries. Diffusiophoresis can penetrate such scenarios of no-flow case. I show results for diffusiophoresis from mixed ion systems and discuss that by tuning physical parameters in the system like ζ- potential, salt type and salt concentration, we were able to engineer flows in the direction we want them to. Such experimental observations were validated with modeling results for flows in 12

28 mixed ion systems. From such analysis, we attempt at understanding diffusiophoretic phenomena from a complex standpoint involving role-play from different ions in the system. A sound understanding of the diffusiophoretic behavior was then utilized to understand naturally occurring electroosmotic micropumps like calcium carbonate, barium carbonate etc. which were shown to drive significant fluid and tracer particle flow in an unsaturated solution of their own salt. Such understanding and application of diffusioosmotic flow mechanism, to our knowledge, hasn t been attempted before in literature. 1.3 Applications of Diffusiophoresis The applications of diffusiophoretic flow mechanism applies to many scientific scenarios like -DNA translocation and capture, decreasing soil salinity and sodicity and infusing helpful chemicals, saving mural paintings to leach out sodium ions, bitumen extraction and dewatering of oil sand deposits, drug delivery and oil recovery from reservoir rocks. Most of these applications have been discovered from the stand-point of electrokinetics, involving external electric fields, but diffusiophoretic study with self-generated electric fields is missing in literature. We anticipate that diffusiophoresis, for its robust nature, could be a better substitute for such applications rather than applying electric fields through an external source. In my conclusion and future work chapter, I discuss these applications in more detail casting light on how diffusiophoresis could work in conjunction with existing techniques and practices. 13

29 1.4 Organization of the Dissertation The chapters in this thesis can be succinctly summarized as: Chapter 2 deals with the physics behind diffusiophoresis, a form of auto-electrokinetic flow. It gives a qualitative and quantitative explanation of the origin of these flows and how I use the information to study my system. Chapter 3 deals with the common experimental techniques I adopt including colloidal particles I consider, suspension preparation and their tracking on salt gradients being some of them. Chapter 4 provides experimental and simulation study of diffusiophoretic flows occurring in dead-end capillaries under applied salt gradients. The study is supported by Supplemental videos and graphs showing flow profiles obtained under gradients of various salt solutions. Chapter 5 shows the mechanism of fluid and tracer particle pumping from a calcium carbonate microparticle being diffusiophoretic in nature. Here too, the study is supplemented with videos and graphs of speeds of tracers spatially around the micropump Chapter 6 exhibits the combined case of flow in a dead-end channel from imposed salt gradients and the understanding fluidic flows in case of mixed mineral systems from a micropump. It shows how flows could be engineered in vertical capillary systems, into-or-out, with mixed ions (e.g. NaCl mixed with CaCO 3 ) which could be used to drive oil emulsion or plugs entterapped inside the inner capillary, out in to the bulk. Chapter 7 provides conclusion and future work statement to my work with diffusiophoretic flows Appendix A.1. deals with solution chemistry of CaCO 3 micropumps on dissolution in water Appendix A.2. concentration profile generated on dissolution of calcium carbonate. 14

30 Chapter 2. Auto-electrokinetic Flows: The Theory of Diffusiophoresis At low Reynolds number, the principles of diffusiophoresis are very similar to that of electrokinetics except for the fact that in diffusiophoretic flows, there is an enhanced contribution from polarization of counter-ionic cloud around the latex particle which either enhances or dampens the flow speeds of these mobile latex particles. In this chapter I will present an overview of the electrical double layer (EDL) around the charged entities and how ionic motion in this layer, creates fluidic flows in the system. I provide below a basic description of electroosmotic and chemiosmotic motion under applied salt gradients with latex particles serving as tracers to track fluidic path. I present the result for fluid velocities in closed-end capillaries and conclude with a brief discussion of how these results combine in my discussion of various motions under different kinds of systems Charges on Entities Most substances acquire a surface charge when brought in contact with an aqueous medium (Everett 1988, Probstein 2003). The evidence for charges comes from electrophoresis which will be dealt at a later stage in this chapter. These charges can arise from various mechanisms (Lyklema 1995) as listed below briefly. 1. Ionization of Surface Groups dissolution of functionalized groups on surfaces 2. Differential Dissolution of Ions from Surfaces of Sparingly Soluble Crystals preferential dissolution of an ion over another leaving a charge on the crystal 3. Isomorphic Substitution like substitution of Al 3+ over Si 4+ in clay giving it a negative charge 4. Charged Crystal Surfaces exposure of new surfaces and breaking of bonds on cleavage of crystals. 15

31 5. Surface Ion Adsorption cationic surfactants can adsorb to negatively charged surfaces to yield a net positive charge, and vice versa Electrical Double Layer The charged surfaces in an aqueous medium attract oppositely charged ions towards itself forming the electrical double layer as shown in a schematic in Figure 2-1 (Masliyah 2006) Figure 2-1: Schematic showing the electric double layer across a charged colloidal particle in an aqueous solution. The zeta potential of the particle is given by the charge at slipping plane of the colloidal particle. (Chapter 16, Malvern Zetasizer Manual) The ions outside the Stern layer, termed as the diffuse layer, are largely mobile when an electric field is present. The movement of ions within this diffuse layer gives rise to electroosmosis or electrophoresis. 16

32 2.3. Zeta Potential The ions in the stern layer are fixed to the surface of the particle and move along with it under application of an external force. This forms the slip plane for the particle. The potential that exists at this boundary is called the zeta potential (ζ) of the particle (Figure 2-1) (Hunter 1981). Due to electrostatic forces which govern stability of colloidal particles in solution, a particle with high zeta potential is more stable in solution than a particle with low zeta potential. These zeta potentials, in most cases, can be altered by changing solution conditions of salt concentration or ph Diffusiophoresis The phenomena of diffusiophoresis includes four types of highly-related electrokinetic processes (Anderson 1989) (Figure 2-3): 1) Electrophoretic transport of the charged particles, 2) electroosmotic flows at charged pore walls, 3) chemiphoretic transport of the charged particles, and 4) chemiosmotic flows at charged pore walls Theory Electrophoresis and electroosmosis arise due to spontaneous electric fields arising from electrolyte gradients. Physical systems tend to approach equilibrium, and so in an imposed salt gradient, ions move from a higher concentration region to the lower concentration region. However, ions, owing to their difference in size, diffuse at different speeds. This sets-up an electric field (E) in the system, which helps to maintain electroneutrality in the solution. But this E field acts not only on the ions, but also on the charged surfaces in the vicinity. For instance, if a negatively charged particle is in the solution, the negative charge on its surface will cause it to swim against the electric field. However the counter-ions in the EDL surrounding the particle move along the direction of E driving fluid flow according to the Navier-Stokes equations. The 17

33 combination of the particle moving in one direction while the fluid around it is pushed in the opposite direction, both due directly to an electric field, is called electrophoresis (Figure 2-3). Figure 1: Schematic showing a negatively charged particle and its oppositely charged electrical doublelayer (dotted ellipse) in a solution. The particle is near a negatively charged surface that has a positively Figure 2-2: Driving fluid movement by diffusioosmosis and diffusiophoresis. A schematic showing a salt gradient, with a low concentration on the left and high on the right. A spontaneous electric field arises, causing fluid flow on any charged surface, such as the particles and the wall below. The E field arises because the anion here (green circles) has a higher diffusion constant than the cation (yellow circles). The flow around the particle causes it to move ~10 m/s, and the flow at the wall which could be a pore wall is similar. A similar affect occurs near any fixed walls in the system. For instance, if the substrate beneath the particle is negatively charged, the substrate will experience a force pulling it in the direction opposite the electric field but because it is a fixed surface, it will not move. The oppositely charged double-layer that is directly above it in solution, however, will move. Thus, in the case of a negatively charged wall, its positively charged double-layer will cause nearby fluid to flow in the direction of the electric field. This fluid flow along a fixed surface due to an electric field is called electroosmosis (Figure 2-3). The magnitude of electrophoresis and electroosmosis depends on the magnitude of zeta potentials of the particle and the wall respectively. 18

34 Like the electrophoretic particle motions and electroosmotic flows, the chemiphoretic particle motions and chemiosmotic flows both arise out of what is essentially the same phenomenon. In their case, the phenomenon is that, for a particle or surface with a given charge, the thickness of the double-layer of oppositely charged ions near its surface is smaller in the the electrolyte-rich regions of the solution (Figure 2-2). On a fixed surface, this always causes fluid to flow along the surface towards the region of the fluid with lower electrolyte concentration, a flow which is termed chemiosmosis. Similarly, the flow in the double-layer of a particle is always down the electrolyte gradient whereas the particle s motion is always towards regions of high electrolyte concentration. Such a flow of particles is call chemiosmosis (Figure 2-3). Although the directions of the chemiosmotic flows and chemiphoretic particle motions are constant and do not depend on the sign of the surface charges, the magnitudes of these two forces do still depend on the magnitude of the wall and particle zeta potentials, respectively. Figure 2-3: Directions of the particle velocity components and fluid flows that together constitute diffusiophoresis. This schematic assumes a system wherein both the particle and the underlying substrate are negatively charged, and the diffusion constant of the anion of the electrolyte is larger than the diffusion constant of the cation (i.e. the system laid out in Figure 1). 19

35 Two constituent flows around the particle (due to chemiphoresis and electrophoresis) are shown, however, the same effect that creates these flows causes the particle to swim in the opposite direction (labeled Particle swim direction, note the corresponding black and red boarder on this arrow). If the diffusion constants were reversed from what is shown here, the electrophoretic and electroosmotic components in this schematic would reverse their directions, but the chemiosmotic and chemiphoretic components would be unaffected. Similarly, if the charge on the particle or substrate were reversed, the respective electrophoretic or electroosmotic components would reverse direction, but not the chemiphoretic or chemiosmotic components. The combination of these four components, electrophoresis, chemiphoresis, electroosmosis, and chemiosmosis, acting together on a given system give rise to a net particle motion which is called diffusiophoresis. As mentioned earlier, the neat thing about these flows is we don t need an external electric field for observing them. Imposed salt gradients automatically set-up this electric field which then drives flows along charged surfaces. Most of my experiments were designed to test this hypothesis under various arrangements like vertical set-up of capillaries with imposed salt gradients, calcium carbonate micropumps with self-generated salt gradients and emulsion flow to test this hypothesis in actual dead-end systems with a backflow Expression for Diffusiophoresis Herein I state the physics behind diffusiophoretic flows in very brief and solve for situations pertaining to my experiments. In order to estimate the thickness of the double layer, we start with bedrock equations of electromagnetism, the four Maxwell equations and for our cases at steady state, the electrical potential ( ) is given by the Poisson s equation: 2 e 2.1 where, e is the volumetric charge density of ions and is the permittivity of the medium, in our case water at 20 C. Applying Boltzmann s distribution of concentration of ionic species and volumetric charge density for a Z:Z electrolyte, the combined Poisson-Boltzmann equation is 20

36 2 2 sinh 2.2 where 1 kt 2CZ e is the Debye layer thickness (in meters) with C is the concentration of ions in bulk, k is the Boltzmann s constant, T is the temperature (Kelvin) Electroosmosis: channel. The figure below shows the conventional electroosmotic fluid flow in a wide open slit Capillary wall Low conc. High conc double layer Figure 2-4: Electroosmotic flow in an open slit microchannel arising from an imposed salt gradient with higher salt concentration at the right and the lower salt concentration at the left. The walls are negatively charged and positive ions form the double layer around it. To solve for the fluid flow, we solve the Navier-Stokes equation within the EDL because that s where the shear forces exist driving the ions tangential to the surface of the tube thereby creating fluid flow in the channels. The momentum equation, with an electric body force can be given by (with the bold letters representing vectors) u 2 u. u u - p + g + e E t

37 and the equation of continuity for conservation of mass being given by.( u) = 0 t 2.4 At steady state conditions, the time derivative drops out. For cases of low Reynolds number ( 10-5 ), there is no inertia in the system. The equation reduces to Stokes equation. 2 e u - p + g + E = Assuming no pressure gradient in the system and gravitational body forces don t affect flow, the equation further simplifies down to 2 u = e E 2.6 There is no E in y-direction but since the EDL varies along y as, E y ~ 0 1. Combining Poisson s equation (Eqn.2.1) with Eqn.2.6, and solving for u and with boundary conditions, Boundary conditions: y 0;, u = 0 y ; 0, u = U 2.7 Solution: we U = It is called the Helmholtz-Smoluchwoski s equation. 22

38 Electrophoresis: The figure below shows the electrophoretic motion of charged colloids under electric fields (Keh 1985, Prieve 2008) Electric field OH - Ca 2+ - Figure 2-5: Electrophoretic flow of a charged colloidal particle under electric fields generated from imposed salt gradients. Since the colloid is negatively charged, it moves against the electric field. For small values of Debye layer thickness compared to particle radius ( a ), radius of curvature of the sphere can be neglected, and the effective electric field can be considered parallel to the surface at all points. Accounting for the forces acting on the particle of any arbitrary shape moving due to an electric field in an aqueous medium, F F electric field drag Force acting on a uniformly charged sphere with surface charge density s, radius a and translating under an applied electric field E is 2 Felectric field 4a s E 2.10 where, s. Again, hydrodynamic drag force can be given by p F nds drag

39 where, Shear stress, T u u I. For the case with no inertia, shear stress s magnitude inside the thin double layer varies as U Substituting in Eqn. 2.11, F 2 drag 4 a U 2.13 Substituting both the eqns (Eqn and Eqn. 2.13) into Eqn. 2.9, we get the electrophoretic velocity of particle as p E U= 2.14 The expression for electrophoresis stays the same for particle of any shape and size (Morrison 1970) Ion Migration To determine the electric field in the system, we need to solve for the ion flux in the solution which is given by the Nernst-Planck equation as ci Ji D izici civ i x x 2.15 where c i is the molar concentration of the ith species, is the electrical potential, v is the bulk velocity, and z i is the valence of the ith species. The Nernst-Planck equation is a combination of Fick s first law of diffusion, Ohm s law and Newton s law. Einstein s relation connects the ionic mobility µ i to the diffusion coefficient D i such that 24

40 FDi i RT 2.16 where F is the Faraday s constant. Electric field is given E 2.17 Also, as the Peclet Numbers in my system are pretty low ( 10-5 ), the convective term in the ion migration term can be neglected. From the condition of electroneutrality. E = = =0 e 2.20 So, z ec 0 which means c + = c - = c i i For no current in the system, z ej 0 i i 2.21 J J 2.22 By substituting the above derived results into Eqn.2.15, we get electric field as E = kt D D C zfe D D C Electrokinetic Speed of tracers The diffusiophoretic velocity of the particles due to electrophoresis and electroosmosis is a simple sum of the above equations. However, the electroosmotic speed decays as we move 25

41 away from the surface of the wall. So, to obtain the exact velocity profile in a closed capillary scenario, we need to take into account the corrections to the electroosmotic velocity across the width of the capillary (Bowen 1981). If the net electrokinetic speed is given by U, then U U ( ) ep vdo y pe where U ep = and vdo ( y ) is cos y cos 3y b 1 2b 2 b y 3 cosha 3 cosh3 a 2 2 3v b b eo vdo ( y) veo 2 2b 192 b a 1 3a 1 tanh tanh a 2b 3 2b 2.25 we where v eo =-. For the case of a square capillary, the ratios of width to height i.e. a/b = 1, and for flows at the center, y=0. Substituting this and combining with the net electrokinetic speed, we get U( y 0) U v ( y 0) ep eo 2.26 E U( y 0) ( p w) 2.27 At the wall surfaces, the speed is E U( y a) ( p w) 2.28 So clearly, the speed at the center is greater than the speed at the wall surfaces. 26

42 Chemiphoresis and Chemiosmosis The expression for chemiphoretic and chemiosmotic velocity could be derived from the Gouy-Chapman model (Prieve 1984). Here we present just the final result and the velocity terms are perfectly additive. U cp 2 2 2k T ln z e 2 p C C 2.29 U co 2 2 2k T ln z e 2 w C C 2.30 ze p where, p tanh 4 kt ze w and w tanh 4 kt 2.6. Total Velocity The total velocity can be expressed as a sum of the electrokinetic effect and the chemipohoretic and chemiosmotic effects. It can be written as Utotal U Ucp Uco 2.31 Since the chemiphoretic and chemiosmotic term is small for most cases, the direction of fluid and particle motion invariably depends on the electrokinetics in the system. However, for the case with KCl, where ions diffuse at same speeds, electrokinetics is insignificant to drive any flow. Here, the other two components determine the path of fluid and particles. 27

43 Chapter 3 Experimental Methods Through the course of this dissertation, I would highlight the various experimental approaches adopted for my study with colloidal transport for some specific set of experiments in order for better understanding and quick reference. However, in this chapter I would elucidate the common experimental techniques to all the sets of experiments which involves materials used, sample preparation techniques, particle suspension in solutions, microfabrication techniques, data collection and flow visualization techniques, microscope and video microscopy equipment and other software packages used for result interpretation. Before we proceed any further it is important to understand that diffusiophoretic phenomena is an amalgam of four different mechanisms, of which diffusioosmosis i.e. the flow of fluid along stationary walls, is the primary focus of this dissertation. However, as we use charged colloidal particles to trace flow paths, the actual velocity of fluid is ambiguous. But, through equations described in the previous chapter, we can decouple these flow mechanisms and account for each individual effect on particle swim. Among the analysis presented in subsequent chapters, we try to establish diffusiophoretic mechanism under various conditions and through multimedia evidences; we show how electrokinetics can dominate over chemiphoretic and chemiosmotic phenomena (Ebel 1988) 3.1. Requirements of the Experiments The experiments described in this thesis were done with the following goal: To qualify and quantify through various experimental strategies and controlled experiments that diffusioosmotic flows can transport fluid and particles to distances of 100s of microns through 28

44 effective tuning of various parameters in the system. The experiments described in subsequent chapters cater to the following objectives: Through controlled experiments, show that on establishing a salt gradient across a capillary, we could move mobile charged latex particles against gravity towards the lower salt concentration regime (without an external pressure component). In a dead-end capillary set-up, these flows have to be circulated back because of the pressure developed at the dead-end junction, which pumps particles and emulsions out through the center. Measuring particle speed at different distances from the high salt concentration zone and plotting them to obtain the spatial decay of speed. I match this result with our results from modeling standpoint and try to understand the degree of overlapping. Diffusiophoresis in case of multi-valent ionic species combined with normal Z:Z electrolytes like NaCl or KCl has not been explored before. This dissertation presents initial evidences of changes in flow patterns which can occur on conjugation of two competing effects i.e. from diffusion of multi-valent ionic species like Ca 2+ and monovalent species like Na + ; and non-unifrom concentration gradient in the system. Alteration of ζ spatially and dynamically on the particle and wall surface could significantly alter speeds and direction of flow. We propose a novel electroosmotic micropump, made of calcium carbonate, based on dissolution characteristics and difference is ionic diffusivities of different minerals which can pump liquid and tracer particles in narrow, porous and confined geologic systems. 29

45 3.2. Materials Monodisperse 3.0 µm sulfate functionalized polystyrene latex (spsl) microspheres (8.0% w/v) and monodisperse surfactant-free, amidine functionalized polystyrene latex (apsl) microspheres (4.0% w/v) were purchased from Interfacial Dynamics Corporation (Portland, OR). For experimental purposes we dilute the colloidal suspension to vol.% by adding 5 and 10 µl of spsl and apsl respectively to 1.5 ml of de-ionized water in microcentrifuge tube obtained from VWR Inc. De-ionized water (DI) was used for all experiments and washing steps (Millipore Corp. Milli-Q Academic system) had a specific resistance greater than 1 MΩ-cm (i.e., equilibrium water ). Salts solutions were used in my experiments for imposing ionic gradient across sink in my vertical capillary experiments described in chapter 4. All the salts were purchased from Sigma Aldrich. Salts that were used are: Table 3-1: A list of salts used in my experiments with their specific molecular weights and diffusion coefficients of the ions produced on dissolution of these minerals in water. Salt MW (gm/mol) D cation (х 10-9 m 2 /s) D anion (х 10-9 m 2 /s) Potassium Chloride Sodium Chloride Anh. Calcium Chloride Calcium Carbonate =1.185 =

46 Sodium Nitrate Sodium Bicarbonate Salts solutions typically used in all my experiments were 0.5, 1 or 10 mm in concentration. Calcium carbonate is the least soluble salt among all the above mentioned salts. The saturation concentration of calcium carbonate is roughly 0.5 mm. Plain rectangular microscope slides (size xx) and Pyrex Petri dishes were obtained from VWR Inc. Borosilicate rectangular capillaries were bought from Vitrocom, NJ. The capillaries were used to build the vertical system of reservoir and sink in the where flows of tracers were observed against gravity under a salt gradient applied across the sink (Figure 3-1). The outer capillary, square in shape (0.9 mm ID, Product # ), formed the reservoir and the inner capillary, also square in shape (0.2 mm ID, Product # ), formed the sink. Paraffin wax was used to seal capillaries forming an enclosed system with a dead-end at the top of the vertical set-up. For experiments described in Chapter 5 with calcium carbonate micropumps, diffusioosmotic flows were noticed to pump out tracers and fluid from the microparticle surface radially in to the bulk. This flow on the substrate s surface is a function of the charge on the substrates. Ionic adsorptions could alter these charges dramatically which in itself is a separate piece of research I intend to carry out in future. However, changing surfaces with various ζ potentials would change speeds, thereby confirming flows to be diffusioosmotic. Poly-ethylene glycol (PEG) coated square glass cover slips were used to study pumping behavior. The PEG coated surfaces, owing to the high hydration layers on their surface, are almost neutral in charge. 31

47 The PEG coating on the glass surface was 3 nm thick. These square cover slips and rectangular microscope slides were obtained from Microsurfaces Inc, TX Zeta Potential Measurements Zeta potential measurements of polystyrene latex particles were done using a Zetasizer Nano ZS90 from Malvern Instruments (MA, #ZEN3690). For measuring zeta potentials in these devices, A 0.01 vol. % of colloidal particels was prepared in the solution it needed to be tested in, and taken in cuvettes which were specifically meant for the Zetasizer equipment. Zeta potential measurements for surfaces like glass and PEG coated cover slips were made using SurPASS instrument from Anton-Parr (VA) 3.4. Instrumentation I examined my systems through optical images taken using a Nikon Eclipse TE2000-U inverted optical microscope. For capturing videos of diffusiophoretic motion of charged mobile particles, Nikon AR software, integrated with our microscope and installed on high-speed computer, was used. The tracking module in this software was used to track particle motion in the region of interest. In some cases, videos were cropped using Nikon AR software to account for the glare at some parts in the videos. An ultrasonicator from VWR International (model 550T) was used to keep particels in suspension. Solution conductivity and ph were measured using a Fischer Scientific Accumet Research AR50 Conductivity and ph Meter respectively. Particle suspensions were dispersed well in salt solutions on a Mini Vortexer (with Speed Control) from VWR International Determining Speeds of Tracer Particles Many techniques exist in literature to determine speeds of tracer particles under application of an electric field. The speed of tracers measured through this is a combination of 32

48 the electroosmotic and the electrophoretic speed (as we saw in Chapter 2, Eqn. 2.31). Determining the speed involves tracking particles as they move under electric field along the length of the capillary tube, with electrodes at each end. In this thesis, there isn t an applied electric field at any point of experimentation. The electric fields in my system, as described before, arise from diffusion of ions at different rates into the bulk. However, from analysis stand point, nothing changes as we still have to account for tracer particle motion under self-generated electric fields. One of the major differences in my system compared to that adopted in literature is my flows happen in a vertical set-up of capillaries. In a way, it is very similar to what Ebel et. al. did with their diffusiophoresis set-up in 1988, but in their case, dynamic fluidic flows were not studied under the microscope and they mostly looked at aggregation of particles at one end of the cell to confirm diffusiophoretic behavior. With the microscope in our laboratory, we could tilt it about its hinge into a vertical position, with the normal of the microscope base now being perpendicular to gravity. Such a system is very idealistic because convective motion of fluid due to difference in density could now be accounted for as the denser fluid would always like to settle at the bottom compared to the lighter fluid. This avoids any induced convective motion imparted to tracers moving through diffusiophoresis in the system The vertical reservoir and sink set-up Figure 3-1 shows the vertical arrangement of capillaries described later in chapter 4 used to study diffusiophoresis of tracers under applied salt gradients. With all ends sealed, the only opening for flows to happen from the reservoir to the sink is through the inlet of the smaller capillary dipped inside the larger capillary. Using the microscope, we focused mostly at the mouth of the inner capillary to see flows against or along gravity depending on the salt gradients set-up across the inner capillary. The flows were tracked to be parabolic in nature (as shown 33

49 earlier in Figure 1-3) which were either directed up or down the inner capillary, depending on the positioning of the salts and the zeta potentials of the walls and particles. Sink Reservoir Microscope Figure 3-1: (a) Schematic of the vertical reservoir and sink system to study diffusiophoresis using colloidal particles and glass walls (b) Picture of the actual set-up showing two capillaries, the bigger at the bottom and the thinner at the top, sealed with the help of wax Predictions from Vertical capillaries As we travel inside the inner capillary, the concentration gradient keeps decreasing (refer to chapter 4 on modeling diffusiophoretic flows in dead-end capillaries). Hence there is a drop in electric field present in the system. Due to this, the particles travel slower as we go up. The parabolic flow across the capillary keeps receding to a perfect plug flow. When the flows start building up, the pressure drop at the dead-end section keeps increasing. With a sufficient enough pressure drop, the fluid flow along the center of the tube starts reversing and pumps out mobile large emulsions which were previously immobile under electric fields, but can move under pressure drops. Under the microscope, to quantify these flows, we look at tracking the charged tracers moving due to diffusiophoresis in various layers of the inner capillary. The protocol followed for tracking these tracers is: 34

50 Table 3-2: Protocol followed for tracking particles undergoing diffusiophoretic in a vertical configuration. 1. A salt gradient was imposed across the inner square capillary with tracers either inside the outer or the inner capillary. For reasons we would discuss later in Chapter 4, imposing a NaCl salt gradient across the inner capillary, with tracers suspended in DI inside it, the tracers start moving towards the salt solution i.e. down the inner capillary, in a parabolic flow profile with maximum velocity across the center compared to that near the wall surfaces. 2. To know the exact layer of focus, we calibrate the depth of field of the capillary with respect to the exact width of the capillary which changes as a function of the refractive index of the medium. 3. After proper calibration of the capillary, we traversed through the various layers of the inner capillary, starting from the layer closest to the wall to the center and then again travelling to opposite wall in our field of view. 4. Particles were tracked at each layer using the Nikon AR software in-built module or through manual calibration techniques. 5. To observe spatial decay of speeds as we travel inside the sink, the particles were tracked at various distances away from the mouth of the inner capillary. 6. Finally, the gravitational settling speeds of these tracers was either added or subtracted from the actual velocity observations to obtain the diffusiophoretic speed. For our case with diffusiophoretic flows from monovalent and multi-valent ionic species under imposed salt gradients in a dead-end capillary configuration, the velocity profiles looked parabolic in nature. 35

51 Additionally, we looked at how these speeds degrade across length scales in the inner capillary and over time too. These results were indicative of an electrokinetic phenomenon in play Tracer particle tracking in CaCO 3 micropumps Depending on the charge on the tracers, the particle flow profiles look different when we have a calcium carbonate micropump in their vicinity. For mechanisms discussed later in chapter 5, negative tracer particles (spsl) get attracted from the bulk on to the CaCO 3 surface. However, on reaching close to the surface, they get pumped out again in to the bulk. To obtain the speeds of this attracting and pumping behavior, these tracers were tracked using Nikon AR software for various positions around the pump surface. Generally, the pumping behavior seizes at few hundred microns away from the surface of the pump after which the tracers undergo Brownian motion. However positively charged tracers (apsl) have a slightly different flow pattern. The same tracking protocol was employed in studying their motion in solution Preparation of emulsions and carbonated water Saturated carbonated water can be prepared by purging DI water with CO 2 at a pressure of 25k Pa for 30 minutes. Figure 3-2 below shows the set-up for preparing carbonated water under a hood in laboratory conditions ( in collaboration with Isamar Ortiz Rivera) Figure 3-2: Set-up showing arrangement to make carbonated water. The needle going into the vial having water injects CO 2 at 25k Pa for 30 minutes. This forms carbonated water. 36

52 Chapter 4 Diffusioosmotic Flows in Capillaries from Imposed Gradients of Monovalent Salts Diffusioosmotic motion of fluid is set-up when a concentration gradient of ions diffusing at different rates is imposed or self-generated across a certain length scale in a microchannel or a porous body system. The electric field generated in this case exerts a tangential force on the ions in the Debye layer of the surface thereby dragging it along to induce a fluid flow in the bulk because of viscous drag (Keh 2005). Such flows, as we discussed before, differ from conventional electrokinetic flows in the sense that there is no applied electric field, rather the electric field is self-generated in all cases. These flows can be argued to be effective in very narrow channels where pressure driven flows seize to exist (Shanon 2008). I thank Tso-Yi Chiang for providing me with the simulation results for different cases of salt gradients set-up along the tubes and for the many useful discussions in analyzing the particle motion flowing under diffusiophoretic effect The Goal The goal of this chapter is to state unequivocally the presence of diffusiophoretic flows from applied salt gradients, and how flows could be engineered in-or-out of dead-end capillaries depending on the governing flow equations for diffusiophoresis from dead-end capillaries. The purpose of this chapter is to look at various flow profiles of tracer particles across specific cross sections which are at measurable distances away from the reservoir and at different positions in the capillary cell; and to compare these results with that obtained from modeling for the same number of positions. Typically, the salts in my system were sodium chloride, potassium chloride, sodium nitrate and calcium carbonate. We chose our salts such that each of them had a different 37

53 effect on our diffusiophoretic study of tracer particles as the difference in diffusion coefficients varied from a case to case basis Experimental Design As a very fundamental approach to analyzing diffusion driven flows, we carried out experiments in a vertical system (Ebel 1988), acting as a sink and reservoir, which showed that by preferentially altering the salt and the reservoir conditions, we can drive flows in-and-out of the system by a diffusiophoretic or diffusioosmotic mechanism. While speaking of these mechanisms we always imply that the other two phenomena, chemiphoresis and chemiosmosis, are also present in the system and can drive flows by themselves alone. A vertical system approach was adopted with the denser solution, typically a salt solution, at the bottom and a lighter solution at the top. Alterations in the positioning of the salts were also tested, as the density of the salt solutions at the concentration levels tested was not too different from that of water. Thus, we expected hardly any density driven flows. Gravity 38

54 Figure 4-1: Microscope inclined on its hinge to a vertical position with gravity acting perpendicular to the normal of the sample base. As shown in Figure 4-1, the microscope was rotated around a hinge to place the stage in an upright position. The sample stage of the microscope was now vertical to the ground, thereby encompassing the effects from gravity in flow cells set-up on it. Square borosilicate capillaries (Vitrocom) of 0.9 mm ID was used as the reservoir, and a smaller inner capillary of 0.2 mm ID or 0.3 mm ID was used as the sink. The capillaries were placed on the glass slide and on to the stage with the reservoir at the bottom and the sink at the top. Figure 4-2 depicts the reservoirsink arrangement where the reservoir normally had the salt (monovalent salts like KCl, NaCl or divalent salt like CaCO 3 ) at different concentrations and the sink normally had DI water or a secondary salt in some cases. The system was completely closed and flows could take place only through the opening of the inner capillary dipped inside the outer capillary. Figure 4-2: Capillary set up of reservoir and sink with high salt concentration in the reservoir and lower salt concentration in the sink. 3 μm sulfate polystyrene latex particles (spsl) tracers can be dispersed in any of the container to test their motion under applied salt gradients. Imposed salt gradients, across a length 39

55 of few centimeters, were seen to create fluid motion depending on charge on the tracer particles and the charges along the walls of the capillaries. Different salt concentrations were prepared by mixing them with DI water on a vortexer. For the case with particles dispersed in the salt and taken in the outer capillary, 5 µl of tracer particles were mixed with 1.5 ml of the salt solution to give a 0.05 vol% of particles in the salt. After letting the particles disperse uniformly in the salt through vortexing and sonication techniques, the salt solution was taken in a 2.5 cm 0.9 mm ID capillary (the capillary was split into half across its length to give enough space for positioning them under the microscope) closed at one by wax. It was then mounted on to a glass slide and fixed on it with the help of wax. The 2.5 cm long inner capillary (i.e. sink) filled with DI and sealed on one end (usually the end where the surface is bit rough due to cleavage) is pushed inside the outer capillary carefully ensuring no bubble trap during the whole process. Wax was then used to seal the opening of the outer capillary thereby giving us a completely closed system. The only opening for fluid flow existed at the mouth of the inner capillary dipped inside the outer and which also had a dead-end at the top. Again, any of these arrangements of salts and particles could be changed or altered depending on the experimental verification we wanted to seek for confirming diffusiophoretic behavior. The glass slide containing the two capillaries was then mounted on to the microscope and with the help of a 10x microscope objective, flows were visualized and recorded on to a computer. The particle velocities were determined either by using the tracking module of the Nikon AR software or by measuring the distance covered by particles for a certain amount of time after proper calibration. 40

56 4.3. Experimental Results Electric fields caused by gradients in concentration drive phoretic motion of particles depending on charges on them. A negatively charged particle through electrophoresis moves in opposite direction to that of the electric field whereas chemiphoresis moves the fluid around the particle towards lower salt regime which propels the particles towards the higher salt concentration zone. Similarly, osmotic flows occur on fixed charged surfaces like glass wall that is negatively charged. Electroosmosis makes the diffuse layer around the wall move along the direction of the generated electric field along with the chemiosmotic flows which cause the fluid around the wall to move towards lower salt regime. Thus, the wall acts as the pump, not as a resistance to flow. This is a key difference between diffusioosmotic flows and pressure-driven flows. As discussed before, the equation 2... gives the velocity profile for particle motion under applied salt gradients. From Table 4-2, as β is negative (cations diffuse slower than the anion in all cases listed in Table 4-1) and the gradient of concentration decreases across the entire length of the inner capillary, the difference in zeta potentials again plays a key role in determining the direction of fluid flows due to diffusiophoresis. Note that for an electrolyte like KCl chemiphoresis and chemiosmosis dominate. However for other electrolytes like NaCl and CaCO 3 this effect is very less. Electrokinetics dominate direction of motion of tracers. Table 4-1:Diffusivities of different ions produced from salts Ions Diffusion Constant (х 10-9 m/s 2 ) Ca HCO OH

57 Na K H Cl Table 4-2: Diffusivities of different ions produced from salts Ions b = D Cation - D Anion D Cation + D Anion NaCl KCl CaCO In the case of KCl, the diffusion coefficients of K + and Cl - ions are quite similar and hence, they diffuse into the low concentration region at the same speed. As a result, there is no electric field set-up in the solution due to ionic diffusion. In such cases, the negatively charged spsl particles do not move due to electrophoretic effects and there is also no electroosmotic transport of fluid in the system. However motion in the system is initiated by the chemiphoretic and the chemiosmotic effects, as these two processes don t depend on the magnitude or the sign of β. The chemiphoretic effect pulls the negatively charged spsl particles towards the higher salt concentration regime i.e. the reservoir containing 10 mm KCl, whereas the chemiosmotic process creates fluidic flows along the walls of the capillary, typically in the sink, in the direction from the higher to the lower salt regime. 42

58 Figure 4-1 shows three time lapse images and two snapshot images of how the tracers and fluidic flows in the system can be manipulated on changing the location of the salt in the capillary arrangement (Also see Supplemental Videos S1 S2 S3). Since the densities of water and 10 mm KCl are in reasonable approximation of each other, they can be either in the inner and outer capillary and still not create any significant density driven flows. Sedimentation speeds of the particles were also compensated for while calculating the actual speeds. The speeds of the tracer particles were found to be 2 µm/s. Figure 4-3: Movement of particles in a vertical capillary system. (a) A snapshot image of the vertical capillaries with DI and 3.0 µm spsl is in the outside capillary (reservoir) and 10 mm KCl in the inside capillary (sink). The inner capillary is sealed at the top to form a deadend. Tracers are pulled in against gravity into the inner capillary (b) Similarly, a dead-end system with 10 mm KCl and 3.0 µm spsl in the outer capillary (reservoir) and DI in inner (sink). There is no flow against gravity into the inner capillary. Particles settle under gravity in outer capillary. (c) 3 time lapse shots of tracers (c.1, c.2, c.3) being pulled inwards by 10mM KCl rather than settling to the bottom. The inner capillary has 10mM KCl and 3.0 µm spsl and the outer capillary has DI. Particle under no salt gradient would have settled under gravity. However, due to chemiphoresis, they are pulled up against gravity. 43

59 Similar to the case of KCl, gradients of NaCl show flows of tracer particles into and out of the dead-end capillary set-up. The ions produced in case of NaCl, Na + and Cl -, diffuse at different speeds (Table 4-1). Because of all the hydration layers around sodium ion, it diffuses slower than the chloride ion in the system. This sets up an automatic electric field (roughly 1 ~ 10 V/cm), directed from sodium to chloride ion acting in the direction of decreasing NaCl concentration in the solution, which acts on any charged entity in the system including the polymer tracers and the wall surfaces. With known zeta potentials of particles and wall surfaces, the flows can be controlled in or out of a dead-end channel. For the case with 1 mm NaCl with tracers inside the inner capillary and DI in the outer capillary, as shown in Figure 4-2, the negatively charged tracer particles move in opposite direction to that of the electric field. In the bulk, they move inside at a speeds of roughly 5 ~ 6 µm/sec while at the wall surfaces, the speeds are low but in the same direction as in the bulk. The motion of fluid near the wall is along the direction of electric field and fresh water is pumped in through the center filling up the void created in the inner capillary. For the time scales we observe this phenomenon, the diffusion flows extend to several hundreds of microns with gradual decrease in speeds owing to saturation of the sink. 44

60 Gravity Inside Outside Figure 4-4: A snapshot image of the vertical capillaries with salt as 10 mm NaCl in the inner capillary (reservoir) which has a closed end at the top and DI in the outer section acting as the sink. 3.0 µm spsl particles are dispersed in the inner capillary and are seen to move against gravity towards the dead end section. The flow profile of these tracers can be tracked and seen to be parabolic in nature, indicating minimum velocity at the wall surfaces (due to no-slip at boundary) and maximum velocity in the middle section. The speeds are roughly 3.5 ~ 4 µm/s up the inner capillary. The combination of all the 4 phenomena results in an increase in particle speed, with the dominant effect being electrokinetics. For the case with 1 mm NaCl at the bottom and with DI and spsl in the inner capillary, it was difficult to find a good distribution of particles near the mouth of the inner capillary (See Supplemental Videos S 2.). In the roughly 100 seconds time gaps between the point when the setting up of the capillary to the capture of videos, particles up until 700 µm in the inner capillary had been pumped out into the sink. Though the flow directions in case of NaCl for the negatively charged tracers predict the same as in case of KCl, the velocity profile looks very different to what is observed in case of the later. Due to a closed-end tube, the speed of the tracers is affected by the electric field in the system, and the flow profile looks parabolic in nature. Such flow profiles have been carefully modeled using basic equations of electrokinetics as discussed in the latter section of this thesis. 45

61 CaCO 3 dissolves in water forming primarily 3 ions, Ca 2+, HCO - 3 and OH -. The reaction chemistry is shown in Appendix A.1. These ions diffuse at different speeds with the OH - diffusing the fastest and Ca 2+ diffusing the slowest. This disparity of charge concentration in the inner capillary sets up an electric field between the ions and the charged tracers which then move in response to it. It also sets up an electroosmotic flow in the system driving fluids in the opposite direction to that of the motion of charged tracers in the bulk. The flow profiles and velocities are very much the same as in case with 1 mm NaCl. However, it is very important to understand the role calcium ions play in altering charges of entities present in the system. Our study of zeta potentials (Table 4-1) is a clear proof of significant changes in charges on introducing calcium ions in to the system. However, these charges do not remain stable during the time of our observation as ions adsorb more on top the surfaces on prolonged exposure. Characterizing this behavior, dynamically and spatially, remains as one of the biggest challenges as we go ahead in our pursuit to engineering fluidic flows (Stone 2004) based on changing salts. Table 4-3: Zeta potential of tracers in various salt conditions. All the values were in range of ±5 mv from the reported values Solution DI water 0.5 mm 1 mm NaCl 1 mm KCl CaCO 3 Sulfate PSL Glass cover slip Amidine PSL

62 4.4. Modeling of diffusiophoresis for multiple ions in a closed tube 1 Many of the significant experiments performed stem from fundamental modeling of our systems. The parameter space is simply too large to ad hoc try various scenarios, and achieve the pumping we want. In this section, we describe our modeling, using the fundamental equations from fluid mechanics (Stokes equations), electrostatics (Poisson equation), and convectivediffusion results. The diffusiophoretic velocity (U dp ) of a charged particle and the diffusio-osmotic flow (v do ) along a charged plate in an applied salt gradient with a z:z electrolyte are 1 : U dp kt DC D e A k T n x t p ze DC DA z e 4 kt n( x, t) p (, ) ln 1 tanh v do kt D D k T e n x t ze D D z e kt n x t 2 2 C A 2 2 w (, ) w ln 1 tanh 2 2 C A 4 (, ) 4.2 where ε is the fluid permittivity, η is the viscosity of the fluid, k B is Boltzmann constant, T is temperature, z is the valence of ion, and n is the salt concentration. However, in our system, the dissolution of CaCO 3 generates three ions and thus the equation needs to be modified. With the assumption of infinitesimally thin κ -1, the bulk ion concentration remains electroneutral and the electrical potential ( ψ ) can be described by Laplace equation The flux of the ith ion (J i ) is given by J Dn z ed n E vn kt i i i i i i i Modeling work carried out by Tso-Yi Chiang 47

63 where D i is the diffusion coefficient of ion type i, n i is the concentration of ion type i, and v is the fluid velocity. The convection term is neglected here because of the low Peclet number. To have no net current, i zej i i an electric field is induced, E kt e i i z D n i i i z D n 2 i i i 4.6 Here, we assume n i = n, but in fact, we can use the equations to solve for any combination of ions. From the continuity equation, n J 0 t 4.7 Bringing Eqn. 4.4 and Eqn. 4.6 into Eqn. 4.7, we have n D * 2 n t In the system of dissolution of CaCO 3, D 2 D ( D D ) 4D D D * where D 1 = D Ca2+, D 2 = D HCO3-, and D 3 = D OH-. For a Z:Z electrolyte, D DD D D * 2 C A C A

64 With the geometry shown in Figure 4-3(a), because L >> b, we solve for the one - dimensional diffusion equation for ion concentration profile along the tube. Initial conditions and boundary conditions are, n x, , 0 n t n n L, t x 0 With the time period at which we observe, the ions don t have enough time to diffuse to the other end of the tube, and the concentration profile can be described by nx, t n0 1erf 4 x * Dt 4.12 The flow profile in a closed tube has been derived by Bowen. We use his equation for the case of a square capillary, and get the expression of the diffusiophoretic velocity of a charged particle at the center of a closed tube (Bowen 1981), U U 1.095v dp do Modeling Results At this point, we can model flows with CaCO 3, and many other mixed mineral systems. Upon calculating the results for particle speeds (Figure 43 b-d) in a vertical system (Figure 4-3 a), we find particle speeds of 10s of m/s near the pore mouth, and after 5 minutes, we find speeds > 1 m/s = 2.6 m/month at 0.5 mm into the pore (Figure 4-3 d). As important as the values are, even more important is that we are able to model these flows, and therefore design 49

65 potential improvements. With a small amount of development to account for recentlydiscovered problems in assuming electroneutrality developments that are not even in the literature we will soon be able to model all such systems. a) 2b b) L x 500 μm 200 μm 100 μm n 0 c) d) 500 μm 200 μm 100 μm 500 μm 200 μm 100 μm Figure 4-5: Speeds of particles in capillaries, for diffusiophoresis in the presence of calcium carbonate. (a) The schematic of a vertical capillary immersed in the reservoir with salt solution. (b), (c), and (d): Particle speed at different distances from the reservoir with respect to time. (b) n 0 = 1 mm CaCO 3, ζp = -30 mv, ζw = -11 mv. (c) n 0 = 1 mm KCl, ζ p = -104 mv, ζ w = -70 mv. (d) n 0 = 1 mm NaCl, ζ p = -101 mv, ζ w = -65 mv Discussion In order to analyze the speeds of particles, we looked at systems having 1 mm NaCl and DI and spsl primarily in opposite containers with diffusiophoretic motion into or out of the tube depending on how we arranged the set-up of salt solution in the capillaries. Typically, to avoid density gradients, DI was taken inside the inner capillary with the salt outside. But as the density of 1 mm NaCl doesn t vary by much compared to that of DI, its positioning in the capillary hardly mattered. In fact, tracer flows in the systems were always seen to be driven towards the 50

66 higher NaCl regime. Controlled experiments with an all NaCl system showed the tracer particles to settle under gravity. This showed that the particles were denser than the solution and their motion against gravity is primarily due to electrokinetic flows in the system. a) b) 8 7 t = 300 s t = 200 s Electric Field 1 mm NaCl + 3 µm spsl Average Particle Velocity (µm/sec) t = 100 s DI water Horizontal Distance from Left Capillary Wall (µm) Figure 4-6: The parabolic flow profile of tracers across the width of the capillary measured at height, h=0, from simulation and experimental data (a) Schematic of the set-up analyzed with 1 mm NaCl and 3 µm spsl at the top and DI water at the bottom. The electric field points into the outer capillary. (b) The parabolic flow profile for tracers at a distance of 200 µm from the mouth of the inner capillary. The simulation results were calculated for 100, 200 and 300 secs after the systems has been set-up. Interestingly, the speeds increase with time and then start decreasing. The dotted points show the experimental data for the particle velocities tracked at the same distance away from the mouth of the capillary. The speeds were couple of orders of magnitudes lesser than that obtained from simulation. For 1 mm NaCl with spsl inside and DI water outside (Figure 4-4 a), we compared the modeling velocities with that found from experiments at a distance of 200 µm from the mouth of the inner capillary. While theoretical predictions for velocity after 100 seconds are roughly 7 µm/s down, experimental values for speeds of tracers was at best 3 µm/sec along the axis of the inner capillary. 51

67 Electric Field The possible explanation for this is though we assumed an infinite sink and a reservoir to base our model on; however we practically never have an infinite sink or reservoir. For the case with particles and NaCl inside the inner capillary, rising up against gravity, with DI in the outer, the particle speeds retard significantly as they keep moving towards a higher particle concentration stationed above. Due to the collisions from the surrounding particles, their speeds decrease with length scales and hence the deceleration. However, in model, as we have an infinite sink, we assume negligible interaction between particles. To add to this, the gravitational pull acting on the particles has not been accounted for in modeling. So there is no retardation force acting on these particles to bring down their speeds. The orders of difference in speeds between model and experiments are testimony to it. Figure 4-5 shows the plots for velocity of DI and spsl inside with 1 mm NaCl outside and particles settling at different planes in the inner capillary a) b) DI + 3 µm spsl Average Particle Velocity (µm/sec) x = 700, 850, 1000 µm; t = 100 x = 150 µm; t = 300 secs x = 150 µm; t = 200 secs x = 150 µm; t = 100 secs -3 1 mm NaCl Horizontal Distance from Left Capillary Wall (µm) Figure 4-7: The parabolic flow profile of tracers across the width of the capillary measured at height, h=0, from simulation and experimental data (a) Schematic of the setup analyzed with 1 mm NaCl at the bottom and DI water and 3 µm spsl at the top. The electric field points into the inner capillary. (b) The parabolic flow profile for tracers at a distance of 200 µm from the mouth of the inner capillary. The simulation results were 52

68 calculated for 100, 200 and 300 secs after the systems has been set-up. Interestingly, the speeds increase with time and then start decreasing. The dotted points show the experimental data for the particle velocities tracked at the same distance away from the mouth of the capillary. The speeds were couple of orders of magnitudes lesser than that obtained from simulation. However, just the opposite effect happens when particles and DI are taken in the inner capillary with 1 mm NaCl at the bottom. The collisions between particles enhance the speeds in this case, and they are pumped out at a faster rate than expected from modeling. Also, on adding gravitational effect onto these tracers, the speeds can be roughly 6~7 µm/s rather than 3.5 µm/s as predicted from modeling. In the 100 sec time interval, these particles would traverse completely 700 µm into the outer capillary thereby creating a void of particles near the mouth of the inner capillary. Particles at a height of 700 µm, 850 µm and 1000 µm were seen to be settling with an uniform speed which didn t decay much over time. The speeds were roughly their settling speeds As we notice particles beyond 700 µm settling at a uniform rate of roughly 1 µm/sec at the center of the tube, it can be concluded that for the 1 mm NaCl solution, diffusiophoretic flows do not extend beyond that Conclusion In conclusion, using a vertical set-up of capillaries under microscope, we can show that dissolution from a mineral or presence of salt can cause active fluid flow and particle movement in the surrounding aqueous medium. Diffusiophoretic pumping is particularly efficient in nano and micro-channels and especially when these channels are blocked on one end, which often is the case with porous reservoir rocks holding oil plugs. From an engineering standpoint, the many system variables that affect the flow strength and directionality should allow us to engineer particles and surfaces that can intelligently move particles and fluid (Stone 2001, Stone 2004) in and out of these channels. 53

69 Our modeling and experimental study for flow velocities are consistent with predictions however, as the modeling doesn t account for gravity and particle-particle collision, the speeds of tracers when compared with experimental values differ by couple of orders of magnitude. I aim to explore this effect in further detail for other forms of salts (e.g. KCl, NaNO 3 and CaCO 3 ) 54

70 Chapter 5 Self-generated Diffusioosmotic Pumping from Calcium Carbonate Micropumps As we saw in the previous chapter, diffusiophoretic flows could drive fluid and particles in dead-end capillaries under imposed salt gradients to a distance of 1 millimeter if the source has a higher concentration of salt, thereby increasing the equilibration time for the system. Such flows form our fundamental understanding of the diffusiophoretic mechanism in microchannels under salt gradients which can act as an alternative for generating flows in nanopores that are otherwise inaccessible. However, to our surprise, we found that self-generated salt gradients from dissolving minerals in an infinite bath can generate similar flows in its vicinity. These minerals behave as miniaturized micropumps which, through electroosmotic pumping, can pump liquid and tracers in to the bulk. This work was initiated by Joseph McDermott in Summer 10, and then when I came in, I took control of it and did several experiments to establish the mechanism behind such flows Introduction An increasing demand in miniaturization of devices has led to a far bigger call for better control of pumping, mixing and moving of fluids to meet the desired needs (Whitesides 2006, McDonald 2000). As pressure driven mechanisms fail in narrow, tight, dead-end spaces, a need for an alternative mechanism of creating fluid flow is imperative to the modern society (Stone 2001, Stone 2004, Squires 2005, Eijkel 2005). The advent of catalytic nanomotors (Paxton 2004, Paxton 2005, Paxton 2006, Kline 2007, Wang 2009) and micropumps (Kline 2006, Solovev 2011, Sen 2009) provide alternate pathways of attaining flow in micro and nanochannels through reaction based chemistries. However, the applicability of these pump systems are limited by their 55

71 solution and reaction parameters. In this article, we show that the simple dissolution of calcium carbonate microspheres a material ubiquitous in natural geologic formations can selfgenerate strong electric fields of roughly 1-10 V/cm that pump fluid and tracer particles over distances many times greater than the carbonate particle radius. We also found that even for simple model systems, the interplay between geochemistry and fluid dynamics is rather complex, and such behavior could be one possible way of generating flows in microporous beds of rocks that are inaccessible otherwise. Electroosmotic pumping in narrow channels has been studied earlier (Harison 1991, Manz 1991, Nguygen 2002, Laser 2004) with much of the focus on centrifugal and electroosmotic pumps. Centrifugal pumps, which work on fluid displacements, give good efficiency and power output but are limited in their usage at low Reynolds number as there is no inertia to the system. On the other hand, electroosmotic pumps need an external power source that isn t feasible in very narrow dead-end spaces. The need for a self-generated pump, based on surface potentials and solution chemistries, enhances the prospect of bridging the gap between the above two extensively studied micropump systems. Diffusioosmotic pumping based on non-electrolyte diffusiophoresis has been studied by our group earlier (Hua, 2012). A non-electrolyte concentration gradient was used to induce fluidic flows that were driven by dissolution of polymers into various analytes with velocities controlled by concentration of the medium rather than the concentration of the dissolving species. However, the need for a more elegant explanation of diffusioosmotic flows can come from our current study with calcium carbonate micropumps which, in itself, is a first of its kind study with self-generated ionic gradients caused from dissolution of the microparticle creating diffusioosmotic flows in an unsaturated solution. These ionic gradients, which give rise to 56

72 spontaneous electric fields in the system, can drive short-range flows even in closed microporous bodies where pressure-driven flows seize to exist. Diffusiophoresis is a well-understood flow mechanism; however, experimentally, this mechanism has been studied primarily using imposed salt gradients in 1-dimensional systems (Ebel 1988). However, self-generated ionic gradients can be established when a solid dissolves into ions in to an unsaturated solution. Such dissolution can occur when the thermodynamic equilibrium between the rock and the surrounding water is disturbed, new surfaces become exposed, and allowing further dissolution of the minerals into surrounding aqueous regions. This physical phenomenon produces local ion gradients originating at the rock surface. The gradients can in turn drive microflows and particle movement along the mineral surfaces and in pores by the mechanism of diffusiophoresis (Prieve 1984, Anderson 1989). Here, we describe how, through the dissolution, passivation, and reaction of geologic materials, self-generated ionic gradients can produce spontaneous phoretic microflows that are efficient, even in micro and nanochannels that are common in rocks. The question we examine is how fast can these flows be, and can we predict and control them? We find out that the dissolution of calcium carbonate, a material found extensively in geologic formations, can generate flows up to 40 μm s -1. Among other minerals, barium carbonate was also seen to exhibit similar flow profiles and even higher velocities. Unlike pressure- driven convective flow, diffusiophoretic flows can penetrate micro/nanoscale pores and dead-end pores, and the flows are active wherever ionic gradients exist (Hatlo 2011). Our research could therefore find important applications for both natural and artificial processes that result in disturbed mineral systems, such as earthquakes, mining, building construction, and oil and gas extraction involving fracturing of the rock and/or injection of water. 57

73 5.2. Materials and Experimental Methods Materials For calcium and barium carbonate microparticle synthesis, sodium carbonate Na 2CO 3, calcium chloride CaCl 2, and barium chloride BaCl 2 were obtained from Sigma-Aldrich Chemicals, USA. Solutions of 0.33 M Na 2CO 3, CaCl 2, and BaCl 2 were prepared. Two sizes of surfactant free sulfate-functionalized polystyrene latex microparticles (d = 1.4 μm ± 2.1%, and d = 3.0 μm ± 2.4%, both had w/v = 8.0%) and one batch of surfactant free amidine-functionalized polystyrene latex microparticles (d = 3.5 μm ± 2.1%, w/v = 4%) were purchased from Interfacial Dynamics Corporation, Portland, OR. For particle surface functionalization, sodium polystyrene sulfonate (MW ~70,000) was obtained from Sigma Aldrich. Calcite samples (~1 mm square) were obtained from Petrobras (Rio de Janeiro, Brazil). Gypsum and barite rock samples (10x2x2 cm, broken into 100 μm shards) were obtained through Amazon.com which were sold by MMP, LLC located at Denver, Colorado, USA. Deionized (DI) water used in all aqueous solutions came from a Millipore Corporation MilliQ system, with specific resistance greater than 1 MΩ cm (due to equilibration with CO2 in air). As we wanted to test changes in speeds on changes in substrate, glass coverslips, polystyrene petri dishes and poly(ethyleneglycol) coated coverslips were used for our observations. Negatively-charged square glass coverslips (22 mm х 22 mm) and petri dishes (10 cm х 1.5 cm) were obtained from VWR International. Poly(ethyleneglycol) (PEG) coated square coverslips (22 mm х 22 mm) were obtained from Microsurfaces Inc., TX. These PEG coated coverslips are very hydrophilic and develop a hydration layer in water. The hydration layer neutralizes the charge on their surfaces. 58

74 Calcium and Barium Carbonate Microparticle Synthesis A simple precipitation synthesis was used to synthesize the calcium and barium carbonate microparticles. In both cases, 25 ml of a 0.33 M solution of CaCl 2 or BaCl 2 was stirred at high velocity on a magnetic stirrer. An additional 25 ml of 0.33 M Na 2CO 3 was then rapidly added to the solution, which turned a milky white as the carbonate particles precipitated. The solution was stirred for an additional 1 2 min., and then quenched with 50 ml of DI water. To remove the remaining Na + and Cl - ions, the particle solutions were rinsed by repeated centrifugation and resuspension in DI water using a Sorvall Biofuge Primo Centrifuge from Kendro Laboratory Products. The rinsing procedure was typically repeated 2-4 times, with additional rinsing steps significantly affecting the microparticle size through carbonate dissolution. The CaCO 3 particles were found to be roughly spherical, with a polydispersity of ~50% and average radius 7~10 μm. They were found to be stable to aggregation processes for at least a day. The BaCO 3 particles were found to be smaller (a ~.75 μm, polydispersity ~50%), and more shard-like Observation of Pumping Behavior of Carbonate Microparticles To observe the pumping behavior, the carbonate microparticles were imaged using a Nikon Eclipse TE2000-U inverted optical microscope, typically at 40x magnification. First, the concentrated carbonate particle solution was diluted to the desired concentration using DI water and using an ultrasonicator (model 550T) along with a Mini Vortexer (with Speed Control), both obtained from VWR International, the microparticles were re-suspended in the solution. 500 μl was quickly pipetted into a glass-bottomed petri dish. An additional 500 μl 0.1% w/v solution of tracer spsl or apsl particles was then added to the dish and the solutions mixed and observed. 59

75 Observation of Pumping Behavior of Natural Rock Samples Similar to the procedure in the previous section, calcite, dolomite, and gypsum rock samples were placed in DI water in a glass bottomed petri dish. Then, 0.1% w/v tracer particle solutions were added and the resulting movement observed using optical microscopy. In certain cases, the experiments were performed in open capillaries that contained the tracer particle solution, to simulate the effect of dissolution into a microchannel or pore Zeta Potential measurements of particles and substrate For zeta potential (ζ) measurement purposes of spsl and apsl particles, Zetasizer Nano ZS90 (Malvern, MA) was used. For measuring ζ-potential of glass substrate, streaming potential technique using SurPASS (Anton Paar, VA) was employed. ζ-potentials of particles were recorded at standard room temperature of 298 K using Disposable cuvettes (DTS1061). For ζ- potentials measurements of particles in salt solutions, the latex particles were first soaked in the salt bath for 15 mins before the measurements were taken. ζ-potential of walls were detected under various salt conditions and then titrated over a range of values to observe consistency Analysis of Pumping Behavior Particle velocimetry was used to generate the plots in Figures 5-4 Particle tracking of tracer particles for a given number of video frames was done by using ImageJ. To produce the velocity vector field plots in Figure 5-4 b and 5-4 e, an appropriate number of tracers (between 700 and 1500) were analyzed over the entire region, encompassing a total analysis time of ~30 seconds. Figure 5-4 c & f were prepared by analyzing tracers surrounding a single microsphere over the course of ~10 seconds for each value of interparticle distance. Average interparticle distances were calculated from the surface fraction of calcium carbonate 60

76 microspheres. For each sample, tracer velocity vs. radial distance was fitted to an exponential decay function, from which both the maximum tracer speed and decay length were taken Results and Discussion We used calcium carbonate (CaCO 3 ) microparticles to study localized microflows both in open fluid and closed channels. CaCO 3 was produced using a simple aqueous precipitation synthesis (Volodkin 2004) ; roughly spherical, porous calcium carbonate particles (initial radii a = 7 to 10 m) formed. Suspensions of the CaCO 3 were then diluted with DI water, and individual CaCO 3 particles were settled onto bare glass substrates. Sulfated polystyrene latex (spsl) particles with a = m were added as tracers to observe the resulting flows. In the case of a solitary calcium carbonate micropump settled onto glass in DI water and surrounded by spsl tracer particles, the particle flow field was readily observed (Figure 5-1). Calcium Carbonate Micropumps 10 µm Figure 5-1: Two calcium carbonate micropumps showing tracers getting pumped away on the glass surface after being pulled in from the bulk. These are 1.5 µm spsl particles and they are suspended in DI water along with the micropumps Tracer particles were pulled in rapidly from above the plate to the micropump surface. They collected near and moved down the surface of the micropump, until, upon reaching the substrate, 61

77 they were rapidly ejected radially outward into solution. Movement away from the calcite was fast near the micropump particle surface, and decayed with distance until Brownian motion dominated the particle movement 10s of m away. Tracers that approached the pump at shallow angles were ejected without ever reaching the micropump surface. Some of these negatively charged tracers get stuck on to the surface of the calcite microparticle and are only ejected upon complete dissolution of the pump (Supplemental video 1 & 2). Such flow fields normally create an exclusion region of tracers near the micropump on the glass surface. Figure 5-2 shows both a schematic of the flow paths for tracers around a calcium carbonate microparticle and optical microscopy images of aggregation on the calcite microparticle and formation of an exclusion region around it. These flow fields can be compared with the ones observed for catalytic micropumps (Kline 2005) where there is a recirculating flow pattern around the pump surface originating from similar mechanisms. 62

78 (a) Ca 2+ + HCO 3 - +OH - - CaCO 3 Electroosmotic Flow Due to Charged Substrate (b) Electrophoresis of Negative Sulfate Tracer Particles (c) Figure 5-2: Schematic of microflows for one single CaCO 3 particle micropump and two images of the same micropump showing aggregation and exclusion region. These systems contained only calcium carbonate pumps (~ 5 µm) and 3 μm sulfatefunctionalized polystyrene latex tracer particles (spsl) in DI water. Scale bars in these images are 10 μm. The videos (S1 and S2 respectively) were filmed on a bare glass substrate using an inverted microscope. (a) Tracers in the bulk get attracted towards the pump, some adhere, and the rest get pumped out in to the bulk radially. (b) The spsl tracers are adhered to the surface of the pump, but not permanently. (c) A clear exclusion region of tracers develops around the micropump on the glass surface. These tracers exhibit Brownian motion mostly and rise up in to the solution. 63

79 The amidine latex particles (3.5 um in size) were observed to have different flow paths as seen in Figure 5-3 (a). Instead of being attracted from the bulk towards the calcite pump, these tracers are pushed away from the calcite since they are positively-charged. However, apsl particles settle vertically downward when they are a few micrometers away from region defined by the calcite particle. They settle until they reach the glass surface where they then are swept outward by the diffusioosmotic flow caused by the glass. This is in addition to their own velocity, which also seeks to move outward in the electric field. Very rarely do any of the apsl tracers settle vertically onto the calcite pump (Supplemental Video 3). Particles settling only in close vicinity to the pump adhere on to the surface of calcite, otherwise most of them are either pumped away at higher speeds or get stuck to the glass surface, which is oppositely charged (Fig. 2 b). It will be discussed later that in case of spsl tracers and two interacting micropumps, a stagnation region of fluid flow is created. However, its not the case with apsl tracers (Fig. 2 c) where particle motion is independent of the presence of two micropumps. An exclusion region is not created in this case (Supplemental Video 4). 64

80 (a) Ca 2+ + HCO 3 - +OH - + CaCO 3 Electroosmotic Flow Due to Charged Substrate (b) Electrophoresis of Positive Amidine Tracer Particles (c) Figure 5-3: Schematic of microflows for one single CaCO 3 particle micropump and two interacting micropumps with no aggregation or exclusion region. These systems contained only calcium carbonate pumps (~10 µm) and 3.5 μm amidine-functionalized polystyrene latex tracer particles (spsl) in DI water. Scale bars in these images are 10 μm. The videos (S3 and S4 respectively) were filmed on a bare glass substrate using an inverted microscope. (a) Tracers settle on to the glass surface vertically around the calcite particle. The settling times are enhanced when the tracers are directly over head the pump. On reaching the surface, they get pumped out by the flow going out radially. (b) Very little aggregation of tracers around the micropump. (c) Two interacting micropumps with no stagnation region of flow. 65

81 Mechanism of flow In trying to establish the mechanism of flow, we have examined the following mechanisms 1) Density driven (Brenner 2011) originating from difference in densities from species produced on dissolution of calcium carbonate into the solution media and the density of the surrounding fluid, 2) Thermophoresis (Vigolo 2010), resulting from the heat of dissolution, and 3) Diffusiophoresis (Anderson 1981) originating from concentration gradients of ionic species produced on dissolution. We look at each of these mechanisms in our analysis of the spontaneous fluid flows occurring in case of these micropumps. Density-driven flows. The observed flows are not pressure-driven, nor are they density-driven. Our studies show that density variations, resulting from the dissolution of the mineral in water especially in case of micropumps, can generate flows in the order of 1 µm/sec. The observed flow speeds for the negatively charged mobile particles are of the order of 10s of µm/sec, and is dependent on a) volume fraction of micropumps in the system b) tracer particle charge and, c) substrate charge. This observation is inconsistent with any density-driven flow mechanism. We performed a simple scaling analysis of the Navier-Stoke s equation for our system: where, ρ is the density of the solution, u is the velocity of the fluid, p is the pressure, η is the viscosity of the solution and F ext is any external force acting in the system. Assuming steady state and low Re number for the system, further analysis reveals that density driven flows scale as 66

82 Since speeds increase as L 2, where L is the dimension of the calcium carbonate microparticle, we expect to see that speeds increase significantly with size. When particle size approaches 1 millimeter, we do indeed see this which is discussed in the later sections. Diffusiophorestic flows: How are the diffusiophoretic flows generated? The physics of diffusiophoresis is fairly well-known (Anderson 1989, Prieve 1984, Ebel 1988, Prieve 2008). The phenomena of diffusiophoresis includes four types of highly-related electrokinetic processes (Figure 2-3): 1) Electrophoretic transport of the charged particles, 2) electroosmotic flows at charged pore walls, 3) chemiphoretic transport of the charged particles, and 4) chemiosmotic flows at charged pore walls. Details regarding the velocities of particles undergoing diffusiophoretic flow can be found in the Appendix (A.2 & A.3) The fluid flow originating from diffusiophoresis is governed by three key factors: 1. Finite concentration gradient giving rise to electric field in the solution 2. A finite difference in diffusivities between the diffusing species i.e. a finite difference between the anion and the cation 3. Difference in zeta potentials between the particle and the wall surface In large number densities, CaCO 3 particles are stable against dissolution since they readily saturate water. However, CaCO 3 is sparingly soluble in deionized water, with a solubility product constant of M 2 at 20 C. [7] When a suspension of CaCO 3 microparticles is diluted with fresh water, dissolution occurs at the particle surface into the fluid. Although eventually the particles disappear from the system, during the dissolution process there is a radial concentration gradient of ions surrounding the particle. A full description of aqueous calcium carbonate equilibrium and the resulting concentration profile can be found in the 67

83 Appendix (A.1 & A.2). The primary ions resulting from this dissolution are 2+ Ca, HCO 3, and OH. These ions contribute to the electric fields generated in the system. For the time scales of our observation, the solution acts as the sink as it is unsaturated with the ions produced upon dissolution of CaCO 3. A finite concentration gradient is thus present at all times until the micropump dissolves completely in the solution. In a control test, calcium carbonate micropumps were suspended in 0.5mM CaCO 3 solution with spsl tracers dispersed in it and the whole sample placed under the microscope for observation. The microparticles didn t exhibit any pumping behavior on the glass surface. This indicated that by having a saturated solution of calcium and bicarbonate ions, the concentration gradient which existed before can now be compensated for thereby seizing any dissolution of mineral and formation of ions. The three ions resulting from each molecule of dissolved calcium carbonate have quite different diffusion coefficients [8] : At 20 C, and D 2+ Ca DOH = m 2 s -1, while DHCO = m 2 s -1 3 = m 2 s -1. The ions cannot diffuse freely, however; coulombic forces act to set up a spontaneous electric field in order to maintain electroneutrality. Since the hydroxyl ion diffuses 4 times faster than the bicarbonate ion in the radial direction, the electric fields are also oriented radially outward from the calcium carbonate microparticle surface. This electric field acts not only on the ions, but on any charged colloidal particles or surfaces in the region. This electric field, which is around 1 ~ 10 Vcm -1, generated in the system causes the electroosmotic and electrophoretic transport of specimen described earlier. This overall process of an ion gradient effecting an electric field which drives electrokinetic transport is called diffusiophoresis. [3] The calcium carbonate micropumps on dissolution sets-up electric fields in the solution. Considering the case of spsl particles, the electric field acts on the protons present in the Debye 68

84 layer of these tracers (which are negatively charged) and induce fluid flow along their surfaces. The flow of fluid is in the same direction as that of the electric filed. This flow makes the tracers move in the opposite direction due to shear forces. Similarly, the protons forming the Debye layer of the substrate experiences this electric field, thus inducing fluid flow motion pointing out from calcite surface in radial direction. As the substrate is stationary, the fluidic flow along the walls drives the tracers away from the pump. Figure 5-4 shows both a time lapse optical image and a vector field plot of the tracers being pumped along the glass substrate, reaching speeds of 39 μm s -1. In the case when two pumps are near enough that their flow fields interact, a stagnation point exists at the midpoint between the pumps (Supplemental Video 5). Tracers ejected from one CaCO 3 particle move toward the other, but often come to a stop midway before escaping in a direction orthogonal to the line of centers between the CaCO 3 particles (Figure 5-4d-f). That is, the surfaces act as pumps rather than as resistances, and the tracers favor movement along these surfaces. Further experiments (Supplemental Video 6) confirm the nozzling phenomenon: by adding additional fixed charged surfaces, the flow of tracers can be focused or directed in the solution. This opens the possibility for designing complex flow patterns in dissolving mineral systems. 69

85 Figure 5-4: Microflows for one single CaCO 3 particle micropump and two interacting micropumps. These systems contained only calcium carbonate pumps and 1.4 μm sulfatefunctionalized polystyrene latex tracer particles (spsl) in DI water. (a,d) time-lapse images. The videos (S1 and S5 respectively) were filmed on a bare glass substrate using an inverted microscope. Optical microscopy time-lapse images were taken at 40 magnification with overlays every 0.2 s. Scale bars in these images are 10 μm. In the vector field plots, axes are distance in μm. (b, e) vector field. The black circles represent the location of the micropumps, and the vector arrows represent the tracer particle direction and speed in μm/s at the substrate surface. The plots were generated by tracking the movement of particles over 0.3 seconds. (c, f) radial speed plots. In (c), the radial speeds of all spsl tracers sampled in (b) are plotted against the distance of those tracers from the center of the lone calcium carbonate micropump. In (f), the radial speed of tracer particles within 6 microns of the line between the two micropumps in (e) (boxed area shown) is plotted against the distance of those tracers from the midpoint between the two pumps. In both cases, curves have been added to guide the eye. 70

86 Substrate charge dependent: The speeds of tracer particles getting pumped on the surface are substrate charge dependent. The surfaces generally develop a negative potential on exposure to water. As a control, poly-ethylene glycol (PEG) coated square glass cover slips were replaced with the regular cover slips to study pump behavior under change in substrate potential. The PEG coated surfaces, owing to the high hydration layers on their surface, are almost neutral in charge. The PEG coating on the glass surface was 3 nm thick. When an isolated calcite microparticle is observed on these PEG coated surfaces, flow speeds for of the tracers change by a few microns per second. Such changes in tracer speeds can be attributed to electrokinetic mechanism as particles close to surface flow at a speed, which is a function of difference in zeta potentials between the particle and the wall surface (ζ p ζ w ). Zeta potential difference governing flows: To understand the complexity behind such flow patterns and velocities of tracers, it is important to characterize the difference in zeta potentials between the mobile charged particles and the surface for flows along the wall (ζ p ζ w, assuming the chemiphoretic and chemiosmotic terms are small (Ebel 1988)). Table 1 below lists the zeta potential measurements of tracers and wall in various solution conditions determined through the Malvern instrument for particles and SurPASS (Anton Paar, VA) for glass cover slips. Our measurements showed a sharp change in zeta potential values for the wall and the tracer particles on adding calcium carbonate to the system. The presence of large multi-valent Ca 2+ ions can bring about significant alteration in the zeta potentials on surfaces due to adsorption (Kosmulski 2003, Grolimund 1996). The dissolution of Ca 2+ into the solution makes them adsorb on the wall and particle surfaces, affecting the zeta potentials on these particles that are local to the pump. As the wall dominates over the zeta potential of the particle, the difference between charges stays positive, which makes the particle to move outwards on the surface. It should be noted here that 71

87 due to the dynamic nature of calcium ion systems which adsorb on the surface of walls and particles, the zeta potentials could go down further in magnitude on larger exposure times. Table 5-1: Zeta potential values (mv) in various solutions Solution DI water 0.5mM CaCO 3 10mM KCl 0.5mM CaCO mM KCl Sulfate PSL Glass cover slip Amidine PSL The diffusiophoretic speed of the tracers depends on both the absolute salt concentrations and their gradients in the usual way. In addition, the speeds also depend upon the local concentration via an adsorption isotherm, because the zeta potentials vary over short distances. For example, the spsl zeta potential, normally highly negative in DI water, is suppressed in the presence of CaCO 3 solution, likely due to interactions between the calcium ions and sulfate groups. This change can be manipulated by the addition of KCl ions to the system (Kosmulski 2003). When the micropump experiments were repeated with a 10 mm KCl solution, the direction of the tracer movement reversed as expected (Supplemental Video 7). At higher KCl concentrations (>100 mm), the motion slowed significantly due to ionic screening, which causes the diffusioosmotic flows mechanisms to become small, at least on the timescales of our experiments. 72

88 Figure 5-5: Barium carbonate microparticle pumping 1.4 μm spsl tracer particles outward, overlays are 0.33 sec apart, scale bar is 20 μm. CaCO 3 particles are not the only ones that drive diffusioosmotic flows. Barium carbonate microparticles (Figure 5-5) synthesized in a similar manner to the CaCO 3 particles show nearly identical behavior. In fact, the pumping of the tracers is even faster for comparable particle surface fractions, due to the greater disparity in ionic diffusion coefficients between the Ba +2 and OH -. Flows in actual geologic systems: As a step further, we analyzed systems of natural rocks made of various minerals like calcite (CaCO 3 ), three crystalline structures of gypsum (CaSO 4 ), barite (BaCO 3 ), fluorite (CaF 2 ) and quartz (SiO 2 ), to look for electrokinetic flows which could be obtained from dissolution of these minerals. These rocks, on dissolution, generate salt gradients and forms ions which can drive electrophoretic and chemiphoretic motion of charged colloidal particles, and electroosmotic and chemiosmotic flows of fluid along the fixed wall surfaces (Figure 5-6). Recent studies with synthetic colloids have shown unusual flow patterns inside the porous spaces of these rocks resulting in sticking or clogging of porous channels, the mechanism behind which is still not well understood (Alaskar 2011). In this work we tried to study the flow 73

89 patterns generated in case of various rocks and the length scales achievable to determine if these were consistent with diffusioosmotic phenomena. Dissolution of naturally occurring gypsum (hydrated calcium sulfate) crystals (Figure 5-6 a) drives tracer particle motion. For calcium sulfate, which is much more soluble than calcium carbonate (K sp = ), the tracers move faster than in case of a calcite rock. Diffusioosmosis suggests variation of speeds to be the other way round i.e. tracers move faster in case of calcite than in case of gypsum as difference in diffusion coefficients of ions in case of gypsum is lower( Ca 2+ (D = ) and SO 4 (D = ) (CRC Handbook)) than that for calcite mineral. This change in behavior suggests density flows kick in when macroscopic dissolution of minerals is considered. So it is not always the difference in diffusion coefficients that determines speeds, but even the solubility of a mineral, with the later effect being more prominent only in the macroscopic scale. Attract Alabaster Pump 40 µm Figure 5-6: Flows for one single gypsum rock particle and three time lapse images of flows for calcite rock particle. The rocks were rough less than 1 µm in size. The scale bars in the image is 40 µm. For Alabaster, the tracers got pumped out at the bottom surface, and as the rock was sandwiched in between two surfaces and closed at the edges, the flows reversed back mostly 74

90 through the middle extending up to the top plate. The flows out at the top did not extend for more than 200 µms into the bulk, whereas flows at the bottom extended for more than a centimeter. For the calcite rock, similar flows were seen. However, in this case the calcite was taken in a capillary and sealed at all the ends. The tracers got pumped out at the bottom layer, and came back from the top. As considered earlier, density driven flows scale as L 2 of the pump particle, and in our case, where the rocks are of macro size, the effect of density gradient flows becomes quite significant. Using the same scaling analogy, the speeds of particles can be as high as 10 μm/s for a particle size of roughly 20 μm. We note that when the particles exceed a size of perhaps 100 μm, the current scaling analysis gives way to one that would include the effects of inertia. The length scales in flows observed from these macrosized crystals exceeded a centimeter with not much decay in velocities at larger lengths. A clear density-driven flow pattern was seen to exist in the system Conclusion In conclusion, using calcium carbonate as a model, we have shown that ion dissolution from a mineral can drive microscale flows and particle movement in the surrounding aqueous medium. Diffusiophoretic pumping is particularly efficient for pumping through micro and nanochannels. Other flow mechanisms were shown earlier to fail in such nanochannels owing to the huge pressure drop required to drive flow (Welty 2009). Such self-generated mechanisms of flows could drive flows in tight dead-end spaces, pumping out oil in to the mainstream of fluid flowing under pressure gradient and bring them on to the refinery collection zones. They pose huge potential for several other applications which we would discuss in the conclusion chapter of this thesis. 75

91 Chapter 6 Diffusioosmotic Pumping of Oil Emulsions from Dead-end Capillaries In addition to the experiments explained in previous chapters, our interest also lies in understanding diffusiophoresis in case of mixed ion systems. The process of diffusiophoresis in the case of binary Z:Z electrolytes and linear concentration gradients is well known in the literature (Ebel 1988), and through many experiments demonstrated in this thesis, we were able to establish experimental validation of the theoretical interpretation of these phenomena. However, understanding flows in case of mixed electrolytes is still a challenge to the scientific community. The natural systems of salt solutions (e.g. sea water) are mostly mixed entities in terms of their chemical composition which surround anisotropic heterogeneous bodies (e.g. rocks) with a dead-end pore Mixed ion system: CaCO 3 with NaCl When a saturated calcium carbonate solution of 0.5 mm was added along with a 10 mm NaCl solution in the vertical capillary system, flows of tracers were directed towards NaCl rich region. Alterations in arrangements show that by placing the salts in or out of the pores, we can direct flows to the desired section. As seen in Fig. 6-1, flows can be driven into the inner capillary if NaCl is present in it and vice versa. Note, in chapter 4, having CaCO 3 in the outside capillary with DI in the inner, attracted particles towards the higher calcite region. The particles never got pumped in the direction of decreasing salt concentration. However, here we can show alteration in direction of motion. 76

92 Inside Gravity Outside Figure 6-1: A snapshot image of the vertical capillaries with 10 mm NaCl in the inner capillary which has a closed end at the top and 0.5 mm CaCO 3 in the outer capillary which is sealed too. 3.0 µm spsl particles are dispersed in the outer capillary and are seen to move against gravity towards the dead end section of the inner capillary. Particles in the bulk of the outer capillary seem to settle under gravity until they reach the mouth of the inner capillary where they are rapidly pulled inside. The velocities increase with increase in NaCl concentration. In this case, the direction of electric field produced from the leading and the lagging ions of each system act opposite to each other. However in such mixed ion systems, there is not a simple prediction regarding the direction of field The ability to engineer flows in-and-out of capillaries, as discussed in previous sections, can be useful for oil extraction. It provides a new impetus towards understanding the physics behind spontaneous generation of fluidic flows from salt gradients in reservoir rock systems. These rocks have oil entrapped in deep, dead-end cavity spaces and its extraction is seemingly impossible through any of the current EOR techniques including CO 2 flooding. Pressure driven flows are non-existent in closed end capillaries. 77

93 6.2. Diffusioosmotic pumping of oil emulsions Use of surfactants like dioctyl sodium sulfosuccinate (AOT) have proved to be useful in changing the wetting properties of porous spaces which can make the oil flow into larger open channels where pressure driven flows are efficient. However, one major drawback in their usage lies in their cost. Diffusioosmotic and diffusiophoretic flows can assist conventional pressure driven flows in extraction of oil from such dead-end capillaries. Similar to the case of vertical capillary systems we discussed in the previous section, diffusioosmotic flows into narrow dead-end crevices of rocks can extract oil plugs out and inject nanoparticles in. By having a concentrated salt solution in the bulk compared to a lower concentration of salt inside the porous crevices entrapping these oil plugs, we can set up ionic gradients across these microcapillary junctions. The salt gradient thus generated can drive nanoparticle from the bulk into the inner capillary through a combination of electrokinetic effects (as discussed earlier) as shown in Fig 6-2. When nanoparticles are driven in along with fluid flow along the walls of the porous network, the oil plugs are driven out of the cavity spaces when the fluid reverses its path and tries to come out in order to maintain fluid continuity in the system. Also, by changing the salts present in the system, we can change the direction of these diffusion induced flow Dead-End Low conc. Capillary wall Salt (Reservoir) Oil emulsion Oil Droplet Nanoparticle 78

94 Figure 6-2: A schematic showing oil plug extraction through diffusioosmotic flows induced by external salt gradients set-up in the confined system. The inner capillary, acting as the sink, has the lower salt concentration and oil plugs whereas the outer capillary, acting as the reservoir, has the higher salt concentration and nanoparticle tracers. The disparity in salt concentrations sets up diffusioosmotic flows along the walls of the inner capillary thereby driving particles in, and oil plugs out. Emulsions were prepared by mixing 450 μl of water, 40 μl of an organic solvent, like chlorobenzene or hexadecane, and μl of a stabilizer, like oleic acid or a solution of 2% of Tween 20. The size of the emulsions obtained depended on the rate of mixing of the solution: fast rates lead to emulsions as small as 2 μm, and slow rates lead to emulsions of sizes around 20 μm. Stability of the emulsions was higher with the combination of hexadecane as the organic phase and Tween 20 as the stabilizer. These emulsions are stable in water and have a negative charge. The hexadecane emulsions were diluted with water to obtain a volume fraction of 0.01% and then added 0.2 mm square capillary (Vitrocom, USA). This capillary, with one end sealed, serves as the sink in our experiments. A saturated 0.5 mm calcium carbonate solution with 3 μm spsl particles (0.01% vol.) was added to a 0.9 mm square capillary which formed the reservoir for our system. With a higher salt concentration in the reservoir compared to that in the sink, a salt gradient is immediately set-up in the solution with the OH - and HCO - 3 ions diffusing faster in to the inner capillary than the Ca 2+ ions. Zeta potentials of the particles and the wall surfaces decide the direction of particle motion and fluid flow. 79

95 (a) (b) (c) Figure 6-3: (a) Extraction of oil droplets from a dead-end pore. A time lapse image showing oil plug extraction through diffusioosmotic flows induced by external salt gradients set-up in the confined system. The salt outside in the reservoir is 0.5 mm CaCO 3 with 3.0 µm spsl particles in it. The inner capillary has DI with roughly 10 ~ 20 µm (or even larger sized) oil emulsions formed through emulsification of hexadecane with 2% Tween-20 solution. Along the wall of the inner capillary, tracers are transported inside along with fluid flow due to chemiosmosis and electroosmosis, respectively. As it is a dead end capillary, the fluid comes back through the middle section of the inner capillary carrying with it the oil plugs and drains them off into the reservoir. In case of 0.5 mm CaCO 3, the particles and the fluid, flow in along the walls of the inner capillary towards the dead-end section. To maintain fluid continuity, this flow in has to be supplemented with a flow out along the centre of the inner capillary that drives the emulsions out into the reservoir (Figures 6-3 (a) and 6-3 (b)). (a) (b) (c) Oil plug Figure 6-4: A time lapse image showing a hexadecane oil plug emulsified with oleic acid being pumped out of inner capillary having DI, and outer capillary having 0.5 mm CaCO 3 Thus, based on the principles of flows induced through ionic diffusion, oil plugs could be driven out of tight, dead-end channels existing in reservoir rocks through, and only through, diffusioosmotic pumping caused from flows along wall surfaces. While pressure and gas 80

96 flooding fail in these cases, through diffusioosmosis we can make the wall itself a pump which could then drive spontaneous flows in and out of these cavity spaces Extraction of oil emulsions through carbonated water 2 The oil recovery process has three stages: primary, secondary, and tertiary recovery or enhanced oil recovery. In the first two stages 30-40% of the oil in the reservoir can be recovered through conventional drilling and fracking techniques. Depending on the technique used, flooding the ores could also increase the oil extraction by a further 10-15%. Our research has shown that through introducing carbonated water artificially and even present naturally underneath, we can induce flows in tight rock spaces with oil plugs entrapped inside them. These flows, the physics of which is very similar to vertical systems discussed earlier, can drive out oil from these dead-end pores. Ion gradients in oil reservoirs can arise from two different sources: the spontaneous dissolution of minerals and salt creating a salt gradient and producing ions which sets up a spontaneous electric fields driving flows. There is also a possibility of ion gradients being created by dissolution of gases like carbon dioxide in water under earth s crust. The resultant carbonic acid dissociates protons and bicarbonate ions. These ions diffuse at different rates thereby giving rise to equivalent electric fields (1~10 V/cm). Carbon dioxide is one of those gases that exist in oil reservoirs as nearly pure form or associated with raw natural gas. It has been used also as part of secondary oil recovery and enhanced oil recovery stages, in procedures in which the gas is injected by pressure to increase the amount of oil recovered. The percentage of carbon dioxide in an oil well is not known with 2 Done in conjunction with Isamar Ortiz Rivera 81

97 precision, but considering the high pressures and temperatures that exist in a reservoir it is possible that a considerable part of it will be dissolved in water, leading to the formation of ions as shown below. CO 2 + H 2 O H 2 CO 3 H + + HCO 3 - ΔH = kj/mol [13] In Figure 6-4, as the proton and the bicarbonate ions diffuse from the lower capillary in to the upper capillary, there is an electric field generated pointing inwards i.e. towards the lower capillary. This electric field acts on the spsl tracer particles in the thereby making them move diffusiophoretically out into the sink. A control test with an all carbonated water system showed particles settling under gravity in to the bottom capillary. As an outcome of diffusiophoretic studies with carbonated water, we show that it is not mandatory to have flows generated only in case of existing or imposed salt gradients. Fluidic flows can also be initiated under situation of gases dissolved in water, forming ions, which then on exposure to a sink give rise to diffusion-driven flows. Such movements can be utilized efficiently at higher depths below the earth s crust where due to pressure and temperature, gases tend to stay dissolved in water and can create natural gradients across the pore spaces of reservoir rocks. 82

98 Dead End DI water/ Salt Emulsions 0.9 mm ID capillary Carbonated water 0.2 mm ID capillary Figure 6-5: (a) A similar vertical capillary set-up to visualize flows under carbonated water gradients with different solution in the other chambers. However, the set-up is inverted in comparison to the previous ones for a better visualization of flows (b) Snapshot images of the experiments with carbonated water. Inner capillary contained carbonated water and 3.0 µm spsl particles, while outer capillary was filled with: (a) DI water, (b) CaCO 3 solution (5mM), (c) NaCl solution and (d) carbonated water (control). In experiments (a), (b) and (c) particles showed movement against gravity, while in the control (d) particles move along the direction of gravity 83

99 Chapter 7 Conclusion and Future Work 7.1. Summary of the thesis Flows of any nature play a pivotal role in our understanding and manifestation of science and technology in general. The need to pump reagents and sweep surfaces at the micron scale has re-kindled the interest in low Reynolds number flows. As pressure drop required increases on shrinking channel diameters, an alternative flow mechanism needs to be sought after. My thesis addresses one such key issue of obtaining flows in dead-end channels. And the procedure I adopted for this is diffusiophoresis. Succinctly, the key points in my dissertation have been 1. I showed that self-generated salt gradients from dissolving minerals, acting as micropumps, could drive significant diffusioosmotic flows in confined systems. To the best of my knowledge, reports of such flows from naturally occurring minerals have not been reported yet. Geological disruptions, whether manually or naturally, could disturb the thermal equilibrium of the system thereby re-igniting dissolution of minerals. Such dissolution patterns can drive electrokinetic flows in micropores of rocks and other sea bodies 2. I showed that through applied or self-generated salt gradients, diffusiophoretic flows in dead-end capillaries could be set-up. Again, to the best of my knowledge, I have not come across any literature addressing this issue of flows in closed microchannels. In fact, through several controlled experiments I could show that the back pressure created at the dead-end can drive reverse flows, thereby pumping out oil emulsions or plugs entrapped inside the channels. Normally, pore spaces are clogged by particles or fine grain deposits which can t be accessed by normal sweeping flows because of dead-ends. Through 84

100 diffusioosmotic flows, such clogging can be disrupted and flows could be possible through very thin nanopores. 3. Length scales of flows were shown to be dependent on availability of salt in the reservoirs. For actual infinite reservoirs with high salt concentrations, these flows would sustain for large length scales of about a centimeter, as equilibrium would be harder to reach. 4. My initial results with mixed ion systems showed flows can be engineered by understanding the complexity of mixed ion systems in diffusiophoretic phenomena along with monovalent salts. Before understanding such complex behaviors, it is essential to interpret the precise adsorption properties of multi-valent ions on surfaces of particles and walls. Such adsorption phenomenon could alter the charges on surfaces significantly affecting the diffusiophoretic flow. As I predict from our experiments, such changes are dynamic and spatial in nature Future work 1. Transport rates of tracers through diffusiophoretic behavior in complex, heterogeneous containers (Ajdari 1995, Ajdari 2000) simulating exact rock systems and calculating its efficiency over pressure driven flows. The hypothesis to test here is: Auto-electrokinetic flows assisting pressure driven flows by removing oil plugs from narrow tight channels and making them available to the main stream. And how do complex networks of heterogeneous bodies respond to diffusioosmotic flows along its walls. 85

101 tributaries larger tube a b! c Figure 7-1: Tributary networks. a) Marble Canyon Section of the Grand Canyon. Small tributaries feed a larger stream of water. b) Our model experimental system. The larger horizontal tube will contain aqueous solution driven by pressure. The smaller tributaries will contain oil rich phase(s), which will be actively transported into the main channel by diffusio-osmosis. The tributaries could enter straight, or slanted (as shown). Both types will be built at the Penn State Nanofabrication Lab, which we have extensive experience using. c) The net effect of the extraction process. 2. Quantifying effect of multi-valent ions on preferential enhancement of diffusiophoretic flows in case of mixed ion systems. Characterizing diffusiophoretic flows under extreme conditions of pressure and temperature. And understanding the dynamic variation in surface and wall potentials. Kosmulski 2003 article on co-adsorption of heavy ions throws light on cadmium and other multi-valent salt adsorption on surfaces and their subsequent impact on ζ-potentials. However for a dynamic case like diffusioosmotic flows along walls, evidence of any such study hasn t come to my notice. 3. Squeezing of oil emulsion droplets through pores based on shear flows at surfaces created by diffusiophoretic flows. Mitigating pore clogging of colloids and sweeping along the walls due to electroosmotic flows (Anderson 1985, Pit 2000). 86

102 The hypothesis to test here is: Can enough shear stress be generated by diffusioosmotic flows across a hexadecane emulsion to deform it and make it pass through small pore openings? 4. Colloidal encapsulated surfactants: Controlled method of synthesis, study of diffusiophoretic behavior and release of surfactants under sink conditions (Caruso 2000, Hong 2003). By encapsulating surfactants in soft spheres, we can test their mobility under applied salt gradients. The hypothesis to test here is: Can these capsules flow under salt gradients; and can we trigger the release of surfactants by changing solution conditions like salinity, temperature or ph. 5. Dynamic assembly and patterning of soft spheres in multi-valent salts. While working in the lab one day, I found large patterned aggregates of 3 µm spsl particles (as shown in Figure 7-2) on a cover slip which were initially suspended in 1 ml 0.5 mm CaCO 3. When I re-did the experiments in a closed centrifuge tube by letting these particles soak in dilute CaCO 3 solution for an hour, they aggregated and settled to the bottom. I couldn t re-disperse the particles even on vigorous vortexing and sonication. The interesting cross-linking structure looks like an assembly under the optical microscope. Our lab has been dealing with making assemblies for a long time now (Yake 2006, McDermott 2010, Ramirez 2012) and in all cases, a high concentration of KCl was used to prepare these assemblies. 87

103 My hypothesis to test here is: Can we make long chain assemblies of colloids through lower concentration of a multi-valent salt like CaCO 3 which has been found to alter charges on colloids significantly over time periods of exposure? Can we predict through the classical Derjaguin-Landau-Verwey-Overbeek (DLVO) theory the inter-particle forces between the colloids in a non-symmetric electrolyte? Figure 7-2: Long cross-linked chains of colloidal spsl particles exposed to 0.5 mm CaCO 3 for 1 hour 7.3. Applications Some of the applications of diffusiophoretic flows can be enumerated succinctly as: 1. DNA Entrapment: The DNA capture rate in water is enhanced under applied salt gradients in the system (Wanunu 2010). Later, it was found that the mechanism behind enhanced capture rates had to do with the electrophoretic and electroosmotic components across DNA and wall surfaces (Roij 2011, Abgrall 2008) 2. Soil Sodicity: Field scale desalinization of soils aims at removing the ions present in the soils which degrade its quality over a period of time and affect its viability for 88