ABSTRACT USING SURFACE TENSION GRADIENTS AND MAGNETIC FIELD TO INFLUENCE FERROFLUID AND WATER DROPLET BEHAVIOR ON METAL SURFACES.

Transcription

1 ABSTRACT USING SURFACE TENSION GRADIENTS AND MAGNETIC FIELD TO INFLUENCE FERROFLUID AND WATER DROPLET BEHAVIOR ON METAL SURFACES by Mohan Panth In this work, three different projects related to surface wettability were studied. First, the controlled motion and stopping of individual ferrofluid droplets due to a surface tension gradient and an uniform magnetic field down the length of a wedge towards the more hydrophilic aluminum end due to a net capillarity force was studied. We observed that applying a magnetic field parallel to the surface tension gradient direction had little or no effect on the droplet while a moderate perpendicular magnetic field could stop the motion altogether effectively pinning the droplet. Furthermore, the directional dependence of the magnetoviscosity observed in this work was in disagreement with a well-established model of rotational magnetoviscosity found in the literature for dilute ferrofluids and might instead be understood as a consequence of the formation of nanoparticle chains in the fluid due to a minority of relatively larger magnetic particles. Second, a radial gradient surface was studied via injected droplets and spray testing. The goal of this surface was to promote water droplet coalescence and increase drainage. Droplet motion down the gradient was analyzed to determine how the position and volume of the water droplet influences travel distance.

2 USING SURFACE TENSION GRADIENTS AND MAGNETIC FIELD TO INFLUENCE FERROFLUID AND WATER DROPLET BEHAVIOR ON METAL SURFACES Thesis Submitted to the Faculty of Miami University in partial fulfillment of the requirements for the degree of Master of Science Department of Physics by Mohan Panth Miami University Oxford, Ohio 2016 Advisor Khalid Eid Advisor Andrew Sommers Reader Herbert Jaeger Reader Lei Kerr 2016 Mohan Panth

3 This Thesis titled USING SURFACE TENSION GRADIENTS AND MAGNETIC FIELD TO INFLUENCE FERROFLUID AND WATER DROPLET BEHAVIOR ON METAL SURFACES by Mohan Panth Has been approved for publication by Miami University and Department of Physics Khalid Eid Andrew Sommers Herbert Jaeger Lei Kerr

4 TABLE OF CONTENTS Page List of Tables... List of Figures... iv v Nomenclature... vii Acknowledgements... ix Chapters 1. Literature Review Introduction Ferrofluid Radial Gradient The Effect of Roughness on Wettability Ferrofluid Experimental Methodology Surface Preparation Metal Deposition and Coating Contact Angle Measurement Results and Discussion Contact Angle Measurement at 0G Contact Angle Measurement at 1000G Motion Along the Gradient Radial Gradient Experimental Methodology ii

5 3.1.1 Surface Preparation Coating on Surface Experimental Setup Results and Discussion Injected Droplet Analysis Force Experienced by a Droplet in a gradient Spray Test Analysis Finding Average Volume Distribution Horizontal Spray Test Vertical Spray Test The Effect of Roughness on Wettability Experimental Methodology Surface Preparation Experimental Setup Contact Angle Measurement Results and Discussion Effect of Sand Paper Roughening Sand Blasting Contact Angle Analysis on Hydrophilic Sample Contact Angle Analysis on Hydrophobic Sample Conclusions and Future work References iii

6 LIST OF TABLES 1. Table 1: Summary of gradient wedge angles Table 2: List of diameters having different volumes in wetting regime Table 3: List of quadrants with respective roughness, contact angle and roughness factor in hydrophilic sample Table 4: List of quadrants with respective roughness, contact angle and roughness factor in hydrophobic sample iv

7 LIST OF FIGURES 1.1Schematic sketch of magnetic particles with surfactants Interfacial energies acting on a liquid drop placed on a solid surface Wenzel model of droplets Cassie Baxter model of droplet Shadow mask made from aluminum Creation of the gradient pattern copper was first deposited onto an aluminum plate via physical vapor deposition (PVD) and then selectively hydrophobicized using HDFT Creation of the uniform surface to measure the contact angle on copper and aluminum surface at different sets of magnetic fields Experimental setup and equipment to study motion of ferrofluid Top-view schematic of the magnetic field orientations Images of the Cu/HDFT and Al regions at 0G from the top, side, and end views Images of the Cu/HDFT and Al regions at 1000G from the top, side, and end views The circular three-phase contact line of a model water droplet placed on a wedge-shaped suface tension gradient. The directions of the parallel and perpendicular magnetic fields (relative to the droplet motion) are also indicated The net capillary force divided by the surface tension of the liquid increases linearly with the head angle of the wedge, Motion of a ferrofluid droplet on a wedge in both zero field and 200 G parallel and perpendicular magnetic fields. The time interval between images is one second Evolution of a ferrofluid droplet on Wedge 4 in both parallel and perpendicular magnetic field orientations at 250 Gauss. Droplet pinning is observed in the perpendicular orientation v

8 2.12 Maximum droplet velocity versus the magnetic field strength. Results show a pinning effect at approximately 250G when the field is oriented perpendicular to the gradient direction Instantaneous droplet velocity versus time for two magnetic field strengths. Results show a slowly moving droplet at 200 G on Wedge 1 and a pinned droplet at 250 G on Wedge 4 in a perpendicular field Variation of the position of the fluid droplet front with the square root of the elapsed time. The linear dependence that is initially observed for the first second of the droplet motion is in agreement with the Washburn prediction Radial gradient surface and zoom out image of outer section of circle Difference in contact angle on the outer (hydrophobic) edge and on the center (hydrophilic) of those radial gradient circles Experimental setup to study water droplets on radial gradient Location of injected droplets on the circular radial gradient Spliced images of starting and final position of 5µl water droplet at the circular region of radial gradient Spliced images of starting and final position of 10µl water droplet at the circular region of radial gradient Spliced images of starting and final position of 27µl water droplet at the circular region of radial gradient Spliced images of starting and final position of 38µl water droplet at the circular region of radial gradient Schematic of a droplet on a (a) homogeneous surface and (b) a surface with an underlying gradient Symbolic representation of net force experienced by water droplet when placed on the outer edge of the boundary vi

9 3.11 Plot of position vs travel distance for 38µl, 27µl, 10µl and 5µl volume of water droplets Plot of position vs travel distance for 38µl, 27µl, 10µl and 5µl volume of water droplets Plot of position vs travel distance for 38µl, 27µl, 10µl and 5µl volume of water droplets Plot of position vs travel distance for 32µl and 7µl volume of water droplets Combined plot of position vs travel distance for 32µl and 7µl volume of water droplets Plot of diameter vs travel distance of different volume of droplets with same starting position Droplets distribution while doing with the different spray test from varying height Snapshot images of coalescence of water droplets during spray test while the sample was placed horizontally Snapshot images of coalescence of water droplets during spray test while the sample was placed vertically Sample with four different quadrant with different roughness Ramé-Hart precision goniometer Different grits of sandpaper Sand blasted copper surface Images of water droplets on different quadrants of the hydrophilic sample Images of water droplets on different quadrants of the hydrophobic sample vii

10 B, B1 Magnitude of magnetic field NOMENCLATURE D Fs f1, f2 f G ᵞSG ᵞLS ᵞLG KB M r dr dx V Diameter of the critical droplet Net Surface tension force on a droplet on a horizontal surface surface fractions of the two different materials ratio of the projected area to the actual area of the surface for the Cassie model Abbreviation of Gauss Interfacial energy between solid-gas interfaces Interfacial energy between liquid-solid interfaces Interfacial energy between liquid-gas interfaces Boltzmann constant Intensity of magnetization distance between two ferrofluid droplets Minimum gradient needed for water droplets travelling along a horizontal surface based upon Wenzel s model of wetting Volume of the droplet in wetting regime µ 0 Permeability of free space Θc Θadv Θrec Θw Θ * τ Contact angle of the droplet Advancing contact angle Receding contact angle Contact angle in Wenzel case Contact angle in Cassi-Baxter case Torque acting on a ferrofluid droplet µ, µ 1 Permeability of the medium viii

11 Acknowledgements I am deeply appreciative of those individuals who have supported me and made this thesis possible. Foremost, I would like to express my sincere gratitude to my advisors, Dr. Khalid Eid and Dr. Andrew Sommers for their inspiration, encouragement, and enthusiasm. Their systematic guidance helped me in formulating and writing my thesis. They have been very supportive since the first day I began doing my research. I feel fortunate to have had an opportunity to work under their professional and rewarding supervision. I am also grateful to Miami University for supporting me as a Graduate Assistant for whole two years. As an international student, it was fruitful working with the well-known, cooperative professionals on different fields during my stay at Miami University. Finally, I would like to thank my parents, friends and my wife for their encouragement and support. They have helped me a lot since the first day I decided to go overseas and pursue my graduate study. I thank them for providing me with unfailing support during my two years at Miami University. This achievement would not have been realized without them. ix

12 Chapter 1: Literature Review 1.1 Introduction Micro/Nano fluidics refers to the behavior and control of fluids in micro/nano scale. The behavior of fluids in the micro/nano domain significantly changes from that of macroscopic fluids as well as their physical and chemical properties. Micro/Nano fluidics is a multidisciplinary field with a wide variety of applications in bio and nanotechnologies [1]. Droplet-based micro/nano fluidics has some potential benefits over the continuous micro/nano fluidics. Surface tension forces dominate the gravitational force when we delve into the micro/nano realm of fluids. This technology gets rid of the conventional liquid pumps, gas valves etc. Every microfluidic process is performed in a discrete manner, where the fluid is transported, stored, mixed, reacted and analyzed as individual droplets. The most successful commercial application of microfluidics is inkjet print head [2]. Additionally, advances in microfluidic manufacturing allow the device to be produced at low cost with higher efficiency. The degree of wettability is characterized by hydrophobic and hydrophilic surfaces. Hydrophobic means water repellant and hydrophilic refers to water loving surfaces, where the contact angle is used to distinguish the hydrophobic and hydrophilic surfaces: If the contact angle is greater than 90 then the surface is hydrophobic and it is hydrophilic if the angle is less than 90. If the contact angle is 0 to 15 o, then such surface is said to be a completely wetting surface, like glass, and a zero wetting surface if the contact anle is 155 o to 180. Making Superhydrophobic surface is a difficult task because of issues with its durability and the high cost of manufacturing. For example, Lotus leaf, which has contact angle greater than 150 o, is a super hydrophobic surface with selfcleaning properties. Recently Nike Company has launched self-cleaning superhydrophobic coated shoes [3]. Self-cleaning windows are also in commercial use. Due to the roughness created on the surface, droplets take a spherical shape and roll off the surface. [3] Ferrofluid is formed when nano-sized magnetic particles having a typical dimension of 10nm are evenly dispersed in a colloidal liquid. Ferrofluids show very interesting and peculiar physical and chemical properties that can also be tuned with the application of a magnetic field [4]. Surface tension gradients can be used to manipulate and control the motion of droplets. Surface tension gradients facilitate the motion of droplets towards the more hydrophilic region due to the difference in contact angle around the contact line of a droplet, leading to a net surface tension 1

13 force which is responsible for the motion of fluids. Wedge shaped gradients are very useful for the spontaneous motion of droplets toward hydrophilic regions [12]. Such gradients have recently been used in many studies to accurately manipulate the liquid droplets. Radial gradients are especially suited for use in heat transfer applications like in heating, ventilation, air- conditioning and refrigeration (HVAC & R) systems because directionality of water droplets is achieved. Since copper and aluminum are the most suitable metals used in HVAC & R systems because of low cost and their high efficiency while using in heat exchangers [12]. Different kinds of gradients can be made by physical deposition or chemical coating [5]. Research on the dynamics of fluids has substantially increased over the past decades and has been ever increasing since then. The shape and behavior of the fluid droplet play a key role in manipulating and controlling droplet. In this thesis, the behavior of fluid droplets on metal surfaces with surface tension gradients, including three distinct sets of experiments were studied: The first used a magnetic field in addition to the surface tension gradient to control the flow and stopping of ferrofluid droplets. The second focused on radial surface tension gradients for water droplets management, and the third studied the effect of surface roughness and a wedge-shaped surface tension gradients on water droplets in an educational context. 1.2 Ferrofluid The control of the flow of small amounts of fluid (in the microliter to nanoliter range) continues to attract considerable research interest due to the unique problems encountered and the many potential applications, like DNA amplification [6], DNA sequencing [7], cell separation and detection [8, 9], ultrafast inkjet printers [10], and micro-chemical reactors [11]. Micro-scale surface tension gradients offer a unique way to control the flow of fluid droplets on smooth metal or semiconductor surfaces [12]. Ferrofluids, however, offer additional manipulation ability over water droplets since they can be impacted by uniform as well as varying magnetic fields. Ferrofluids are colloidal suspensions of single domain magnetic particles having typical diameters of a few to a few tens of nanometers in a carrier liquid. Brownian motion keeps the nanoparticles from settling under gravity and a surfactant usually provides the steric repulsion between particles to prevent them from agglomerating [13, 14]. Ferrofluids are used in dynamic sealing as well as heat dissipation and can also be used in different biomedical applications like hyperthermia, image 2

14 contrast-enhancing, magnetic drug targeting, etc [15]. A slightly different kind of ferrofluids is the magnetorheological fluids (MRF), which are made from micron-sized particles. MRFs are used in brakes, clutches, and shock absorbers, among other mechanical devices, owing to their tunable viscosity that can become very high in moderate magnetic fields [16, 17, 18, 19]. The strong magnetoviscosity associated with MRFs is due to the formation of particle chains in the presence of relatively small magnetic fields. Such chains resist the shearing of the fluid, giving rise to magnetoviscosity. Ferrofluids which have small nanoparticles on the other hand, are predicted not to form particle chains due to the much smaller interparticle interactions; as a result, they typically have a much smaller magnetoviscosity [20]. To date, significant research efforts have been focused on the behavior of ferrofluid droplets in magnetic fields and field gradients, where understanding their flow characteristics is of special importance [21, 22]. For example, transverse forces (i.e. the Magnus effect) have been used to explain the motion of ferrofluid droplets in a rotating magnetic field [22]. When a sufficiently large magnetic field gradient is applied, ferrofluids will flow toward regions of stronger magnetic field, and the hydrodynamic properties of the fluid such as viscosity can be significantly altered [23, 24, 25]. Magnetic fields have also been used to control the surface tension (i.e. contact angle) of fluids on specialized surfaces [26] and to directly change the shape and behavior of ferrofluid droplets [27, 28, 29]. The behavior of ferrofluid droplets placed on a surface tension gradient in the presence of a uniform magnetic field, however, needs more study. In this research, we study the behavior of ferrofluid droplets placed on surfaces that either contains a surface tension gradient or are uniformly hydrophilic or hydrophobic in the presence of various uniform magnetic fields. Of special interest is the case where the uniform magnetic field is either parallel or perpendicular to the surface tension gradient direction. While magnetic fields can change the behavior of fluid droplets in different ways, this work is focused on the field-dependent magnetoviscosity of individual ferrofluid droplets placed on a surface tension gradient Surfactants Magnetic nanoparticles are thoroughly coated from outside with a surfactant to inhibit clumping. Thermal energy prevents the magnetic nanoparticles of size 10nm from sedimenting under the influence of gravity or from agglomeration due to the dipole-dipole interaction. But this 3

15 does not prevent magnetic nanoparticles from clumping together from attractive van der Walls force. To prevent this clumping, surfactants are used to coat thoroughly from outside of the particles. A surfactant is made of a long chain of polar and non-polar head depending on the dielectric properties of carrier liquid. The typical dimensions of surfactants are 2-3nm [see Figure 1.1]. Oil, water, kerosene etc are used as a carrier liquid in ferrofluid solutions. Common surfactants used in ferrofluid solutions are i Oleic acid, citric acid, and soy lecithin [23]. Fig. 1.1: Schematic sketch of magnetic particles with surfactants Stability against magnetic agglomeration Surfactants are coated on the magnetic nanoparticles to provide the steric repulsive force between them. The steric repulsive force is balanced by the attractive (van der Waals and dipole-dipole) force leading to the stability of the ferrofluid. R. E. Rosensweig calculated the typical particle diameter to avoid magnetic clumping by comparing the dipole-dipole pair energy with thermal energy [30]. The typical diameter is given by the equation D ( 72K BT πµ 0 M 2)1/3. (1) Where, K B = Boltzmann constant 4

16 T = absolute temperature µ 0 = permeability of free space M = intensity of magnetization Putting these values at room temperature in equation (1), we get D 10nm. 1.3 Radial gradient The wetting phenomenon of microfluidics continues to attract considerable attention in research since the last decade. The management of water droplets plays a key role in heating, ventilation, air-conditioning and refrigeration (HVAC & R) systems where generally copper or aluminum is used as the heat exchanger surface. Both Cu and Al are naturally hydrophilic (water loving) and water condenses on the heat exchanger surface affecting the heat transfer efficiency. These condensate droplets may coalesce with other droplets and form bigger droplets thereby reducing the efficiency of heat exchangers by reducing the effective heat transfer surface area and increasing the core pressure drop [5]. These droplets should be managed such that we can increase the efficiency of heat exchangers by removing the droplets in a controlled way and in the desired path for the drainage. Surface tension gradients can be used to facilitate droplets motion in such desired ways. Patterned anisotropic wetting may be preferred for the motion of droplets in a specified way. Anisotropic patterning can move the droplets a short distance in a preferred direction, but the chemical coating on those patterned surfaces may further enhance the motion. The method of creating topography-based surface tension gradients on a metallic surface especially on Cu and Al is described in the paper by Sommers et.al [5]. Parallel micro-channels having fixed width but variable spacing are created on the surface by laser etching. They reported a horizontal spontaneous motion between 0.5 to 1.5mm and spontaneous vertical motion at an inclination of 5.7. The motion they observe is only due to the surface anisotropic wettability without deliberately applying any chemical coating. Chemically treated radial gradients with a hydrophobic PFDTs circle in the center, surrounded by the radially oriented alternating hydrophobic and hydrophilic stripes was used to move droplets [31]. Further, surface chemistry approach is also used to generate radial gradients with hydrophilic centers and hydrophobic surroundings, to harvest water droplets at the center [32]. Spontaneous movement was observed both in flat and tilted surface towards a hydrophilic center. Hydrophobicity was created on Silicon 5

17 wafers by SAMs of 10-undecenyltrichlorosilane. Oxidation of initial drop followed by dilution by dropping method creates the radial wettability gradient surface [33]. Furthermore, triangular wedge of Aluminum on Cupper background were prepared and used for the horizontal and vertical motion. The surface tension gradient created at the tip of the wedge forces the droplets to move spontaneously towards the more hydrophilic parts both horizontally and even against gravity. Wedge angle and the contact angles on Cu and Al determine the speed of droplets [34]. Research has been done recently on the equilibrium shape of the droplets. Qian Zhou and his group discuss a magnetic technique for altering the contact angle of aqueous liquid droplets placed on a nanostructured surface. 15 reduction in the contact angle of aqueous liquid droplets has been observed when a 500G magnetic field has been applied using a bar magnet. The nanostructured surface is prepared via layer by layer deposition in 800nm-diameter pores of polycarbonate track etched (PCTE) membranes [26]. The key parameters affecting the shape of the droplets on inclined surfaces have been thoroughly investigated under various conditions. They built a setup to study profiles, contours, contact angles and volumes for liquid droplets of different sizes and at various inclination angles [35]. The critical droplet size was also calculated. They observed a critical droplet size 50% smaller on micro grooved surfaces than without micro-grooves on the same surface. Droplet size is critical in applications like air cooling and dehumidifying applications where management of liquid droplets is necessary [35]. Surface tension gradients are more efficient in manipulating droplets of sub-microliter volume than gravity, because the gravitational force is negligible compared with the surface tension force. Manipulating droplets distributions also play a key role in maximizing the heat transfer efficiency [36, 37]. A hybrid energy minimization algorithm was used to find the equilibrium droplet shape on a wettability gradient surface [38]. Furthermore, Sommers et.al [39] calculated the critical air velocity for water droplets departure from the vertical channels in a cross flow. Required air flow rate across channels with PDMs coating was 1-1.2mm/sec larger than movement along the channels. They also suggest micro-channels which are aligned parallel to the gravity to assist in condensate drainage and not to carry the condensate into an occupied space [39]. 6mm of radial movement of droplet along the surface tension gradient was measured by Zamuruyev and group. This kind of movement is essential to achieving a self-cleaning surface [40]. In addition, the actuation mechanism of droplets has been studied with potential applications in microfluidics. When two droplets are placed in immediate proximity, a surface energy gradient causes two 6

18 different droplets to coalesce. In this experiment, they have used water and ethanol as two droplets [32]. Several methods to spatially control the condensate nucleation and maximum droplet sizes have been demonstrated to facilitate pump-less drainage in dropwise condensation using wettability gradients. That will help to make the heat transfer and drainage process more efficient. In this process, they have used wedge-shaped super hydrophilic tracks to collect liquid pumplessly [41]. 1.4 The effect of roughness on wettability Research on superhydrophobic materials has been especially inspired by nature. Lotus leaf shows superhydrophobic nature having a contact angle greater than 150 due to the micro and nano-roughness on the substrate (Lotus leaf). There are many potential applications in industry and materials engineering where the shape of droplets plays a crucial role [42]. Nonsticky cooking pots, self-cleaning windows, speedboats, recently launched Nike s shoes, clothes etc. are some potential applications of superhydrophobic surfaces. So understanding how these surfaces can be created has attracted our attention on this project. We have tried to develop an easy and cost effective method to create superhydrophobic/superhydrophilic surfaces targeted for undergraduate students with little background in this field. Different levels of roughness have been created on the substrate to understand how micro-, nano-, as well as micro plus nano roughness affect the behavior of both initially hydrophobic and hydrophilic surfaces. Hydrophobic surfaces after sand blasting and annealing shows dramatic improvements in mechanical properties, wear, and corrosion resistance. They also calculated the contact angle of water and found that it increases to 135 when applying fluoroalkyl silane on sand blasted surface [43]. Physical and thermal stability along with the durability of the superhydrophobic surface are the most significant issues for applying them to commercial use. Esmaeilirad and his group develop a cost effective way to make these surfaces. Layer by layer deposition, chemical deposition, anodizing, plasma surface, electrospinning, sputtering and etching followed by surface modification with low surface energy materials, are the best methods to make superhydrophobic surfaces. The contact angle of aluminum alloy they calculated was 165 with contact angle hysteresis less than 3. And the superhydrophobicity is preserved when heating to 375 C, 30 min of sonification, after immersing in water for 100h, and storing for 180 days [44] 7

19 Our project is geared towards undergraduate-level students in order to develop a set of inexpensive hands-on activities and apply basic principles that allow them to understand the nature of superhydrophobic/superhydrophilic surfaces in the lab within a short period of time. We used sand blasting to create micro-roughness on copper surfaces and immersed them in AgNO3 to create nano-roughness. This was followed by immersion into HDFT solution for some samples in order to make them superhydrophobic Contact Angle Contact angle quantifies the wettability of the solid surface by a liquid. Wetting refers to the degree of spreading of the liquid over the solid surface. A wetting liquid makes a contact angle less than 90 with the solid surface whereas the non-wetting liquid makes a contact angle between Young s equation is used to determine the contact angle(θ c ). Interfacial energy of the liquid-gas (γ LG ), liquid-solid (γ LS ) and solid-gas (γ SG ) interfaces determines the contact angle and is given by the equation [see Fig1.2] : cosθ c = γ SG γ LS γ LG.. (2) Fig. 1.2: Interfacial energies acting on a liquid drop placed on a solid surface Figure 1.2 shows the net force on the equilibrium droplets placed on a solid surface. Obviously, the net force on the droplet is zero here. This equation is only valid for the equilibrium case and for the smooth surface only. In fact, roughness on the surface may give an incorrect value of contact angle as predicated by the above equation (2) Wenzel Model 8

20 In 1936, Wenzel described the homogenous wetting properties enhanced by the roughness. In this model droplet is assumed to wet the surface and fill the protrusion created by the roughness. Wenzel model for the rough surfaces is described by the equation (3) [see Fig 1.3] cosθ w = rcosθ c (3) Where r is the roughness factor which is defined as the ratio of the actual wetted area of the rough surface to the projected geometric area. Since the roughness factor is always greater than 1, the above equation shows that, cosθ w > cosθ c. (4) From this equation, it is inferred that if the solid/liquid interaction gives hydrophobic behavior, then the surface is expected to be more hydrophobic, and if solid/liquid interaction gives hydrophilic behavior, then the surface is expected to be more hydrophilic Cassie-Baxter Model Fig. 1.3: Wenzel model of droplets The Wenzel model is not suited for dealing with the heterogeneous surfaces. Cassie and Baxter derived the equation for finding the contact angle for a hydrophobic surface in In this model, the droplet is assumed to wet the surface and to not fill the protrusion created by the roughness [see Fig. 1.4] 9

21 Let θ 1 and θ 2 be the contact angles for each individual material, and f 1 and f 2 are the surface fractions of the two materials, then: cos θ = f 1 cos θ 1 + f 2 cos θ 2.. (5) Once the droplet sits on the top of the protrusion features like in fig 1.4, the Cassie-Baxter equation can be used to predict the contact angle. Since the contact angle of water on air is θ 2 = 180 o, then equation (5) becomes cos θ = f(cos θ c + 1) 1... (6) Where f is the geometric projected area to the actual area of the surface. The contact angle increases with decreasing the factor f. Fig. 1.4: Cassie Baxter model of droplets 10

22 Chapter 2: Ferrofluid 2.1 Experimental Methodology In this section, we briefly discuss how we make surface tension gradients samples, experimental setup and the software s used to collect and analyze the datas in detail Surface Preparation Mirror-finish aluminum plates (Alloy 6061) with dimensions (50.8 mm 50.8 mm 2.54 mm) were used to study the motion of ferrofluid droplets on a surface tension gradient. To prepare the gradient, the aluminum surface was first cleaned in Alconox immediately after peeling off the protective coating. The surface was gently rubbed with a Kimwipe during the Alconox soaking followed by a rinsing in acetone, isopropyl alcohol (IPA) and deionized water separately. A gentle oxygen plasma etching was then performed for two minutes to remove any organic residue left on the surface. Next, a wedge-shaped shadow mask made out of aluminum was used to cover the surface during the deposition of copper on the surface [see Fig. 2.1]. Fig. 2.1: Shadow mask made from aluminum The angles of the various wedges that were examined in this work are shown in Table 1 11

23 Table 1 Summary of gradient wedge angles Wedge 1 Wedge 2 Wedge 3 Wedge 4 Angle Metal deposition and coating The thermal deposition of 80 nm of copper was done in a background pressure of approximately Torr resulting in a final sample [see Fig. 2.2]. After copper deposition, the surface was immersed in a 0.1M heptadecafluoro-1-decanethiol (HDFT) solution for six minutes to create a self-assembled monolayer (SAM) on the copper surface. The SAM was observed to selectively grow on the copper but not on the aluminum, possibly due to the formation of a strong oxide layer on the aluminum which served as a barrier. This rendered the copper regions of the surface hydrophobic, while the aluminum regions remained hydrophilic or even super-hydrophilic. These wedges and their associated wettability contrast thus formed a surface tension gradient (in the direction of increasing aluminum contact area) when a fluid droplet was placed at the vertex of the wedge. Fig. 2.2: Creation of the gradient pattern copper was first deposited onto an aluminum plate via physical vapor deposition (PVD) and then selectively hydrophobicized using HDFT Contact angle measurement 12

24 To measure the contact angles of these different surface regions, copper was thermally deposited on a second aluminum block on half of the surface to form two distinct regions each with an area of 1 2 (25.4 mm 50.8 mm) using the same protocol as described above. This enabled the contact angle of individual ferrofluid droplets to be studied independently on both the Cu and Al regions in the presence of a uniform external magnetic field without the gradient [see Fig. 2.3] Fig. 2.3: Creation of the uniform surface to measure the contact angle on copper and aluminum surface at different sets of magnetic fields Experimental Setup The experimental setup used in this study is shown in [see Fig. 2.4], where an electromagnet was used to produce a uniform magnetic field of up to 2000 Gauss. A 14 MP Pentax camera with a wide-angle 5 optical zoom lens (28-140mm equivalent) was used to take both the still images and videos of the ferrofluid droplets in magnetic fields of different magnitudes and directions relative to the wedges. The camera was capable of capturing video at a rate of 30 frames per second. For an experiment, the camera was either placed on the top of the pole pieces of the magnet for getting top-view images, or placed on a tripod outside of the magnet's frame to get side images that allow the contact angles to be estimated at the two points closest to the poles (i.e. where the droplet s contact line is perpendicular to the magnetic field direction). A third position (i.e. end view) involved placing the camera above the sample and using a mirror tilted at 45 o in order to get the contact angles at the two points where the droplet contact line is parallel to the magnetic field. The droplets are injected on the surface horizontally between the poles of the magnet to eliminate the effect of gravity. The magnetic field direction can be either parallel or perpendicular to the surface tension gradient, but is thus always kept in the plane of the metal surface [see Fig. 2.5]. 13

25 Camera Camera holder Electromagnet DC power Supply Sample Ferrofluid Light source Micropipette Fig. 2.4: Experimental setup and equipment to study motion of ferrofluid Two different magnetic particle concentrations of a commercially available water-based ferrofluid from Ferrotec Corp. were studied in this work namely, EMG 700 (5.8% vol.) and EMG 705 (3.9% vol.). The nominal average particle diameter in both cases was 10 nm. The EMG 700 ferrofluid had a saturation magnetization at 25 C of Gauss ( 10%), and the EMG 705 ferrofluid had a saturation magnetization of 220 Gauss ( 10%). Ferrofluid droplets were dispensed/injected on the surface using an adjustable micropipette with a typical droplet volume of 15 L. The micropipette was capable of dispensing droplets in the volume range of 2 to 20 µl. To begin an experiment, the camera was positioned in one of the three locations indicated above. A ferrofluid droplet was then placed at the vertex of a wedge, and video of the droplet travel was recorded. Next, Free studio software was used to splice the videos into a sequence of still images showing the time-elapsed motion of the droplet. These images were then used to calculate the velocity and acceleration of the droplet down the gradient. After each test, the surface was cleaned and re-energized through a soak and gentle rinse in Alconox. 14

26 PARALLEL FIELD PERPENDICULAR FIELD Fig. 2.5: Top-view schematic of the magnetic field orientations. (Note: The sample surface is kept horizontal, and the surface-tension-driven flow proceeds along the long axis of the triangles.) 15

27 2.2 Results and discussion Contact angle at 0G Figure 2.6 shows pictures of ferrofluid droplets on the Cu/HDFT and Al surfaces in zero external magnetic field. Top-view pictures of droplets on Cu and on Al are shown in Fig. 2.6(a) and 2.6(d) respectively, where the contact lines are relatively smooth circles, with small deformations due to imperfections at each surface that act as pinning sites to the contact line. The side-view pictures show much more contrast between the shape of droplets on HDFT-coated Cu and bare Al. It is seen from Figs. 2.6(b) and 2.6(c) that the contact angles on Cu are about 90 o. On the other hand, Figs. 4e) and 4f) clearly show extremely small contact angles of less than 15 o confirming that the Al surface is strongly hydrophilic and can be characterized as superhydrophilic. Both droplets are isotropic in shape and not elongated in any direction, showing that there is no residual magnetic field in the electromagnet. It should be noticed that the droplet placed on Cu is significantly thicker than that placed on Al and yet the total volume is the same for both droplets since the one on Al spreads out much more. (a) (b) (c) 0.5cm ± 0.1cm B=0G, Cu top view B=0G, Cu side view B=0G, Cu end view (d) (e) (f) 0.6cm ± 0.1cm B=0G, Al top view B=0G, Al side view B=0G, Al end view Fig. 2.6: Images of the Cu/HDFT and Al regions at 0G from the top, side, and end views 16

28 2.2.2 Contact angle at 1000G Figure 2.7 shows pictures of two ferrofluid droplets on Cu/HDFT and Al in an external magnetic field of 1000 Gauss. Apart from the expected elongation of the droplets in the direction of the magnetic field and a reduction in the apparent contact angle on both the Cu and Al [26,45], the overall behavior is quite similar to that in zero external magnetic field as shown in Fig The most important observation about these droplets is that despite the expected change in the droplet shape, there is no net translational motion of the droplets (i.e. the center-of-mass of the droplet never moves with the application of a uniform magnetic field): a uniform magnetic field is not expected to cause a net translational motion of a ferrofluid because it does not give rise to any net force. (a) (b) (c) 1.5cm ± 0.1cm B=1000G, Cu top view B=1000G, Cu side view B=1000G, Cu end view (d) (e) (f) 1.6cm ± 0.1cm B=1000G, Al top view B=1000G, Al side view B=1000G, Al end view Fig. 2.7: Images of the Cu/HDFT and Al regions at 1000G from the top, side, and end views 17

29 2.2.3 Motion along the gradient When considering the net force on a magnetic fluid placed in a magnetic field: F = (μ. B ), π where μ = M 0 V = M 0 6 d3 is the magnetic moment, M0 is the magnetization of the material, V is the volume of the nanoparticle (assumed to be spherical), d is the particle diameter, and B is the magnetic field. The formula simplifies to the so-called Kelvin body force given by: F = (μ )B in a uniformly magnetized ferrofluid [46, 47]. This shows that a uniform magnetic field (i.e. with no field gradient) exerts no net force on a ferrofluid. A magnetic field gradient, on the other hand, causes a net force on the ferrofluid, which is why ferrofluids move to areas with stronger magnetic fields. This force is sometimes utilized in the process of filtering larger nanoparticles from the fluid in order to have a relatively monodisperse particle size distribution [48,49]. Placing a ferrofluid droplet on the wedge-shaped hydrophilic Al pattern surrounded by the hydrophobic Cu results in a net capillary force on the droplet towards the base of the Al wedge. Figure 2.8 is a schematic diagram showing the three-phase contact line of a circular droplet placed on the wedge. In a simplified model that assumes there to be only two different contact angles around its perimeter, the net force on the droplet can be found by integrating around the threephase contact line which yields the following expression: F sx = 2γR{cosθ philic cosθ phobic }[sinφ B sinφ F ] Hydrophobic Cu Hydrophilic Al Fluid Droplet B F Net Force Fig. 2.8: The circular three-phase contact line of a model water droplet placed on a wedge-shaped surface tension gradient. The directions of the parallel and perpendicular magnetic fields (relative to the droplet motion) are also indicated. 18

30 Here Fsx is the net surface tension (i.e. capillary) force, is the surface tension of the fluid, R is the radius of the droplet, phobic and philic are the contact angles on the hydrophobic Cu and the hydrophilic Al respectively, and B and F are angles related to the geometry as shown in Fig The triangular shape serves a crucial role. Since the front of the droplet in contact with the Al is longer than the rear part, which is also in contact with Al, a net capillary force forward is produced. It should be noted that the part of the droplet in contact with the hydrophobic surface also gives rise to a net force in the same direction. This latter force would be zero if the triangle was replaced with a simple rectangular shape instead with parallel sides. The effect of the wedge angle on the net capillary force is shown in Fig It is evident from the figure that there is a linear relationship between the angle and the net force divided by the surface tension parameter, which is in good agreement with our observations as well as other published experimental and theoretical reports [50,51,52]. 1 Fx/ (mm) Wedge angle (degrees) Fig. 2.9: The net capillary force divided by the surface tension of the liquid increases linearly with the head angle of the wedge,. 19

31 Figure 2.10 shows time-elapsed images of a droplet placed on a wedge-shaped surface tension gradient both in the absence of an external magnetic field and in the presence of 200 G parallel and perpendicular fields. In the case of zero field, the large difference in contact angles between the parts of the droplet on the Al and on the Cu leads to a net capillary force that pulls the droplet towards the Al end. This force leads to a spreading motion of the droplet. This behavior was observed previously with water droplets, which was the reason behind the choice of a water-based ferrofluid for this study in order to offer a direct comparison thereby enabling better isolation of the effect of the magnetic field on the droplets. When a magnetic field is applied, on the other hand, a completely different behavior emerges, which depends on the orientation and strength of the magnetic field relative to the surface tension gradient direction. In the case of the 200 G field, the droplet is observed to travel approximately the same distance independent of the field orientation; however, the shape associated with the advancing front of the droplet is observed to be flatter in the perpendicular field, whereas it is more rounded and raised up in the parallel field. Droplet movement also proceeded more slowly in the perpendicular field. In both zero field and the parallel field, the droplet stopped moving after approximately 2-3 seconds, whereas for the perpendicular field, the droplet continued moving for more than 10 seconds. The movement of the droplet front proceeded even slower when the perpendicular magnetic field was just below the critical stopping field. In this case a precursor (i.e. hemi-wicking) film first extends outward followed by more flow from the main droplet. This is consistent with earlier observations involving water droplet behavior. 20

32 0 sec Zero Field Perpendicular 200 G Parallel 200 G 1 sec 2 sec 3 sec 4 sec 5 sec 6 sec 7 sec 8 sec 9 sec 10 sec 11 sec Fig. 2.10: Motion of a ferrofluid droplet on a wedge in both zero field and 200 G parallel and perpendicular magnetic fields. The spontaneous motion of the ferrofluid droplet is observed even in the absence of a magnetic field. The time interval between images is one second. 21

33 Figure 2.11 contains two panels of spliced pictures showing a moving droplet in a parallel magnetic field and a stopped droplet in a perpendicular magnetic field. Although the uniform external magnetic field exerts no net force on a ferrofluid droplet, it induces a highly anisotropic change in the viscosity of the fluid (i.e. magnetoviscous effect) which in turn affects the behavior and flow of the droplet. While the ability to stop the motion or allow it in a magnetic field can have many potential biomedical applications, the details of the behavior are also important from a basic science point of view. Magnetic Field Parallel to Motion 0 sec Magnetic Field Perpendicular to Motion 0 sec 0.33 sec 0.33 sec 0.66 sec 0.66 sec 0.99 sec 0.99 sec 1.32 sec 1.32 sec 1.65 sec 1.65 sec 1.98 sec 1.98 sec 22

34 Fig. 2.11: Evolution of a ferrofluid droplet on Wedge 4 in both parallel and perpendicular magnetic field orientations at 250 Gauss. Droplet pinning is observed in the perpendicular orientation. Magnetoviscosity was first discovered more than four decades ago [53], and the underlying microscopic behavior of the ferrofluid was also modeled successfully soon after that by M.I. Shliomis [54]. The Shliomis model assumes that the ferromagnetic particles will rotate within a flowing ferrofluid under shear flow. In the absence of a magnetic field, the magnetic nanoparticles can rotate freely and only have to overcome the inherent viscosity of the ferrofluid. When a magnetic field is applied, however, it will tend to align the dipole moment of the particles in its direction due to the torque: τ = μ XB. This magnetic torque in turn can increase the magnetoviscosity when the magnetic field is not in the same direction as the vorticity of the flowing fluid, since the field will prevent the particles from rotating in a way that misaligns their moments with the field direction. A magnetic field parallel to the vorticity will have no effect on the flow, since the magnetic nanoparticles can rotate with their magnetic moment still aligned with the field. Thus, the Shliomis model suggests that the magnetoviscosity is highest when the magnetic field is perpendicular to the vorticity and is zero when it is parallel. Since the fluid in our experiment flows down the wedge in the surface tension gradient direction, the vorticity vector is expected to be perpendicular to the flow direction. So, when the magnetic field is parallel to the surface tension gradient, it is assumed to be perpendicular to the vorticity vector, and when the field is perpendicular to the flow, it is assumed to be parallel to the vorticity vector. Following this line of reasoning then, one might expect the magnetoviscous effect to be highest when the magnetic field is parallel to the motion. This is in sharp contrast however with what we observed namely, that the magnetoviscosity was apparently higher when the field was perpendicular to the flow and did not seem to change much when the field was oriented parallel to the flow. In fact, for moderate magnetic fields, droplet pinning was observed when the field was perpendicular to the flow direction, while no pinning was observed in the parallel orientation. It is important to point out that the Shliomis model assumes no interaction of particles (i.e. a highly diluted suspension). The 23

35 commercial ferrofluid that was primarily used in this work had a volume concentration of magnetic material of 5.8 vol.%. While this is likely considered dilute, it is important to note that the thickness of the surfactant layer can effectively increase the particle diameter leading to a larger apparent concentration of suspended material. It should also be pointed out that due to the low droplet speeds involved in this work and the presence of an adjoining solid surface, the vorticity of the fluid is likely to be quite small. Figure 2.12 shows a histogram of the speed of propagation of the moving front of the ferrofluid droplet down the surface tension gradient in different applied magnetic fields. The histogram shows clearly that a relatively small or moderate uniform magnetic field is sufficient to prevent ferrofluid droplets from moving even in a strong surface tension gradient. At the same time an order-of-magnitude larger magnetic field applied parallel to the surface tension gradient does not even slow the flow of the droplets down the surface tension gradient. Next, the critical field for droplet pinning in the perpendicular orientation was determined. Although small variations were observed experimentally when trying to quantify the critical field, a magnetic field of 250 Gauss was observed to pin the droplet and prevent motion on multiple wedges. (Note: Due to small differences attributed to the coating and/or the cleaning process between tests, droplet motion was observed during one set of tests at 275 Gauss; however, at higher magnetic field, droplet pinning was once again observed.) Wedge 4 Wedge 3 Fig Maximum droplet velocity versus the magnetic field strength. Results show a pinning effect at approximately 250G when the field is oriented perpendicular to the gradient direction 24

36 Figure 2.13 shows the instantaneous droplet velocity as a function of time for Wedge 1 and Wedge 4 in both parallel and perpendicular fields. On Wedge 1 at 200 G, the droplet is seen to move more slowly in the perpendicular field than the parallel field (i.e. 0.4 cm/s vs. 1.7 cm/s); however, droplet motion is detected for a longer period of time (i.e sec vs. 2.3 sec). On Wedge 4 at 250 G, however, the droplet is pinned (after initial placement on the wedge) in the perpendicular field but is observed to still move along the gradient in the parallel field. These plots also reveal that the droplet traveled for a longer period of time on Wedge 4 versus Wedge 1 in the parallel field. This could be explained both in terms of the smaller angle associated with Wedge 4 and the increased field strength used here. Wedge 1 Wedge 4 Parallel Parallel Zero Field Zero Field Droplet is pinned after initial placement. Perpendicular Perpendicular Fig. 2.13: Instantaneous droplet velocity versus time for two magnetic field strengths. Results show a slowly moving droplet at 200 G on Wedge 1 and a pinned droplet at 250 G on Wedge 4 in a perpendicular field. 25

37 As mentioned earlier, the Shliomis model attributes the moderate magnetoviscosity observed in dilute ferrofluids to the hindrance of rotational motion of the nanoparticles due to the magnetic field torque. This model however makes at least one major assumption namely, that the ferromagnetic particles are non-interacting. The more likely cause of the directional dependence of the magnetoviscosity in our study is the formation of nanoparticle chains within the ferrofluid. The formation of such chains was earlier thought to not be possible, due to the very small coupling between low concentrations of magnetite particles with an average diameter of 10 nm. It can be shown that a magnetic particle (i.e. magnetic dipole) creates a field B 1 = μ 0 [(3μ 4πr 1. r )r μ ], 3 1 and the force between two such particles having a diameter d and interparticle spacing r depends on the strength of the magnetic field B1 at the location of particle 2 (with magnetic moment 2 ) through the relation: F 1,2 = (μ 2. B 1 ), which is always proportional to μ 1μ 2, so that F~ M 0 2 d 6 r 4 This equation shows that the coupling force between two particles depends on the particle diameter to the power six! Thus, there is a very strong size dependence, which has been supported by experiments which have shown that monodisperse ferrofluids with a 10 nm particle diameter generally exhibit no measurable interaction effects. Furthermore, this strong size dependence explains the extremely strong magnetoviscous effect in magneto-rheological (MR) fluids, since their particles have diameters in the micrometer range. Such micron-sized particles have a much stronger coupling force which therefore leads to the formation of robust particle chains in the presence of a magnetic field. Thus, for more concentrated fluids, as r decreases, the interaction force might not be negligible. Another way that researchers have increased the coupling force (and thus promoted the formation of particle chains in fluids with relatively small particles) is to use cobalt nanoparticles, rather than magnetite, since their magnetization is higher. Researchers have also found that while commercial ferrofluids are quite stable, they often have a significant particle size distribution [55]. According to the equation above, if a ferrofluid contains even a small fraction of particles that are 30 nm (or even 20 nm) in diameter, then the interaction force can be three orders of magnitude higher, which may support the formation of these particle chains [56]. It should also be noted that the thickness of the surfactant layer can also effectively increase the particle diameter as mentioned earlier. These small variations in the composition of the ferrofluid were predicted by others to have a significant effect on the magnetoviscosity property [57]. Our findings on surface-tension-driven magnetoviscous flows certainly support this idea of r 4. 26

38 particle chains forming in the fluid. When an external magnetic field is applied, these chains (i.e. magnetic dipoles) align themselves in the direction of the field and lead to the observed anisotropic viscosity. Moreover, the behavior of the fluid when these chains are oriented parallel to the overall flow direction is quite different from its behavior when the chains are oriented perpendicular. Thus, these chains seem to be the main cause of the behavior that we see, rather than the rotational viscosity model proposed by Shliomis, which was developed for dilute ferrofluid suspensions and was shown to work best at high shear rates where magnetic particle chains would be broken. The ferrofluid principally used in this work had a volume concentration of 5.8% (according to the supplier) and therefore may not be sufficiently dilute for explanation by the Shliomis model. It should also be noted that the droplet speeds observed in this work were relatively small (i.e. < 3 cm/s); thus, only modest shear rates are expected. Figure 2.14 shows the position of the fluid droplet front as a function of the square root of the elapsed time. Typically, during the early stages of capillary wetting, droplet motion follows the Washburn equation [58] such that r cos x 2 where r is the effective capillary radius, is the contact angle, is the surface tension of the fluid, and is the dynamic viscosity. According to the Washburn equation, a linear behavior should be observed at the onset of droplet motion since the position is proportional to the square root of the time. Good agreement is seen in the figure, with a straight line showing agreement with the Washburn equation for approximately the first second of droplet motion. After this initial period (so-called inertial regime), droplet spreading slows due to viscous effects, and the dynamics of the spreading are limited by viscosity, not inertia. 1/ 2 t 1/ 2 27

39 Wedge 1 Wedge 4 Fig. 2.14: Variation of the position of the fluid droplet front with the square root of the elapsed time. The linear dependence that is initially observed for the first second of the droplet motion is in agreement with the Washburn prediction. 28

40 Chapter 3: Radial Gradient 3.1 Experimental Methodology In this section, the method that was used to make the radial surface tension gradient samples will be discussed in detail along with the experimental setup, and the software that was used to collect and analyze the data Surface Preparation Circular micro-channels having a variable width and a depth of 100µm were laser-etched into a copper plate to form several circular test regions each mm in diameter. The width of the microchannels themselves is 25 µm with a variable spacing between them. This variable spacing in turn affects the local roughness of the surface and its resulting wettability (i.e. hydrophilic vs. hydrophobic). The surface is hydrophobic where the microchannels are spaced closely together, and is more hydrophilic where they are spaced farther apart. Thus, this variable spacing creates the surface tension gradient necessary to facilitate the motion of liquid. Using the methodology shown in Sommers et al. (2013), the gradient term dr/dx was calculated to determine appropriate spacing values between channels. Copper was chosen as a test sample because it is naturally hydrophilic, and it has been used in many heat and mass transfer applications such as HVAC&R systems. The laser etching was performed by the Mound Laser and Photonics Center, a company based in Dayton, Ohio using a 355nm YVO4 laser system [see Fig. 3.1]. Before etching, the sample was thoroughly cleaned with acetone and isopropyl alcohol and dried using a stream of nitrogen gas. 29

41 Fig. 3.1: Radial gradient surface and zoom out image of outer section of circle Surface Coating The sample was made hydrophobic by immersing the plate in a 0.1M heptadecafluoro- 1-decanethiol (HDFT) solution for 6 minutes and followed by immersion in dimethylchloride for 20 sec. This process results in a self-assembled monolayer (SAM) that selectively grows on the copper making it hydrophobic (even super-hydrophobic). Alconox cleaning is performed to reenergize the surface after the HDFT coating wears off after several days. In our case, the static contact angle at the center and outer edge of the circle differed by approximately 55. This difference between the trailing and leading contact angle creates the surface tension force which ultimately causes the droplet to move spontaneously on the surface. The contact angle at the center and outer edge were 95 and 150 respectively which can be seen in Fig Fig. 3.2: Difference in contact angle between the outer edge (hydrophobic) and the center (hydrophilic) for one of those gradient circles. 30

42 3.1.3 Experimental Setup Figure 3.3 shows the experimental setup used for this work. A 14 MP Pentax camera with a wide-angle 5 optical zoom lens ( mm equivalent) was used to take both the still images and videos of the water droplets on the radial gradient circles. The camera was capable of capturing video at a rate of 30 frames per second. For an experiment, the camera was either placed on the top of the camera holder over top of the sample or next to the sample to get side images of droplets as a means of determining the contact angle. The droplets are injected on the surface from above with the help of a micropipette. Camera Camera holder Sample Sample holder Fig. 3.3: Experimental setup showing the camera placed over top of the sample The range of the injected droplet we used was 2-38µl. To begin an experiment, the camera was positioned just above the sample, to record the videos. Droplets were generally dispensed along the 31

43 outer edge of the circle not touching the boundary. The position of the droplet from the outer edge was also varied to determine the relationship between the initial placement (i.e. droplet position) and the droplet travelling distance and velocity. Different droplet volumes were also used to see how volume affected those relationships and parameters. Next, Free Studio software was used to splice the videos into still images showing the time elapsed motion of the droplet. These images were then used to calculate the average velocity, instantaneous velocity, position and travel distance of the dispensed droplet along the radial gradient. Kappa Image Base software was used to measure the initial position, velocity and travel distance of the droplet using the pixel counting method. Figure 3.4 shows the location of injected droplets on the radial gradient. Three different locations within the circular gradient were chosen to help facilitate the data collection process. We collected the data from three different locations called location 1 ( ), location 2 ( ), location 3 ( ) and then analyzed these locations both separately and combined. Fig. 3.4: Location of injected droplets on the circular radial gradient 32

44 3.2 Results and Discussion Injected Droplet Analysis In this work, the surface was fabricated with microscopic topography and then further modified with chemical treatment to make a super-hydrophobic, self-cleaning condenser surface. Although condensation experiments were not performed, the physics behind these experiments were closely reproduced by injecting individual water droplets on those sample surfaces using a micro-syringe. In this way, we have studied the spontaneous motion induced by the gradient and how the droplet travel distance depends on the volume and position within the gradient. Various droplet volumes were studied including 5µL, 10µL, 27µL and 38µL volume of water droplet. Figure 3.5 shows spliced images of the starting and final position of a 5µL droplet at location 1 in one of the circular radial gradient. The first image in Fig. 3.5 shows the initial placement of the water droplet. The initial position of the droplet was determined by measuring d1 (i.e. distance to the trailing edge of the droplet from the boundary of the circular radial gradient), d2 (i.e. distance to the leading edge of the droplet from the boundary of the circular radial gradient) and then taking the average of both. Thus, the initial position would be the center of the droplet if the droplet was spherical in shape. Alternatively, the initial position could be calculated by solving for the diameter of the droplet (assuming the droplet to be spherical) and then adding the radius of the droplet to d1 described above. This later process however is not as accurate in our case because the gradient distorts the shape of droplet from being spherical [59]. Because the trailing edge will be more hydrophobic than the leading edge, the droplet possesses an elongated shape. 33

45 Starting position of 5µL droplet Final position of 5µL droplet Fig. 3.5: Spliced images of the starting and final position of a 5µL water droplet on a circular region of the radial gradient In Fig. 3.5, the second image is the final position of the droplet after it moved from its initial position of placement. The droplet traveled within a 1/10 th of a second to the final position. The final position was calculated by measuring the distance from d2 to the leading edge of the droplet at its final position. Figure 3.6, Figure 3.7, and Figure 3.8 contain spliced images of a 10µL, 27 µl and 38µL droplet, respectively as shown below. Starting position of 10µL droplet Final position of 10µL droplet Fig. 3.6: Spliced images of starting and final position of 10µL water droplet on a circular region of the radial gradient 34

46 Starting position of 27µL droplet Final position of 27µL droplet Fig. 3.7: Spliced images of starting and final position of 27µL water droplet on a circular region of the radial gradient Starting position of 38µL droplet Final position of 38µL droplet Fig. 3.8: Spliced images of starting and final position of 38µL water droplet on a circular region of the radial gradient 35

47 3.2.2 Force Experienced by Droplet on a Gradient The net force experienced by a droplet when placed on a horizontal homogeneous surface is zero because the surface tension force acting in any one direction is canceled out by another. But when that same droplet sits on a gradient surface, the net surface tension force is not zero because of the differing contributions from opposite sides of the droplet. Fig. 3.9: Schematic of a droplet on a (a) homogeneous surface, and (b) a surface with an underlying gradient. [5] Consequently, the droplet experiences a net surface tension gradient force that tries to move the droplet in the direction of the radial gradient [5]. When the droplet sits on a gradient, the droplet deforms [see Fig. 3.9]. Now let us consider the situation where the contact angle of the droplet varies from one end to the other due to the presence of a gradient as shown in [5] such that, cos θ (x) = a 1 x 3 + a 2 x 2 + a 3 x + a 4 (1) where cos θ (0) = cosθ max. (2) cos θ (D) = cosθ min. (3) d(cos θ) dx d(cos θ) dx (x = 0) = Ѱ... (4) (x = D) = Ѱ... (5) Equations 4 and 5 are based on the assumption of a linear gradient with a constant rate of change. Using these boundary conditions, we can solve for the constants a 1, a 2, a 3, a 4 and find that cosθ(x) = 2[(cosθ min cosθ max ) ѰD]x 3 D 3 + 3[(cosθ min cosθ max ) ѰD] x 2 D 2 + Ѱx + cosθ max... (6) 36

48 The surface tension force associated with the droplet deformation can be calculated using the equation: π F s = γd cos θ 0 cos d.. (7) π F s = γd (a 1 x 3 + a 2 x 2 + a 3 x + a 4 ) 0 cos d.. (8) Substituing x = R(1 cos ) into the expression and integrating yields the following as shown in [5] F s = γd [ 15π 8 a 1 ( D 3 2 ) πa 2 ( D 2 2 ) πa 3 2 (D )]. (9) 2 F s = γd [ 9π (cosθ 32 min cosθ max ) πd Ѱ]. (10) 32 If the variation of the contact angle is assumed to be linear around the base of the droplet, then Ѱ = ( cosθ min cosθ max ). In this case, the surface tension force equation simplifies to, D F s = 8π 32 γd[cosθ min cosθ max ]. (11) Thus, for the droplet to move, it must overcome the contact angle hystereris (i.e., cosθ min cosθ max ). According to El Sherbini [60], the surface tension force on a homogenous surface is represented as, F s = 24 x 3 γd [cosθ rec cosθ adv ]. (12) Thus, when the droplet is moving, θ max = θ adv and θ min = θ rec. In this case, equations 11 and 12 above would nearly give the same value. In our case, however, the variation of the spacing of the micro-channels is not completely linear so the expression obtained using equation 11 needs to be corrected slightly to account for this difference. 37

49 Figure 3.11 shows plots of the droplet starting position versus travel distance when the droplet was injected at location 1 ( ). When the droplets were placed close to the edge of the circle, it travels a greater distance than placing away from the outer boundary of radial gradient. This is best explained by the effect of the radial gradient on the surface. Since the spacing of the micro-channels on the sample surface was not varied in a completely linear fashion, the force experienced by the droplet placed on the outer boundary is slightly greater than locations farther away from the boundary. Figure 3.10 shows a symbolic representation of the force experienced by a droplet when placed on the circular radial gradient. The red circles drawn on Fig represent the radial microchannels made on the sample surface. The density of these micro-channels determine the wettability of the sample surface. (Note: The hydrophobicity decreases as you move from the outer boundary towards the center because the density of the micro-channels decreases.) Fig. 3.10: Symbolic representation of net force experienced by water droplet when placed on the outer edge of the gradient boundary 38

50 Travel distance (mm) Travel distance (mm) Travel distance (mm) Travel distance (mm) µL 27µL Starting Position (mm) Starting Position (mm) µL 5µL Starting Position (mm) Starting Position (mm) Fig. 3.11: Plot of position vs. travel distance for 38µL, 27µL, 10µL and 5µL water droplets at location 1 ( ) As might be expected, the travel distance also depended on the volume of the droplet. Figure 3.12 shows the plots of the droplet starting position versus travel distance for 38µL, 27µL, 10µL and 5µL respectively at location 2 ( ). It is seen that the 38µL droplet travels farther than either the 27µL, 10µL or 5µL droplets. Volume is thus the key factor in determining the travel distance covered by the droplet. A maximum travel distance of approximately 4 mm was observed with a 38µL droplet and continuously decreased as the droplet volume decreased. A maximum travel distance of approximately 2 mm was measured with the 5µL droplet. The travel distance is not linear with the position because of the varying wettability along the radial gradient. Figure 3.13 shows the plots of the starting position versus travel distance for the 38µL, 27µL, 10µL and 5µL water droplets at location 3 ( ). 39

51 Travel distance (mm) Travel distance (mm) Travel distance (mm) Travel distance (mm) Travel distance (mm) Travel distance (mm) µl 5 27µl Starting Position (mm) Starting Position (mm) µl 5 4 5µl Starting Position (mm) Starting Position (mm) Fig. 3.12: Plot of position vs travel distance for 38µl, 27µl, 10µl and 5µl volume of water droplets at location 2 ( ) µl 27µl Starting Position (mm) Starting Position (mm) 40

52 Travel distance (mm) Travel distance (mm) Travel distance (mm) Travel distance (mm) µl 5µl Starting Position (mm) Starting Position (mm) Fig 3.13: Plot of position vs travel distance for 38µl, 27µl, 10µl and 5µl volume of water droplets at location 3 ( ) These plots are all very similar in trend with respect to one another. These plots also clearly shows the role of the gradient in facilitating the motion of individual water droplets down the gradient. 32µl 7µl Starting Position (mm) Starting Position (mm) Fig. 3.14: Plot of position vs travel distance for 32µl and 7µl volume of water droplets 41

53 Travel distance (mm) Starting Position (mm) Fig. 3.15: Combined plot of position vs travel distance for 32µl and 7µl volume of water droplets Figures 3.14 and 3.15 contain the plots of droplet starting position versus travel distance for 32µl and 7µl water droplets first shown separately and then combined. It can be seen here that the behavior of these plots is not linear, but rather parabolic in nature. Droplet velocity can be determined by dividing the travel distance by the time it takes for the droplet to move from the initial to the final position. Chaudhary [61] and his group calculated the droplet velocity using the equation V = γ lv η, where γlv is the interfacial surface tension and η is the viscosity of the liquid droplet. In this work, we calculated the droplet velocity using simple kinematics and noticed that the droplet velocity was larger for bigger droplets than smaller ones. Instantaneous droplet velocities of 30cm/sec - 70cm/sec were observed depending on the droplet volume which is comparable with speed about 100cm/sec of fused drops moving towards the hydrophilic region found by Chaudhary [61]. Figure 3.16 shows the droplet diameter versus the travel distance for different water droplet volumes. Each plot has the same initial starting position. The diameter of the droplet was calculated knowing the droplet volume using the equation shown below which assumes a wetting regime with a spherical droplet shape [62]. The diameter of the droplet in wetting regime calculated using equation 13 is shown in table 4. 42

54 Travel distance (mm) Travel distance (mm) Table 2: list of diameters having different volumes in wetting regime Volume 5µl 10µl 27µl 38µl Diameter (regular 2.12mm 2.57mm 3.72mm 4.17mm spherical droplet) Diameter (In wetting 2.18mm 2.75mm 3.83mm 4.32mm regime) v = π 3 a3 2 3cosθ m+cos 3 θ m sin 3 θ m. (13) where, a = radius of the droplet and θ m = average contact angle of the advancing and receding angles. The nature of these plots is linear. Since the base circumference of the droplet is in contact with the sample surface, only the area of the droplet that sits on the gradient surface contributes to the net force experienced by the water droplet. Thus, integrating over the diameter of the droplet yields the net force experienced by the droplet. Larger droplets will have a larger contact area and hence experience a larger force, and consequently travel a greater distance as compared with smaller droplets. This linear relationship between the diameter and travel distance can be seen in Fig Diameter (mm) Diameter (mm) 43

55 Travel distance (mm) Diameter (mm) Fig. 3.16: Plot of diameter vs travel distance of different volume of droplets with same starting position Spray Test Analysis Spray tests were also performed in both a horizontal and vertical orientation. The control and management of water droplets is essential in applications involving heat and mass transfer such as HVAC&R systems. Droplets formed on the surface by condensation should be managed in a proper way to increase the efficiency of the heat exchangers used in these systems. In other work, liquid droplets in contact with a surface have been made to move spontaneously by using a surface energy gradient, chemical gradient, thermal gradient, and/or due to external excitation via sound waves [63, 64, 65]. In our case, a radial gradient surface was used and spray tests were performed to study how effective the radial gradient was in manipulating and directing water droplets to preferred locations on the surface Finding Average Volume Distribution Spray tests were first performed to determine the average volume distribution of water droplets on a bare copper surface. This was done at three different heights above the surface namely, 25 cm, 20 cm and 10 cm. These experiments were all performed under the same environmental conditions with the same equipment. The volume distribution was calculated by counting the number of water droplets and the weight of the sprayed water on the sample surface. The weight of the sprayed water was measured immediately after spraying to reduce water loss due to evaporation. Images were taken and then the number of droplets appearing in those images was 44

56 counted. Dividing the weight of the sprayed water by the number of droplets gave an approximate average weight for a single drop. The average droplet volume was then determined by dividing this average weight by the density of the water. As shown in Fig. 3.17, the volume distribution increased as the spraying distance was decreased and vice versa. Fig 3.17: Droplet distribution while doing spray tests from varying height In other words, on average, larger droplets were formed as the spraying distance was decreased, and thus there was a greater distribution of droplet sizes at these smaller heights due to the coalescence of droplets on the surface. The range of the average calculated droplet volume for height 25cm was 0.04µL and for 10cm was 0.1 µl. These spray tests were important because knowing the average droplet volume distribution on an actual sample can facilitate easier analysis in the future Horizontal Spray Test Figure 3.18 shows images which capture the coalescence of water droplets during a spray test when the sample was placed horizontally. The average volume distribution for the droplets dispensed by the sprayer was µl range. In the first images, small droplets can be seen landing on the sample surface and moving a short distance. Given the time scales involved, this 45

57 movement was difficult to capture using the Pentax camera. It should also be pointed out, that in order for a droplet to move, the critical droplet diameter needs to be greater than the capillary length scale. Thus, the droplets need to be situated on at least two micro-channels to have a motion down the gradient [66]. The critical diameter is determined by the radial length of the micro-patterns. As the droplet grows in size, its volume increases and thus the droplet moves a little farther and eventually coalesces with other droplets to form a bigger droplet as shown in the last image of Fig Coalescence occurs due to both local spreading and radial spreading. Local coalescence occurs when two or more stationary growing droplets merge with neighboring droplets resulting in the formation of a single bigger droplet. The droplet then moves if it has a diameter greater than critical droplet diameter along the wettability gradient. In this way, droplets go through a series of local coalescence events until the diameter exceeds the critical diameter. In radial spreading, droplets moves radially merging with other droplets on the way to the collection point. For example, other researchers [33] have done experiments on surfaces having a hole at the center, such that droplets coalesced and moved to the center towards this collection point. On a real condenser surface, the droplets were initially in the Wenzel state and then later transitioned to the Cassie state as the droplets grew in size and moved along these micro-patterned regions toward the one end of the wettability gradient [66]. Fig. 3.18: Snapshot images of the coalescence of water droplets during spray testing while the sample was placed horizontally 46

58 3.2.6 Vertical Spray Test Figure 3.19 shows images of the coalescence process of individual water droplets when the sample was placed in a vertical orientation. As can be seen in the figure, the water droplets kept getting bigger in size as they coalesced with each other to form larger droplets. Of course, small droplets possess insufficient weight to drain under the influence of gravity. Here, the surface tension force dominates gravity in the microscale range. As the droplet gets bigger, however, the gravitational force becomes larger enough to pull the droplet down along the hydrophilic region of the gradient. Manipulating droplets plays a crucial role in enhancing the efficiency of heat exchangers. Initially large no. of small droplets land on the sample surface and becomes a bigger droplets as spraying was done over the sample. Local spreading and radial spreading is responsible for driving the droplets towards the center of the gradient. Once a large enough droplet is formed in the hydrophilic center, it is drained out from this section of the circular gradient as shown in last image in Fig Fig. 3.19: Snapshot images of the coalescence of water droplets during spray testing while the sample was oriented vertically 47

59 Chapter 4: The Effect of Surface Roughness on Wettability 4.1 Experimental Methodology In this section, the role of surface roughness in affecting surface wettability change was explored from an educational perspective. A simple experiment was devised that could be incorporated into a teaching laboratory where a copper surface was divided into four quadrants each with a different surface roughness. The surface was then either kept hydrophilic or coated with a self-assembled monolayer (SAM) that rendered it hydrophobic. This chapter outlines that experiment, the surface preparation, and the contact angle measurements that were performed Surface Preparation Two copper plates with dimensions 2 in 2 in 0.1 in (50.8 mm 50.8 mm 2.54 mm) were used to study how the contact angle changes with the different levels of surface roughness in both hydrophobic and hydrophilic samples. To prepare the surface, the mirror-finish copper surface was first cleaned thoroughly in Alconox immediately after peeling off the protective coating. The surface was gently rubbed with a Kimwipe during the Alconox soaking followed a rigorous rinse in water and then by rinsing in acetone, isopropyl alcohol (IPA) and deionized water separately. Next, pressurized sand (i.e. sandblasting) was used to introduce micro-scale roughness on half of the surface of each copper block, while the other half was protected by covering it with a metal sheet. Afterwards, copper block was rotated by 90 degrees and half of it was immersed in a silver nitrate solution for 2 minutes to create a nano-roughened silver surface on the copper. This process created four different quarters on the top surface of Cu: The first quarter (the baseline surface), seen on the lower left of Fig. 1, has the cleaned mirror-finish copper surface with the factory finish of the surface intact. The upper left quadrant has only been exposed to sand blasting and thus shows the micro-scale roughness. The top-right quadrant was exposed to both the sand blasting and the silver nitrate reaction, acquiring both micro-scale and nano-scale roughness. Finally, the lower-right quadrant was only exposed to the silver nitrate wet reaction that created nano-scale roughness on its surface. The silver nitrate reacts with the Cu surface according to [67] Cu 0 + 2AgNO 3(aq) Cu(NO) 3 2(aq) + 2Ag0 48

60 This reaction produces a very rough silver-coated surface on the Cu block. The resulting rough surface appears as a black shade due to the nano-roughened silver which is deposited on the copper. The surface is then rinsed in deionized water for 20 seconds and dried. It should be emphasized that the sandblasting technique creates a surface roughness with features as large as the sand grains, which are typically tens of micrometers in diameter. In contrast, the chemical reaction shown above creates a nano-scale roughness on the surface. The aim of studying the roughness effect was to examine its impact on the behavior of water droplets on these different quadrants of the surface. Our hypothesis here is that the sand blasting will increase the roughness parameter (r) slightly, while the nanoscale roughness will enhance (r) more and the combined roughness will increase that parameter significantly. These four values of roughness will allow us to qualitatively and quantitatively study the effect of surface roughness on the contact angles of water droplets for both hydrophilic and hydrophobic cases, depending on the SAM layer growth. By repeating this process twice, one sample could be created for the experiment which was hydrophilic. The second sample was immersed in 0.1M heptadecafluoro-1-decanethiol (HDFT) solution for 6 minutes, followed by 20 seconds of immersion in methylene chloride to make it hydrophobic. This process (as explained previously) creates a self-assembled monolayer on the copper which renders it hydrophobic. The final surface can be seen in Fig Micro-roughness Nano + micro-roughness (Baseline) Nano-roughness Fig. 4.1: Sample showing the four quadrants each with a different roughness 49

61 4.1.2 Experimental Setup After the samples were prepared, we took images and videos of droplets of the water on both the hydrophilic and hydrophobic Cu blocks. A 14 MP Pentax camera with a wide-angle 5 optical zoom lens ( mm equivalent) was used to take both the still images and videos of the water droplets. The camera was capable of capturing video at a rate of 30 frames per second. We took images from the side view to measure the contact angle on those regions of surface. 38µl droplets injected from a micropipette were used to measure the contact angles. Free Studio software was then used to splice the videos into a sequence of still images. The still and spliced images were then used to measure the contact angles of water droplets on those respective regions Contact Angle Measurement A Ramé-Hart precision goniometer [see Fig. 4.2] was used to measure the static contact angles of the different quadrants of the surfaces examined in this work. After samples were mounted on the stage, droplets were placed on the surface using a high-precision micro-syringe. This goniometer is connected to software called DROPimage Standard, which allows the determination of the contact angles using a high-resolution CCD camera. Droplets of 15 l in size were measured at room temperature. The average uncertainty in the measured contact angles was ±2. The contact angle is a measure of the wettability of the surface. It is the angle where the air/gas interface meets the surface/solid interface. A water droplet on a hydrophobic surface has low surface energy where its contact area is minimized while the contact area is maximized on the Fig. 4.2: Ramé-Hart precision goniometer 50

62 hydrophilic surfaces. In addition to the static contact angle, the goniometer can measure the advancing and receding angles by either adding or removing water to the droplet gradually. Adding water increases the contact angle until the maximum volume is achieved, which gives the largest possible contact angle before the contact line of the droplet moves. On the other hand, the receding angle is the opposite where it is measured by removing water from the droplet until the minimum volume is obtained. It is important in both advancing and receding situations to not change the interface between the liquid and the surface. The difference between the advancing and receding angles is called contact angle hysteresis [68]. The contact angle hysteresis is used to quantify contamination, surface chemical heterogeneity, and the effect of surface treatments. 4.2 Results and Discussion Effect of Sandpaper Rubbing Sandpaper is a type of paper which has an abrasive material on one surface. It has been used to make the surface smoother or rougher whatever you want. The common abrasive material used in common grits is aluminum oxide. The particle size of abrasive materials embedded in a sandpaper is referred to as the grit size. Generally, the higher grit number indicates a smoother sand paper and a lower the grit number means a rougher sand paper, or a paper with larger abrasive particles size [see Fig. 4.3]. The average particle diameter of grit 50 sand paper is 342 µm. [69] 51

63 Fig. 4.3: Different grits of sand papers In our experiment, we first rubbed the naturally hydrophilic copper with sand paper then checked the wettability of surface. The wettability changes due to rubbing because it creates a micro roughness on a surface and exposes fresher and cleaner Cu. From the Wenzel s equation, as the roughness increases the hydrophilicity/hydrophobicity increases too. Hydrophilic copper becomes hydrophobic when rubbed with sand paper of 50 grit and then immersed in HDFT. We observed the mean contact angle of when treated with HDFT after rubbing. Similarly hydrophilic copper becomes more hydrophilic when rubbing by sand paper. But creating a nanoroughness on a surface solely with sand paper was not achieved. We tried to create nano-roughness using sand paper only by rubbing with smoother grits on top of the surface which was already rubbed by coarse grits. It did not seem to create any measurable additional roughness and it might even have destroyed the initial roughness created by earlier rubbing with the coarse sand paper. When we rubbed on top of surfaces that were already rubbed by the more coarse sand paper, the force that we applied may have destroyed the existing roughness and hence decreased the overall roughness. We measured the contact angles on these surfaces and found results that contradicted with what we had hypothesized initially. So, we developed another way to create a combination of micro and nano-roughness on a single block of copper surface. 52

64 4.2.2 Effect of Sandblasting Sandblasting is a process of forcibly propelling a stream of micron sized sand particles against a surface under a high pressure to make rough surface. We did sand blasting on two copper surfaces on half of the plates covering another half with protective plates. Sand blasting creates micro roughness on a copper surface and enhances the surface s hydrophilic or hydrophobic behavior depending on the wettability of the surface. A sandblasted sample is shown below in Fig Baseline Sandblasted Fig. 4.4: Sand blasted copper surface Contact Angle Analysis of the Hydrophilic Sample Contact angles were first approximated by visually inspecting the images on respective quadrants. Each quadrant has a unique roughness factor due to the different kind of roughness created on those quadrants. Table 2 lists the four quadrants with the respective roughness-creating process on them along with the corresponding contact angles and the calculated roughness factor on each quadrant using the Wenzel model. The contact angles were measured precisely using a Ramé-Hart precision goniometer. 53

65 Table 2: List of quadrants with respective roughness, average contact angle and roughness factor Quadrants Q1 Q2 Q3 Q4 Roughness scale Contact angle (θ c ) Roughness factor (r) Baseline (factory finish) Micro-roughness (sand blasting) Nano-roughness (AgNO3) Micro + Nanoroughness (sandblasting + AgNO3) The contact angles listed above are the mean of at least 5 sets of measurement. Fig. 4.5 shows pictures of representative water droplets placed on each of the five quadrants. The contact angle decreases as we move from Q1 to Q4. Since the sample is hydrophilic, the added roughness created on these surfaces enhances the hydrophilicity, which is in agreement with the Wenzel model. Q2 quadrant has micro-roughness created due to sand blasting and the resulting contact angle on that quadrant is 69.5 which is less than the baseline contact angle of The roughness factor (r) was calculated using Wenzel s equation [see equation 6] and the value of r on quadrant Q2 is We assumed the value of r for Q1 to be 1.The value of the roughness factor was calculated solely using Wenzel equation, cosθ w = rcosθ c. The roughness factor might be slightly different if a Cassie-Baxter or a mixed state of Wenzel and Cassie-Baxter model was assumed. Q3 only has nano-roughness on its surface created due to the reaction of copper with the AgNO3 solution. Silver nano-sized particles adhere to the copper surface forming nano-roughness. The contact angle on Q3 was found to be 37.3 which gives a roughness factor (r) of Moreover, due to the sand blasting and chemical reaction, Q4 quadrant is even rougher than the other three quadrants because of the presence of both micro and nano-roughness combined. The contact angle on this quadrant is 24.6 with a roughness factor We see that contact angle keeps decreasing as we move from Q1 to Q4 as conversely the roughness factor keep increasing. These results clearly show that silver nitrate treatment creates a significantly larger roughness factor (i.e. effective surface area of the Cu) than the sand-blaseted surface, which is in turn significantly rougher than the base line. 54

66 Quadrant 1 Quadrant 2 Quadrant 3 Quadrant 4 Fig. 4.5: Images of water droplets on the different quadrants of the hydrophilic sample Contact Angle Analysis of the Hydrophobic Surfaces The contact angles were again first approximated by visually inspecting the images on respective quadrants. Each quadrant has a unique roughness factor due to the different surface treatment and size of the roughness grains created on those quadrants. Table 3 lists the four quadrants with the respective roughness mechanism used to create them along with the respective contact angles and the roughness factor on each quadrant. Contact angles were measured precisely using Ramé-Hart precision goniometer. 55

67 Table 3: List of quadrants with respective roughness, contact angle and roughness factor Quadrants Q1 Q2 Q3 Q4 Roughness scale (mechanism) Baseline (factory finish) Micro-roughness (sand blasting) Nano-roughness (AgNO3) Micro + Nanoroughness (sandblasting + AgNO3) Contact angle (θ c ) Roughness factor (r) The contact angles listed above are the mean of at least 5 sets of measurement. Images of water droplets on each quadrant are shown in Fig The contact angle increases as we move from Q1 to Q4. Since the sample is hydrophobic, roughness created on those surfaces enhances the hydrophobicity, according to the Wenzel equation. Q2 quadrant has micro-roughness created due to sand blasting and resulting contact angle on that quadrant is which is greater than the baseline contact angle of Furthermore, the roughness factor (r) was also calculated using the Wenzel s equation and the value on Q2 quadrant is 3.67 whereas the value of r for Q1 quadrant is supposed to be 1. Q3 quadrant only has nano-roughness on its surface created due to the reaction of the copper with the AgNO3 solution. During this reaction, silver particles get deposited on the copper surface forming the nano-roughness. The contact angle on Q3 is having a roughness factor (r) of Moreover, due to the sandblasting and chemical reaction, Q4 quadrant is rougher than the others because of presence of both micro and nano-roughness combined. The contact angle on this quadrant is giving a roughness factor of In conclusion, we see that both the static contact angle and the roughness factor increase as we move from Q1 to Q4 on the surface. A weakly hydrophilic surface has a contact angle just less than 90 degrees and the cosine of that angle is small and positive. According to the Wenzel equation, introducing roughness on such a surface will make it more hydrophilic since the cosine of the new contact angle is equal to the roughness parameter multiplied by the baseline (weakly hydrophilic) contact angle. This gives a new contact angle with a larger value of its cosine, but still a positive sign, which means that the contact angle will get farther away from 90 o, or will get smaller. The same argument applies to the hydrophobic surfaces. 56

68 Quadrant 1 Quadrant 2 Quadrant 3 Quadrant 4 Fig. 4.6: Images of water droplets on the different quadrants of the hydrophobic sample Finally, we notice that the roughness factors are higher for the hydrophilic surfaces than the identical surfaces that were converted to hydrophobic through introducing the water-repelling HDFT film. A plausible reason for this discrepancy is that the HDFT might accumulate around small particles and in small voids on the surface, thus reducing its overall roughness or that the HDFT coating does not cover the surface completely. Another possible cause for this difference (which is larger for the surfaces involving the nano-scale roughness) is that the silver nitrate treatment changes the surface from Cu to Ag, thus the contact angle can also be different. 57