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1 Proceedings of ICMM2005 3rd International Conference on Microchannels and Minichannels June 13-15, 2005, Toronto, Ontario, Canada Paper No. ICMM DIRECT MEASUREMENTS OF VISCOELASTIC FLOWS IN MICRO-CONTRACTIONS Shelly Gulati Joint Graduate Group in Bioengineering University of California, San Francisco and University of California, Berkeley Susan J. Muller Dept. of Chemical Engineering University of California, Berkeley Dorian Liepmann Dept. of Bioengineering University of California, Berkeley ABSTRACT Direct measurement techniques are employed to quantify the kinematics of DNA flows in micro-contraction devices. Flow through micro-contractions subjects the fluid to large spatial gradients in velocity, thereby eliciting viscoelastic effects. Additionally, in this microfluidic flow environment, the fully extended length of the macromolecule L will approach the characteristic length scale of the channel geometry h. This is a unique flow environment that is not yet well understood. Knowledge of the fundamental physics that govern this flow regime will have a profound impact on optimization of lab-ona-chip systems incorporating macromolecular flows. This study investigates the flow of semi-dilute λ-dna solutions in a 2:1 micro-contraction where L/h ~ Video microscopy and streak images of semi-dilute DNA flows reveal large vortex regions in the corners of the contraction, which are indicative of strong elastic behavior. Velocity fields constructed using Digital Particle Image Velocimetry (DPIV) demonstrate the first use of this tool for obtaining velocity measurements of viscoelastic flows in microfluidic systems. INTRODUCTION The micro-flow of large molecules such as DNA or proteins presents a number of challenges absent in macro-scale flows. Surface-to-volume ratios are extremely large in microchannels increasing the importance of interactions with the walls. Additionally, the characteristic lengths of the macromolecules approach those of the fluid channels and the small characteristic length scale for flow leads to increased importance of elasticity and viscous forces relative to macroscale flows. The effects of flow on the conformation of DNA have been shown experimentally [1,2]. DNA molecules stretch out in accelerating flow regions and recoil in decelerating flow or stagnant regions [3]. A deeper understanding of the fundamental physics of biopolymer flow in the micro-regime will enable optimization of future lab-on-a-chip device designs, such as advanced biosensors using single molecule identification. This investigation explores flows in microscale abrupt contraction devices. Abrupt contractions serve as appropriate test structures because they are canonical microfluidic components and a benchmark problem in viscoelastic fluid dynamics. In this flow environment, the test fluid is forced to accelerate spatially as the fluid enters the smaller downstream channel. Viscoelastic flow through macroscale contractions have been observed experimentally and simulated numerically [4]. Some recent work used flow visualization for characterizing flows of dilute and semi-dilute polyethylene oxide (PEO) solutions in micro-contraction-expansion systems [5]. This investigation focuses on the flow of semi-dilute concentrations of DNA in 2:1 micro-contractions. The molecular contour length L approaches the device length scale 1 Copyright 2005 by ASME

2 h, defined here as the downstream channel half-width; L/h ~ 0.32 for these flows. λ-dna serves as the biopolymer model for this investigation because of its direct use in lab-on-a-chip applications, the extensive characterization of its relaxation time and dynamical behavior in purely extensional and purely shear flows, and the ease with which it can be fluorescently labeled. Direct measurement techniques are used to determine the effects of micro-contraction flow on the conformation of DNA, and the reciprocal effects of DNA conformation on flow. Streak images and video microscopy are used to characterize flow behavior of water and a semi-dilute DNA solution in the 2:1 micro-contraction. The size of the upstream corner vortices is determined for varying flow conditions. Digital Particle Image Velocimetry (DPIV) is used to quantify the velocity fields for these flows, including in the corner vortices. EXPERIMENT Device Design and Fabrication All microdevices are fabricated at the UC Berkeley Microfabrication Laboratory using conventional silicon microfabrication methods. The advantages of using silicon microfabrication to create the devices include (1) excellent control of device design and dimensions, (2) compatibility with a range of biologically important fluids, and (3) bonding to glass allows optical access, and (4) stability and rigidity of the device dimensions over time and under varying pressure. Features were patterned using standard MEMS lithography. The test channels and through-holes for fluidic inlets and outlets were etched in a 500 µm thick, p-type <110> single crystal silicon wafer using a Surface Technology Systems deep reactive ion etch (DRIE) system. The DRIE system employs a plasma etch alternating with a passivation step depositing a Teflon-like coating (Octafluorocyclobutane, C 4 F 8 ) to fabricate high aspect ratio features with vertical channel walls. Patterned etch masks of silicon dioxide and photoresist are used for the DRIE. A 500 µm thick Pyrex glass wafer is anodically bonded to the silicon at 450 C at 1000 V with a Karl-Suss SB6 bonder. Figure 1 is a schematic diagram of the micro-contraction test system. External components consisting of a glass syringe connected by Tygon flexible tubing (Cole-Parmer) complete the fluidic pathway. The tubing is affixed to the through-holes on the backside of the device using epoxy. Flow through the device is mechanically controlled using a syringe pump. Figure 2 is a diagram of the micro-contraction geometry. The 2:1 micro-contraction device has an upstream width (2H) of 200 µm, a downstream width (2h) of 100 µm, and depth (d) of 200 µm. The upstream and downstream channels are each 3 cm long. Fluid enters and exits the system through fabricated circular inlet and outlet reservoirs connected to the upstream and downstream channel of the micro-contraction device. Dimensional Analysis Viscoelastic flows are characterized by the dimensionless parameters, the Reynolds (Re) and Deborah (De) numbers, defined by the following, ρuh Re = (1) η λu De = λ & γ =, (2) h where η is the solution viscosity, ρ is the solution density, γ& is the shear rate, and h is the channel width. The average velocity u is calculated from the flow rate Q and the cross-sectional area of the downstream channel, u = Q/(2hd). Re compares the magnitude of inertial forces to viscous forces. De is a dimensionless ratio relating the time scale of the polymer relaxation λ to the time scale of the flow. Additionally, the Elasticity number (El) relates the De and Re, De El =, (3) Re and is constant for a given fluid and geometry. As noted by Rodd et al. [5], since El~1/h 2, microscale devices allow much higher El flows to be accessed than macroscale flows. The dimensionless vortex reattachment length is given by the following, L V χ = (5) 2h where the vortex length L V is the distance along the upstream channel wall between the boundary of the secondary flow vortex and the contraction plane. Figure 1. Schematic diagram of side and top view of microcontraction device. Figure 2. Diagram of micro-contraction geometry where H is the upstream half-width, h is the downstream half-width, and d is the depth. 2 Copyright 2005 by ASME

3 Fluid Rheology The biological macromolecule to be studied is λ-dna (New England Biolabs) with molecular weight 31.5 x 10 6 Daltons or 48,502 base pairs. The contour length or the fully extended length of this molecule is 16 µm with an equilibrium radius of gyration of 0.6 µm. This DNA was chosen for experimentation because the structure is well known and the dynamics of this molecule in pure shear and pure extensional flows have been carefully documented [1,2]. The DNA was diluted with 1X TAE buffer (40 mm Tris acetate and 1mM EDTA, ph 8.3). Rheological properties were determined using a Vilastic-3 Viscoelasticity Analyzer (Vilastic Scientific, Inc), a oscillatory flow capillary viscometer. The pressure drop and flow rate through a narrow capillary are measured over a range of frequencies and amplitudes. From these measurements, viscosities were determined using a high drive swept from 1 to 45 sec -1 at a frequency of 2 Hz. The relaxation time of the solution is calculated using the Rouse Model. The intrinsic viscosity [η] is 0.01 ml/µg determined using the method described in detail in Shrewsbury et al. [3]. The overlap concentration c* is the concentration where a coiled DNA molecule begins to overlap neighboring DNA molecules. The overlap concentration calculated from the intrinsic viscosity, c* = 1/[ η], is 100 µg/ml. The rheological properties for the test fluids are summarized in Table 1. Flow Visualization Studies characterizing viscoelastic flows through macroscale planar contractions provide a starting point for understanding viscoelastic flows through micro-contractions. For macroscale contraction flow, vortex enhancement, or the increase in the size of vortex length L V, was found to be dependant on the type of contraction, the contraction ratio, flow rate, and the rheological properties of the fluid [4]. For flow visualization, the fluid is seeded with 1.0 µm large orange fluorescent polystyrene tracer particles (FluoSpheres, Molecular Probes) with a peak absorbance at 540 nm and peak emission at 560 nm, which are neutrally buoyant in water. The volumetric flow rate is held constant using a syringe pump to drive the flow. Table 1. Rheological Properties at 23 C Relaxation Viscosity, Density, ρ c/c* time, λ (s) η (cp) (g/cm 3 ) Water µg/ml DNA Table 2. Experimental Operating Space Re De El c/c* Water µg/ml DNA Micro-contraction flow is observed using an epiflourescence microscope. Images were captured using a progressive scanning full frame shutter camera (Pulnix TM- 9701) with 1013 x 1000 pixel resolution at 30 frames/sec. Images were captured for flows of water and 4c* DNA over the range of operating conditions given in Table 2. Images were obtained at the midplane of the channel (100 µm from the top and bottom of the device). Streak images for these flows are found in Figure 3. Streak images indicate large vortices for flows of 4c* DNA. These large recirculation regions observed in the upstream corners of the contraction grow with increasing Reynolds (Re) and Deborah (De) numbers revealing strong elastic flow behavior. Streak images of flows of distilled water indicate small vortices, consistent with those observed in inelastic macroscale flows, which do not grow with Re. The vortex lengths L V were obtained by measuring the distance along the wall from the edge of the vortex boundary to the corner of the contraction in pixels for vortices on both sides of the centerline (the bottom and top corners in Figure 3). The length in pixels was then converted to a dimensional length scale (µm). Dimensionless vortex length χ was computed using equation (5). Figure 4 indicates the relationship between the dimensionless vortex length χ and Re for flows of water and 4c* DNA. As observed in the streak images, the dimensionless vortex length for flows of 4c* DNA grows dramatically with increased Re, while the vortex length for flows of water remain nearly constant. All vortices were stable, and no transient behavior was observed. The top and bottom vortex lengths did not display asymmetric behavior. Figure 5 indicates the relationship between the dimensionless vortex length χ and De for flows of 4c* DNA. The average lengths (averaging the top and bottom vortices) and standard deviations are reported for each flow condition. The increase in the dimensionless vortex length across this low range of De is well described by L v =0.5De Digital Particle Image Velocimetry Digital Particle Image Velocimetry (DPIV) is an optical method of measuring two-dimensional components of fluid velocity simultaneously at multiple points in a flow field. DPIV assigns vector magnitude and direction to a small region of the flow by tracking the displacement of several particles in this small region over time. DPIV was used to construct vector fields for flows of water and 4c* DNA through the micro-contraction. Images were captured using a progressive scanning full frame shutter camera (Pulnix TM-9701) with 1013 x 1000 pixel resolution. Images were obtained at the midplane of the channel (100 µm from the top and bottom of the device). 3 Copyright 2005 by ASME

4 A B C Figure 4. Dimensionless vortex length for flows of water and 4c* DNA through 2:1 micro-contraction device as a function of Re. D E Figure 5. Average dimensionless vortex length for flows of 4c* DNA through 2:1 micro-contraction device as a function of De. The vortex length follows the functional form, L V = 0.5De Figure 3. Streak images of upstream channel of 2:1 microcontraction for flow of water at (A) Re = 0.021, (B) Re = 0.035, (C) Re = and 4c* DNA at (D) Re = 0.002, De = 5, (E) Re = 0.005, De = 13, and (F) Re = 0.009, De = 23. F The size of the interrogation regions used for image processing was chosen such that a minimum of 8-10 particles resided in the region ensuring accurate cross-correlations. For each test condition 300 image pairs were captured with known time difference using a timing system. The time difference was chosen such that particle displacement was less than 33% the length of the interrogation region in the flow direction. Figure 6 shows the vector field for water flow at Re = as well as the x-velocity and y-velocity profiles at six x- positions across the field. Interrogation regions were chosen to be 32 x 64 pix or ~14 x 28 µm (spanwise x streamwise) with a 50% overlap. 4 Copyright 2005 by ASME

5 A A B B Figure 7. 4c* DNA flow (Re = 0.009, De = 23, El = 2500) through 2:1 micro-contraction. (A) Velocity vector field for primary flow. The contraction is located at x=0 and the centerline is located at y=0. The x- and y-positions are normalized by the channel width (w = 100 µm). The largest arrow corresponds to the fastest in the field and all others are scaled proportionally. (B) Velocity vector field in the bottom vortex. This field was constructed with smaller interrogation regions and imaging at the same magnification. Far upstream and far downstream of the contraction, the flow is fully developed. Near the entrance to the contraction, the flow is spatially accelerating, indicated by asymmetric y- velocity profiles. The asymmetry is a consequence of the choice of coordinate frame. Vectors near the corners of the contraction indicate slow and/or nearly stagnant flow regions. Any recirculation in the corner vortices is not captured by DPIV because the interrogation region area covers too large a proportion of the area of the vortex region. Figure 6. Water flow (Re = 0.007) through 2:1 microcontraction. (A) Velocity vector field. The contraction is located at x=0 and the centerline is located at y=0. The x- and y-positions are normalized by the channel width (w = 100 µm). The largest arrow corresponds to the fastest in the field and all others are scaled proportionally. (B) Normalized y-velocity profiles and (C) y-velocity profiles at six normalized x- positions. Velocities are normalized by the average velocity u. C Future work will explore using DPIV in the vortex region at higher magnification for improved spatial resolution in the vortex. It is hoped that these velocity fields will be useful in experimental validation of a computational design tool [6]. Uncertainty Analysis A series of 300 image pairs are taken for DPIV studies. Flow fields for all pairs of images are averaged to construct the velocity vector field. Averaging over a large number of image pairs improves accuracy. For flows of water, the x-velocity and y-velocity profiles for the average velocity fields at positions upstream and downstream of the contraction, where the flow is 5 Copyright 2005 by ASME

6 fully developed, are in good agreement with the exact solution of the equations of motion given by White [7]. The standard deviations for these velocity fields reflect the error associated with the experimental set-up, including the mechanical noise associated with the drive mechanism of the syringe pump. The standard deviations which are between 5-10% of the average value are found to be reduced at higher flow rates. This is due to difficulties associated with achieving low volumetric flow rates. Alternate pumping methods will be explored for future work. Additional uncertainty arises from the cross-correlation associated with the DPIV algorithm, which determines a spatial average for the displacement of a group of particles. This can be problematic in regions where there are large velocity gradients such as in the vortex region and along the interface with the primary flow. Averaging over an ensemble of images minimizes the uncertainty due to poor correlations. Previous studies incorporating an averaging algorithm for microscale DPIV have demonstrated a spatial resolution of 5 µm for unidirectional flow [8]. CONCLUSIONS Direct measurement techniques have been employed to characterize viscoelastic behavior of DNA flows in a 2:1 microcontraction. Flow visualization reveals vortex enhancement with increasing Re and De and indicate strong elastic flow behavior for semi-dilute DNA flow. Velocity fields of primary and vortex flow regions demonstrate the use of DPIV as a tool for obtaining velocity measurements of viscoelastic flows in microfluidic systems. Obtaining detailed velocity fields will elucidate the physics of this unique flow environment where the length scales of the macromolecule will approach the length scales of the device (L/h ~ 0.32). Further, use of DPIV as an experimental validation of a numerical simulation tool will have a profound impact on design and optimization of lab-on-a-chip systems incorporating macromolecular flows. ACKNOWLEDGMENTS The authors would like to acknowledge financial support from Laboratory Directed Research and Development (LDRD) grant 03-ERI-003, the Principal Investigator of the grant Dr. David Trebotich, Dr. Wesley Chang for fabrication of test devices. Device Fabrication was completed at the Microfabrication Laboratory at the University of California, Berkeley. REFERENCES 1. Perkins, T. T., D. E. Smith, Chu, S., 1997, "Single polymer dynamics in an elongational flow," Science, 276(5321), pp Smith, D. E., H. P. Babcock, Chu, S., 1999, "Singlepolymer dynamics in steady shear flow," Science, 283(5408), pp Shrewsbury, P. J., S. J. Muller, Liepmann, D., 2001, Effect of flow on complex biological macromolecules in microfluidic devices, Biomedical Microdevices, 3(3), pp Boger, D. V., 1987, "Viscoelastic flows through contractions," Annual review of fluid mechanics, 19, pp Rodd, L.E., Scott, T.P., Boger, D.V., Cooper-White, J.J., McKinley, G.H., 2004, Planar entry flow of low viscosity elastic fluids in micro-fabricated geometries, Proc. XIVth Int. Congr. on Rheology, pp. NF Trebotich, D., Colella, P., Miller, G.H., Nonaka, A., Marshall, T., Gulati, S., Liepmann, D., 2004, A Numerical Algorithm for Complex Biological Flow in Irregular Microdevice Geometries, Tech. Proc.of 2004 Nanotech. Conf. and Trade Show, 2, pp White, F.M., 1974, Viscous Fluid Flow, McGraw-Hill, New York. 8. Meinhart, C. D., S. T. Wereley, Santiago, J.G., 1999, Micron-resolution velocimetry techniques, Developments in laser techniques and applications to fluid mechanics, Springer, New York. 6 Copyright 2005 by ASME