Uncovering the Contribution of Microchannel Deformation to

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Uncovering the Contribution of Microchannel Deformation to Impedance-based Flow Rate Measurements Pengfei Niu, Brian J. Nablo, Kiran Bhadriraju, and Darwin R. Reyes Anal. Chem., Just Accepted Manuscript • DOI: 10.1021/acs.analchem.7b02287 • Publication Date (Web): 29 Sep 2017 Downloaded from http://pubs.acs.org on September 30, 2017

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Analytical Chemistry

Uncovering the Contribution of Microchannel Deformation to Impedance-based Flow Rate Measurements Pengfei Niu, Brian J. Nablo, Kiran Bhadriraju and Darwin R. Reyes* Engineering Physics Division, Physical Measurement Laboratory, National Institute of Standards and Technology, MD, USA * Corresponding author: [email protected]

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Abstract Changes in electrical impedance have previously been used to measure fluid flow rate in microfluidic channels. Ionic redistribution within the electrical double layer by fluid flow has been considered to be the primary mechanism underlying such impedance based microflow sensors. Here we describe a previously unappreciated contribution of microchannel deformation to such measurements.

We found that flow-induced microchannel deformation contributes

significantly to the change in electrical impedance of solutions, in particular to those solutions producing an electrical double layer in the order of a few tens of nanometers (i.e. containing relatively high ionic strength). Since the flow velocity at the measurement surface is near zero, due to the laminar nature of the flow, the contribution of the double layer under the conditions mentioned above should be negligible. In contrast, an increase in the fluid flow rate results in an increase in the microchannel cross-sectional area (because of higher local pressure), therefore producing a decrease in solution resistance between the two electrodes. Our results suggest that microflow sensors based on the concept of elastic deformation could be designed for in-situ monitoring and fine control of fluid flow in flexible microfluidics. Finally, we show that purposefully engineering a larger deformability of the microchannel, by changing the geometry and the Young’s modulus of the microchannel, enhances the sensitivity of this flow rate measurement.

Keywords Electrically Monitoring, Flow Rate, Channel Deformation, Electrical Impedance, PDMS


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Introduction Controlled transport of fluids is an enabling technology for genomics, proteomics, and the discovery of new drugs in microfluidic/lab-on-a-chip systems1-4. Flow-control is realized by a combination of microflow sensors, micro-pumps, and micro-valves5. Accurate measurement of flow rate in microchannels is a fundamental requirement for attaining fine-control of fluid delivery. When compared to off-chip sensors, flow monitoring integrated on-chip could provide a more accurate view of local flow rates6. So far, there have been many efforts undertaken by the research community to develop on-chip flow sensors and the sensing principles draw from several fields of physics, such as thermodynamics7-9, mechanics10, optics11,12. Specifically, based on the hypothesis that fluid flow could result in the redistribution of ions within the electrical double layer, which then causes changes in electrical impedance across two electrodes, electrical impedance methods were proposed to measure the microfluidic flow rate of electrolyte solutions13-16. The approach has several advantages including simplicity, compactness and ease of integration of microelectrode patterns, as well as the potential for applications in microfluidic biological studies. Most microfluidic lab-on-chip platforms for biological studies are made of flexible poly(dimethylsiloxane) (PDMS), due to the advantages of ease of fabrication, optical transparency, and biological compatibility17. The flexibility of PDMS makes these microchannels susceptible to deformation under pressure-driven flow18. Consequently, the crosssectional area of a microchannel would increase with an increase in flow rate. Lack of consideration in the contribution of microchannel bulging to electrical impedance could lead to



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misinterpretations regarding the real cause of changes in impedance with changes in fluid flow rate. The aim of this study is to examine whether flow-induced PDMS microchannel deformation contributes to the measured electrical impedance in microflow sensors. This study is essential because it is helpful to fully understand the fundamental working mechanism of electrical impedance-based flow sensors, particularly when using flexible microchannels.

Experimental Section Device Fabrication: Parallel coplanar Ti/Au electrodes (10/90 nm thick) with a width of 12.5 µm and the different gap distances used in this work were patterned onto glass slides via standard lift-off process19. Rectangular microchannels of 30 µm to 1000 µm wide, 28 µm deep and 45 mm long, were fabricated of PDMS (Sylgard 184 A/B, Dow Corning, Midland, MI, USA; 10:1 A:B; cured 70oC for 24 h) using standard soft lithography techniques17. Access holes to the microchannels were made with a biopsy punch (ID = 0.75 mm). Molded PDMS microchannels were plasma bonded to glass substrates containing gold-patterned electrodes. The microchannels were positioned perpendicular to the electrodes (Fig.1). This arrangement allows for better measuring the solution resistance and for reduced noise, when compared to electrodes arranged parallel to the flow.

Figure 1. Schematic of the electrode pair arrangement in a PDMS/glass microfluidic device. The channel (dark gray) is 45 mm long, between 30 µm to 1000 µm wide and 28 µm high. The flow direction is first from inlet1 to outlet1 and then reversed (inlet2 to outlet2) to have a direct


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comparison of the impedance measurement using the same pair of electrodes located close to the inlet and outlet of the microchannel. Impedance Measurement: Tygon tubing (ID = 0.80 mm) of about 40 cm long were connected to the inlet and outlet using stainless steel needles (OD = 0.87 mm and ID = 0.67 mm). Channels were filled with solutions of 1X PBS, 0.145 M NaCl, or 0.145 M KCl. The volumetric flow rate was varied between 0 µL/min and 100 µL/min with a syringe pump (Harvard Apparatus Holliston, MA, USA and calibrated using a NIST traceable gravimetric method) and allowed to stabilize for 5 min before any measurement was taken20. The impedance between the electrode pairs was measured with a Modulab potentiostat (Solartron Analytical, Oak Ridge, TN, USA) by applying a 5 mVrms sine wave at Vdc = 0 V between 100 Hz to 100 kHz. The deformation of the microchannel is caused by local pressure and observed non-uniformly across the length of the channel due to the pressure drop at any given flow rate. Consequently, the impedance results vary throughout the length of the channel as well. We illustrate this principle by measuring the impedance at each end of the microchannel using the same pair of gold electrodes located 7 mm from the access port. The measurements were carried out by first injecting solution from inlet1 to outlet1 and then from inlet2 to outlet2 (Fig. 1), therefore allowing the same pair of electrodes to measure the two distances from the inlet: 7 mm and 34.3 mm. Cross-Sectional Area Measurement: Confocal microscopy (LSM 800, Carl Zeiss, Thornwood, NY, USA) was used to image and measure the cross-sectional area of the microchannel under different flow rates. For visualization, the microchannel walls were stained with hydrophobic fluorescent dye Dead Red (ex/em = 488/570 nm) from the LIVE/DEAD cell imaging kit, (Thermo Fisher, Waltham, MA) by flowing a 1/1000 dye solution in 1X PBS for 2 hours at 2 µL/min. After the 2 hours, the dye solution inside the microchannel was replaced with 1X PBS. To enable the use of a high numerical aperture to achieve high-resolution images, the glass



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substrate bonded to the PDMS microchannels used for confocal imaging was a 175 µm thick coverslip. The objective lens being used was a 20X, 0.8 NA Zeiss Plan-Apochromat to allow for the imaging of the entire width of the microchannel. Five locations starting from the inlet and ending at the outlet of the microchannel were imaged at flow rates up to 100 µL/min. The inner borders of the channel were defined and measured using ImageJ to quantify the changes in crosssectional area.

Results and Discussion Flow rate dependent electrical impedance: The electrical impedance measured with our devices at frequencies between 0.1 to 100 kHz showed that at the lower end of this spectrum the complex impedance is dominated by the capacitance of the electrical double layer. The slope obtained within this range of -20 dB per decade is within the expected slope for capacitance dominated impedance processes (Fig. 2a). Within this region, no apparent flow-rate-dependent complex impedance variation is observed. As the frequency increases above 1 kHz, the solution resistance starts governing the complex impedance, as evidenced by a decreasing magnitude of the phase angle (Fig.2a). Within this region, an increase in volumetric flow significantly decreases the complex impedance (Fig.2a), and this behavior is highly reproducible (relative standard deviation, RSD = 0.5%). This is specific to the system plotted in Fig. 2 and Fig. 2S for the frequencies between 10 to 100 kHz. When separating the complex impedance into its real and imaginary components, the influence of volumetric flow is apparent in the resistive component and negligible from the capacitive component until the solution dielectric capacitance starts to be active (> 40 kHz, Fig.2b).


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Figure 2. Electrical impedance responses of 1X PBS solution measured on gold microelectrodes in a 420 µm wide channel. Electrodes had a gap separation of 3.7 mm and are located 7 mm from the inlet and were exposed to flow rates of 0 µL/min – square, 50 µL/min – circle, and 100 µL/min - triangle. (a) Complex impedance (|Z|, closed symbols) and phase angle (θ, open symbols) responses both as a function of frequency, and (b) real (Z′, closed symbols) and imaginary (Z′′, open symbols) components of |Z| as a function of frequency.

To compare the electrode gap separation, electrical conductivity of solutions and the location of the electrodes (inlet versus outlet) the complex impedance was normalized (at 100 kHz) by calculating the ratio of the impedance at flow rates from 0 to 100 µL/min over the impedance at zero flow. When all conditions were plotted as a function of flow rate it was found that the signal decays non-linearly with an increasing flow rate (Fig.3). Adjusting the location of the sensing electrodes to the outlet of the microchannel generates similar non-linear behavior, but with a diminished sensitivity to flow rate. Solutions with comparable electrical conductivity yield nearly identical responses to flow rate. Lowering the electrical conductivity of the solution generates a higher complex impedance (Fig.S3). Scaling up the electrode gap distance increases the real component of impedance by a similar factor (Fig.S4).



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Figure 3. Normalized variation of the complex impedance (|Z|/|Z|0) measured at 7 mm away from the microchannel outlet (open symbol), and inlet (closed symbol), respectively. The impedance measurement was carried out in the following solutions: 1X PBS (square), 0.145 M NaCl (circle) and 0.145 M KCl (triangles) (electrical conductivity of all ≈ 1.66 x 10-2 S/cm). The complex impedances were evaluated at 100 kHz and normalized to the impedances at 0 µL/min. The gap between the pair of electrodes was 3.7 mm.

Change of microchannel cross-sectional area with flow: Under these conditions, the volumetric flow must affect the real component of electrical impedance, i.e. solution resistance which can be defined as follows: ∙ . 1 where ρ is the solution resistivity, S is the cross-sectional area of the microchannel, and L is the distance between the electrodes. The pressure-driven flow will exert pressure on the PDMS microchannel to deform the elastomer, thus causing a change in the cross-sectional area. The cross-sectional area of the microchannel was imaged with confocal microscopy at multiple positions down the channel length and at various flow rates to determine the extent of that deformation (Fig. 4). In our rectangular channel (width/height = 15) on a glass substrate, an applied volumetric flow causes the largest deformation along the width of the ceiling (Fig.4a). As the fluid flows down the channel (from inlet to outlet), the magnitude of the deformation


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decreases (Fig.4b). The observed deformation explains the extent of the change in the electrical impedance caused by changes in flow rate when measured at different channel locations (inlet versus outlet) (Fig.3). The slope of the curve of the cross-sectional area as a function of flow rate (Fig.S5) gradually decreases with an increase in flow rate. This phenomenon could be the cause of the gradual decline in electrical impedance variation with flow rate observed in Fig.3.

Figure 4. Variation in channel cross-sectional area due to flow-induced deformation. (a) Cross-sectional area profile at a distance of 5.6 mm from the channel inlet under flow rates of 0 µL/min (red) and 100 µL/min (green). (b) Cross-sectional area variation along the channel length from the inlet (0 mm) to a distance of 45 mm under flow rates of 0, 10, 30, 50 and 100 µL/min. The cross-sectional areas plotted are an average of three separate experiments. All experiments were done in 1X PBS solution. The predicted solution resistance was calculated using the average cross-sectional area (S) and integrating the fitted surface area data over the separation distance (L) to examine the correlation between the changes in channel cross-sectional area and the electrical impedance. If the impedance variation is due completely to the change in solution resistance, the normalized



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complex impedance will almost entirely be accounted for by the normalized calculated solutionresistance. Plotting the impedance variation as a function of changes in solution resistance (calculated using Equation 1) should produce a curve with a slope approximately of 1. Fig. 5 indicates that the impedance and optical measurements directly correlate to the flow rates investigated herein (slopes of 0.99 and 1.01 at 10 kHz and 100 kHz, respectively). Thus, we are confident that flow induced PDMS channel deformation is the major contributor to the impedance variation for solutions with relatively high ionic strength (producing electrical double layers in the nanometer range).

Figure 5. Plot illustrating the variation of complex impedance and solution resistance, and their correlation. The normalized impedance and resistance were obtained at a frequency of 10 kHz (black squares) and 100 kHz (red open circles) under flow rates of 0, 10, 30, 50 and 100 µL/min. The predicted solution resistance was calculated from the fitted curves of the optically measured cross-sectional area (Fig.4) and Eq.1, then normalized to the calculated resistance at 0 µL/min (R/R0). The normalized impedance |Z|/|Z|0 were taken from Fig. 3 (average values). The coefficient of determination (r2) was 0.9966 and 0.9895 for 10 kHz and 100 kHz, respectively. Rigid SU-8 microchannel walls (420 µm wide and 28 µm high) were patterned on gold/glass substrates and sealed with a piece of glass. In this case, the deformation of the microchannel during increased flow is prevented. Changes in flow rate do not affect the electrical impedance of 1X PBS solution, even though the flow rate is much higher than those in flexible PDMS


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microchannels (Fig.S6). This observation further demonstrates our interpretation of our results with flexible PDMS channels. Influence of channel geometry on flow-rate-dependent impedance: Since we found that flowinduced electrical impedance variation correlates with microchannel deformation, the amount of deformation of the microchannel is then critical for the sensing performance. Hooke’s law equation, defined as follows, is employed to account for the extent of channel deformation:

. 2

where σ is the stress produced by the pressure inside the channel, E is the Young’s modulus and ε is the corresponding strain. Due to the large Young’s modulus of glass, flow induced stretching would only occur on the PDMS walls. The change of the channel height over channel width and the deformation of the channel width over the channel height are on the same order of the PDMS’s vertical and lateral strains, respectively, which were scaled to the pressure (P) in the channel over Young’s modulus21: ~ ~

∆ℎ ~ . 3

∆ ~ . 4 ℎ

where w and h are the width and height, and ∆w and ∆h are the average increases in width and height of the microchannel, respectively. In the case where w ≫ h, as is the case of the microchannels used in Figs. 2-5, a larger deformation of the channel height was observed while the lateral deformation was negligible. This phenomenon was also described in other studies18,22. In general, flow resistance is larger in



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smaller channels. If we keep the same channel height while changing the channel width, the same volumetric flow rate is maintained. The pressure (as well as the stress) is known to be higher in the narrower channels, as proved by inlet pressure measurement shown in Fig. S7. However, narrow channels deform less than wide channels at the same flow rate, as explained below: Strain is defined as the ratio of the change in length (∆#) to the original length (#$ ): ε

∆# . 5 #$

Here the part of the material, having stress field but not the entire PDMS thickness, should be considered as the original length #$ .

Figure 6. COMSOL simulations of stress field distribution in PDMS material created by applying a pressure of 35 kPa in microchannels of different aspect ratios (width/height) (a)


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420/28 (µm), (b) 100/28 (µm), (c) 30/28 (µm), the elastic modulus of the PDMS materials used is 2.5 MPa. The x and y scales are maximized to better observe the stress regions in the different channel. The color scale to the right of the stress profile indicates the local stress mapped to shades of blue color (Fig.6). As it is observed in the simulations in Fig. 6a-c, the stress regions extend as far out into the material as the dimension of the channel width. Therefore, the strain at the channel height is roughly proportional to the width of the channel. The same principle applies to the stretching that occurs at the channel width. This phenomenon explains the decreased deformability in narrow channels and has been previously described. As a direct consequence, narrowing the channel width while keeping a fixed height makes the electrical impedance less sensitive to flow rate as the deformation decreases (Fig.7).

Figure 7. Normalized variation of the complex impedance (|Z|/|Z|0) vs. flow rate measured on an electrode pair separated by 3.7 mm and located near the inlet of the PDMS microchannel. The channel has a fixed height of 28 µm and a varying width from 30 to 1000 µm. The solution used was 1X PBS and the plotted complex impedances were measured at f = 100 kHz. For a channel of width/height being 30/28 (µm), impedance measurement ended at the flow rate of 30 µL/min. Because at flow rates higher than 30 µL/min, the pressure inside channel is too high, and consequently causes delamination between the PDMS and the glass producing fluid leakage. Large deformability of the channel is critical for highly sensitive monitoring of flow rate. Besides channel geometry, the Young’s modulus (E) of PDMS is another key factor affecting the



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channel stretching, based on Hooke’s law. Higher flow sensitivity can be attained using relatively soft PDMS. The specific mixing ratio of base/curing agent in Sylgard 184 substantially affects the elastic modulus of PDMS. Experimental data show that the Young’s modulus decreases as the ratio of base/curing agent increases23. Therefore, the sensing performance of the platform can be tuned by changing the Sylgard 184 mixing ratio. Taking into consideration the channel geometry and the Young’s modulus of the material, the extent of deformation of a flexible microchannel can be predicted using Comsol simulations, as shown in Fig. 6 and Fig. S8. There are many biological environments in which fluid flow in enclosed geometries is of critical importance. Their characteristics are determined by a balance of fluid properties, pressure and structural deformation. Therefore, our findings could greatly benefit biological studies. For example, in studies where endothelial cells will be exposed to a changing flow rate (in PDMS channels) to investigate the effects of shear stress, the concept of elastic deformation can be used to determine the local flow rate when using cell culture media.

This technique utilizing

impedance-based measurements is possible despite having a system with high ionic strength. Solutions with high ionic strength produce electrical double layers in the order of approx. < 2 nm, and under flow conditions in a non-elastic microchannel, impedance-based measurements are beyond their measurement capabilities at the studied frequencies (1kHz to 100 kHz). On the other hand, this system allows for the local and continuous monitoring of flow rate within microfluidic systems. Other studies that have attempted to control and manipulate fluid flow in flexible microfluidic platforms24,25, require the building of a database linking external actuation (such as pressure and mechanical force) with structural deformation. However, there are deviations in these systems that cannot be predicted due to difficulties in the reproducibility of the actuation. By placing an impedance sensor in the area where elastic deformation occurs, and


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giving a direct feedback of impedance variation, the flow rate could be more accurately measured and controlled.

Conclusions When measuring fluid flow in flexible microchannels using an electrical impedance-based method, the contribution of the flow-induced microchannel deformation to impedance variation cannot be neglected. For solutions containing relatively high ionic strengths (yielding an electrical double layer of nanometer scale), the microchannel deformation is almost the entire contributor to the impedance variation caused by flow. The microchannel deformation is determined by its geometry and the mechanical properties of the used flexible material. Larger deformability of microchannels yields higher sensitivity of the impedance sensors to fluid flow. Our findings could greatly benefit the field of microfluidic-based biological studies, where insitu monitoring and fine control over the flow of biological media can be achieved.

Supporting Information Typical ion distribution between two electrodes and the equivalent electrical circuit, reproducibility of the impedance measurements at low and high frequencies, influence of electrode gap distance and solution electrical conductivity on the complex impedance, change of cross-sectional area with flow rate, change of inlet and outlet pressures with flow rate, impedance variation measured in rigid SU8 microchannels, and Comsol simulation boundary conditions and the corresponding channel deformation.



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Acknowledgements PN was supported by the NIST on a Chip Initiative. This research was performed in part at the NIST Center for Nanoscale Science and Technology.

References (1) Beebe, D. J.; Mensing, G. A.; Walker, G. M. Annu. Rev. Biomed. Eng. 2002, 4, 261-286. (2) Kovarik, M. L.; Ornoff, D. M.; Melvin, A. T.; Dobes, N. C.; Wang, Y.; Dickinson, A. J.; Gach, P. C.; Shah, P. K.; Allbritton, N. L. Anal. Chem. 2013, 85, 451-472. (3) Roper, M. G. Anal. Chem. 2016, 88, 381-394. (4) Patabadige, D. E.; Jia, S.; Sibbitts, J.; Sadeghi, J.; Sellens, K.; Culbertson, C. T. Anal. Chem. 2016, 88, 320-338. (5) Teng, J. T. Chu, J. C.; Liu, C.; Xu, T. T.; Lien, Y. F.; Cheng, J. H.; Huang, S. Y.; Jin, S. P.; Dang, T. T.; Zhang, C. P.; Yu, X. F.; Lee, M. T.; Greif, R. In Fluid Dynamics, Computational Modeling and Applications, Hector Juarez, L., Ed.; InTech, 2012; pp 403-436. (6) Stone, H. A.; Stroock, A. D.; Ajdari, A. Annu. Rev. Fluid Mech. 2004, 36, 381-411. (7) Hoera, C.; Skadell, M. M.; Pfeiffer, S. A.; Pahl, M.; Shu, Z.; Beckert, E.; Belder, D. Sens. Actuator. B Chem. 2016, 225, 42-49. (8) Etxebarria, J.; Berganzo, J.; Elizalde, J.; Llamazares, G.; Fernández, L. J.; Ezkerra, A. Sens. Actuator. B Chem. 2016, 235, 188-196. (9) Deng, S.; Wang, P.; Liu, S.; Zhao, T.; Xu, S.; Guo, M.; Yu, X. Sensors 2016, 16, 964. (10) Sadegh Cheri, M.; Latifi, H.; Sadeghi, J.; Salehi Moghaddam, M.; Shahraki, H.; Hajghassem, H. Analyst 2014, 139, 431-438. (11) Lindken, R.; Rossi, M.; Grosse, S.; Westerweel, J. Lab Chip 2009, 9, 2551-2567. (12) Wang, H.; Wang, Y. Measurement 2009, 42, 119-126. (13) Collins, J.; Lee, A. P. Lab Chip 2004, 4, 7-10. (14) Arjmandi, N.; Liu, C.; Van Roy, W.; Lagae, L.; Borghs, G. Microfluid. Nanofluidics 2012, 12, 17-23. (15) Hassan, U.; Watkins, N. N.; Edwards, C.; Bashir, R. Lab Chip 2014, 14, 1469-1476. (16) Mavrogiannis, N.; Fu, X.; Desmond, M.; McLarnon, R.; Gagnon, Z. R. Sens. Actuator B Chem. 2017, 239, 218-225. (17) Qin, D.; Xia, Y.; Whitesides, G. M. Nat. Protoc. 2010, 5, 491-502. (18) Hardy, B. S.; Uechi, K.; Zhen, J.; Pirouz Kavehpour, H. Lab Chip 2009, 9, 935-938. (19) Park, B. Y.; Zaouk, R.; Madou, M. J. In Microfluidic Techniques: Reviews and Protocols, Minteer, S. D., Ed.; Humana Press: Totowa, NJ, 2006, pp 23-26. (20) Certain commercial equipment, instruments, or materials are identified in this paper to foster understanding. Such identification does not imply recommendation or endorsement by the National Institute of Standards and Technology, nor does it imply that the materials or equipment is necessarily the best available for the purpose. (21) Gervais, T. Mass Transfer and Structural Analysis of Microfluidic Sensors. Ph.D. Dissertation, Massachusetts Institute of Technology, February 2006. (22) Kang, C.; Overfelt, R. A.; Roh, C. Biomicrofluidics 2013, 7, 054102. (23) Wang, Z.; Volinsky, A. A.; Gallant, N. D. J. Appl. Polym. Sci. 2014, 131, 41050. (24) Attia, R.; Pregibon, D. C.; Doyle, P. S.; Viovy, J. L.; Bartolo, D. Lab Chip 2009, 9, 1213-1218.


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(25) Mosadegh, B.; Kuo, C. H.; Tung, Y. C.; Torisawa, Y. S.; Bersano-Begey, T.; Tavana, H.; Takayama, S. Nature Phys. 2010, 6, 433-437.



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241x128mm (72 x 72 DPI)


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Uncovering the Contribution of Microchannel Deformation to

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