Accelerated Transport of Particles in Confined Channels with a High

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Accelerated transport of particles in confined channels with high roughness amplitude Hubert Ranchon, Jean Cacheux, Benjamin Reig, Olivier Liot, Pattamon Teerapanich, Thierry Leichlé, Pierre Joseph, and Aurélien Bancaud Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.7b03962 • Publication Date (Web): 02 Jan 2018 Downloaded from http://pubs.acs.org on January 4, 2018

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Accelerated transport of particles in confined channels with high roughness amplitude

Hubert Ranchon1*, Jean Cacheux1*, Benjamin Reig1, Olivier Liot1, Pattamon Teerapanich1, Thierry Leichlé1, Pierre Joseph1, Aurélien Bancaud1

1

LAAS-CNRS, Université de Toulouse, CNRS, Toulouse, France

*

These authors equally contributed to this work.

Correspondence: Aurélien BANCAUD, [email protected]

Keywords: microfluidics, velocimetry, particle transport, roughness

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Abstract We investigate the pressure-driven transport of particles of 200 or 300 nm in diameter in shallow microfluidic channels of ~1 µm in height with a bottom wall characterized by high roughness amplitude of ~100 nm. This study starts with the description of an assay to generate cracks in hydrophilic thin polymer films, together with a structural characterization of these corrugations. Microfluidic chips of variable height are then assembled on top of these rough surfaces, and the transport of particles is assessed by measuring the velocity distribution function for a set of pressure drops. We specifically detect anomalous transport properties for rough surfaces. The maximum particle velocity at the centerline of the channel is comparable to that obtained with smooth surfaces, but the average particle velocity increases non-linearly with the flow rate. We suggest that the change in boundary condition at the rough wall is not sufficient to account for our data, and that the occurrence of contacts between the particle and the surface translates the particle away from the wall and speeds up its motion. We finally draw perspectives for separation by field-flow fractionation.


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Introduction The development or improvement of lab on chips dedicated to the separation of molecules or particles has been accompanied by numerous studies focused on particle motion analysis in microfluidic channels.1–3 In the context of confined flows, the consequences of surface-solute interactions has called for the implementation of specific velocimetry techniques to probe the behavior of particles near solid surfaces.4–7 The transport of particles at the vicinity of hydrophilic or hydrophobic surfaces has been extensively studied with smooth or rough corrugations (see ref.

8

for a review). It is commonly accepted that no-slip

boundary conditions apply for smooth hydrophilic surfaces. Conversely slip lengths of ~30 nm can be detected for hydrophobic surfaces,9 and the engineering of textured surfaces with super-hydrophobic properties has been performed to reach slip lengths of tens of µm.10,11 For hydrophilic surfaces, the study of particle-particle collisions has shown that the existence of microscopic surface roughness breaks the common assumption that the fluid acts as a lubricant to prevent solid-surface contacts.12 The occurrence of contacts violates the timereversibility of Stokes equations for smooth surfaces and Newtonian fluids, and leads to a reduction of the effective viscosity of suspensions.13 At the level of individual colloids, the study of transport over surfaces with “smooth” roughness (see e.g. 14), i.e. with a corrugation height smaller than the radius of the tracer, indicated that when contacts occurred, the translational velocity generally decreased, while the rotational velocity increased, due to solid–solid friction. In the field of colloidal transport, many studies have been focused on colloid retention through porous material. Whenever the roughness size is comparable to or larger than the particle size, particle retention is controlled by water velocity and surface roughness

15,16

.

Despite its relevance for e.g. geosciences, this regime has been poorly investigated in microfluidic channels. In this report, we therefore set out to investigate the transport of


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fluorescent nanoparticles of diameter 200 nm in shallow channels of 0.5-2.0 µm in thickness with an average maximum peak-to-valley height of ~100 nm. After the description of a process to generate hydrophilic surfaces with high roughness amplitude, we monitor the transport of tracers conveyed by pressure-driven flows using wide field fluorescence microscopy and the nanoparticle velocimetry distribution analysis (NVDA) method.4 We report anomalous transport properties over rough surfaces and discuss their physical origin.

Materials and Methods Rough surfaces were produced through the formation of cracks during the reticulation of a thin layer of 6 µm of “hard” poly-dimethylsiloxane (hPDMS).17 The unreticulated silicone elastomer was spin coated at 3000 rpm during 30 s on 170 µm glass coverslips. Due to the difference in thermal expansion coefficient between the polymer film and the substrate, a temperature onset resulted in tensile stresses accompanied by the formation of cracks.18 We used a slow ramp with a slow baking at 60°C during 4 hours, or a rapid one at 80°C during 45 min. Surface topography characterization was carried out with atomic force microscopy (AFM, Veeco Dimension 3100), optical profilometry (Wyko, Veeco), and scanning electron microscopy (SEM, Hitachi S4800). Image analysis of SEM micrographs was carried out in ImageJ using (i) the bandpass fast Fourier transform (FFT) filter with size thresholds of 250 nm and 15 µm, followed by (ii) the “Find maxima” algorithm with a noise tolerance set to 50 and contour identification, and finally (iii) the “particle analysis” algorithm to infer the perimeter and surface of each crack pattern (see Supplementary Figure S1A). The channels of microfluidic chips were engraved in silicon wafers using reactive ion etching performed after conventional photolithography, as described in ref.

19

. The depth of

the channel spanned in the range 0.9 to 1.9 µm. The silicon channels were then sealed to the glass coverslips covered with hPDMS. The bonding step was performed right after surface


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activation using oxygen plasma (200 W, 30 s). Note that this treatment did not induce detectable modifications of the crack patterns (Supplementary Figure S1B) and formed a native silicon oxide layer on the silicon chip. The walls of the resulting chips were transiently hydrophilic, and our experiments were conducted immediately after the bonding step. Unless stated, chemicals were purchased from Sigma-Aldrich. Fluorescent polystyrene nanoparticles with surface carboxyl groups (ThermoFisher) were conveyed in the microfluidic chips using a pressure controller operating in the range 10-500 mbar (microfluidic flow control system, MFCS Fluigent). The viscosity of the fluid was set to η=5 mPa.s with a 40% (vol:vol) glycerol in water mixture containing the ionic species Tris-HCl (160 mM), boric acid (160 mM) and EDTA (5 mM; pH=8.3). Note that the Debye layer λD, as defined by the length scale over which mobile charges in the buffer screen out electric fields, was ~1 nm,20 i.e. much less than the surface roughness. The pressure was set to induce a flow maximum velocity typically slower than 300 µm/s, implying that the flow and particle Reynolds numbers were 10-4 or less. The transport of nanoparticles was assayed by tracking them with a wide field Zeiss fluorescence microscope equipped with a 100X objective (numerical aperture=1.3) and Zyla sCMOS camera with a pixel size of 160 nm. Fluorescent particles of diameter 2a=200 or 300 nm were diluted at a typical (v:v) ratio of 1:5000 in order to neglect inter-particle hydrodynamic interactions and to ensure independent tracking. The focal depth of the objective of ~1.5 µm was comparable to the channel height, so tracers remained in focus throughout their migration across the field of view of the microscope. In each experimental condition, 30-50 particle trajectories with a total of ~5000-8000 positions were recorded in order to extract the velocity distribution along and transverse to the flow direction in the field of view of the microscope.

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hPDMS surface roughness characterization Smooth hPDMS thin films were obtained with a baking process at low temperature, whereas crack patterns were systematically detected using sharper temperature ramps during the reticulation of hPDMS (Fig. 1A-C). These cracks had a lateral extension of a few microns, and their vertical topography showed corrugations of maximal height ~80 nm, as inferred from AFM (Fig. 1D). Note that these cracks were superficial, because their depth was much smaller than the thickness of hPDMS films of 6 µm. We then focused on the perimeter-area relationship of crack patterns based on the analysis of AFM and SEM images (Fig. 1E, see methods in Supplementary Fig. S1). The resulting graph showed a constant power law response over three decades associated to an exponent of ~0.7. For simple Euclidian patterns, the perimeter is expected to scale with the square root of the area, i.e. the exponent is 0.5. More complex shapes with fractal characteristics are instead characterized by higher exponents,21 confirming earlier observations that the formation of cracks in thin films is associated to fractal geometries.22 Next we assayed the roughness parameters of the surface, as inferred from the root mean square average and the average peak-to-valley height, which are denoted Rq and Rz, respectively. For flat surfaces, the roughness parameters (Rq,Rz) were (1, 11) and (2, 20) nm according to AFM and optical interferometry over scanning areas of 25×25 and 100×100 µm2, respectively. Enhanced roughness parameters of (15, 193) nm and (18, 100) nm, respectively, were detected after a baking process at high temperature. Our measurements therefore demonstrate that hPDMS surfaces with roughness amplitude and fractal topology can be generated using sharp temperature gradient during the baking process.


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Figure 1: Characterization of hPDMS surfaces with high roughness amplitude. (A) Atomic force micrograph of hPDMS thin films after a baking process with a sharp temperature gradient. (B) Same as (A) with a smooth temperature gradient (see Methods). (C) Scanning electron micrographs of crack patterns on hPDMS surface. (D) The plot shows the surface topography of hPDMS films inferred from AFM for the two baking processes, as indicated in legend. (E) The plot shows the perimeter vs. surface characteristics of the cracks obtained from the analysis of the AFM and SEM images, as shown in panels (A) and (C). Note that the plot is based on the analysis of n=1030 patterns.

Particle velocimetry over smooth hPDMS surfaces We fabricated silicon chips of height 2h=930 {+/-} 15 nm, as inferred from mechanical profilometry (not shown), with a smooth hPDMS bottom wall (Fig. 2A). We investigated the transport of Brownian particles of diameter 2a=200 nm for a set of pressure drops (see Supplementary video), and analyzed it with the nanoparticle velocimetry distribution analysis (NVDA) model.4 The breadth of the transverse velocity distribution was dictated by thermal fluctuations 4, and it was fitted with the same Gaussian function for every pressure drops in order to determine the particle diffusion coefficient (data not shown). The


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longitudinal velocity distribution was instead increasingly skewed as the pressure drop increased (colored datasets in Fig. 2B). This distribution resulted from the convolution of the parabolic fluid velocity profile with thermal fluctuations. Qualitatively, the peak of the distribution corresponds to the maximum flow velocity v0, and the minimal velocity occurs for particles traveling at the vicinity of the walls at ~2v0a/h. We showed that the longitudinal distribution could be fitted with a numerical function calculated with hydrodynamic first principles.4 This function was defined by two parameters, namely v0 and the confinement ratio a/h, which could be determined with precisions of 1% and 8%, respectively, as inferred from simulations and experiments in glass microchannels of 2 µm in height.4 By setting the confinement ratio to 0.21, we could fit the longitudinal velocity distributions on smooth hPDMS surfaces using the maximum flow velocity as adjustable parameter (line plots in Fig. 2B). The variation of v0 as a function of the pressure drop showed a linear response expected for Newtonian fluids (Fig. 2C). Furthermore the slope of h2/2η allowed us to independently estimate the channel height. Its value of 2.3 10-11 m2/Pa.s corresponded to 2h=960 nm, given the viscosity of η=5 mPa.s. This estimate was therefore in good agreement with our calibration of 2h=930 {+/-} 15 nm by mechanical profilometry. Consequently particle transport in smooth hPDMS chips was consistent with the behavior observed on flat glass surfaces. Notably this result was consistent with the consensus view that slippage is negligible even at nm scale on hydrophilic surfaces 9,23.


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Figure 2: Velocimetry in a smooth chip of 930 nm in height. (A) Schematics of an experiment with particles traveling in a silicon chip bonded to a glass coverslip covered with an hPDMS layer. (B) The colored data points represent the experimental longitudinal velocity distributions recorded at four different pressure drops, as indicated in the inset, for 200 nm particles flowing in a channel of 930 nm. The corresponding fits shown as black lines are obtained with the NVDA model.4 This model assumes a Poiseuille flow with a confinement ratio a/h of 0.21, and the fitting parameter is the fluid maximum velocity v0 at the centerline of the channel as indicated in the inset. Each histogram contains between 5000 and 8000 measurements. (C) The plot represents the fluid maximum velocity deduced from the fit as a function of the pressure drop and the corresponding linear trend expected for a Newtonian fluid.


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Particle velocimetry over surfaces with high roughness amplitude Next we carried out the same experiment in microfluidic chips of height h=1.2 µm with a rough bottom wall. We extracted the longitudinal velocity distribution for a range of pressure drop of 10-100 bar/m (colored datasets in Fig. 3A). We set the confinement ratio to 0.17, and attempted to fit this data with NVDA with the maximum velocity v0 as adjustable parameter. In contrast to smooth hPDMS surfaces, the distributions were not reproduced, because the proportion of low velocity states, which is zoomed in on the plot in Fig. 3B, was much lower than the prediction of the model. We also investigated particle transport with a set of microfluidic chips of height 0.95, 1.4, and 1.9 µm. In every setting, we detected that the velocity distribution had an anomalous shape in comparison to the canonical response recorded over flat surfaces (Supplementary Fig. S2A). Finally, we investigated the response of two different types of tracers of 200 and 300 nm simultaneously flowing, i.e. traveling at the same flow rate, in a channel of height 1.6 µm. The different types of particles were segmented based on their difference in intensity of ~3 fold in order to extract their respective velocity distributions (histograms in Fig. 3C). We noted that the velocity distribution for 300 nm particles was slightly more skewed toward high velocities than that obtained with 200 nm beads. Both distributions were also shifted for low velocity states in comparison to the canonical response over flat walls (black curve, Fig. 3C).


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Figure 3: Velocimetry in a rough channel of 1200 nm. (A) The graph shows a set of velocity distribution functions for a 200 nm tracer flowing in a channel of 1.2 µm in height with high roughness amplitude. The pressure drops spanned between 10 to 100 bar/m, as indicated in inset. The fits are performed with the NVDA model for a channel height set to 1.2 µm and maximal velocities as indicated in the inset. (B) The plot of experimental vs. theoretical normalized velocity distribution (NVD) obtained for a pressure drop of 54 bar/m is zoomed in to show that low velocity states are infrequent with rough surfaces. (C) The two histograms correspond to particles of 200 and 300 nm in diameter simultaneously flowing in a channel of height h=1.6 µm (red and blue data set, respectively). The fit with the NVDA model is obtained for a confinement ratio of 0.19 and a maximum fluid velocity of 337 µm/s.

Analysis of the maximum and average velocity with a rough surface Because we have no model to fit the velocity distribution with rough walls, we wished to characterize the anomalous shape of the velocity distribution based on the average and maximal particle velocity, as inferred from the first raw moment and position of the peak of the distribution. We plotted the variation of the maximum velocity as a function of the pressure drop (blue dataset in Fig. 4A), and observed a linear trend with a slope of 3.35 10-11 m2/Pa.s (solid black line in Fig. 4A). Assuming flat surfaces, the measure of the slope could be used to estimate the channel height of 2h=1.24 µm. This measurement was in good agreement with our characterization of silicon chips by mechanical profilometry. Interestingly, this result was consistent with the observation that surface roughness had a minor effect on the hydraulic resistance in the laminar regime.24 11 / 18 ACS Paragon Plus Environment

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Next, we focused on the variation of the average velocity as a function of the pressure drop (green dataset in Fig. 4A). We expected the average velocity to be equal to 2/3 of the maximal velocity due to the slit-like geometry of our channels, as indicated by a dashed line in Fig. 4A. Yet, we observed that the average velocity tended to increase non-linearly with the pressure drop with a power law exponent of 1.2 (green line in Fig. 4A). This effect is a consequence of the changes of the velocity distribution function shown in Fig. 3A-B associated to the reduction in low-velocity states. Noticeably, the linear and power-law responses for the particle maximum velocity and average velocity, respectively, were detected for different the different levels of confinement (Supplementary Fig. S2).

Figure 4: Analysis of the anomalous velocity distribution over rough walls. (A) The maximum and average velocity (blue and green datasets, respectively) of 200 nm particles flowing in channels of 1.2 µm in height is plotted as a function of the pressure drop. Note that this data is extracted from Fig. 3A. The solid black line is a tend line for the blue dataset, the dashed line corresponds to the expected average velocity, and the green curve is a trend line for the green dataset. (B) By fitting the velocity distributions with the NVDA model including


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slippage, we estimated the apparent slip velocity as a function of the shear rate at the wall in every experimental setting. The black dashed curve is a trend line.

Discussion Because alterations of the boundary conditions at the walls would change the density of low velocity states, we tested whether slippage could account for our data.9 Notably, effective slip lengths have been theoretically and numerically studied for laminar flows over rough surfaces.25,26 Qualitatively, the up-and-down motion of the particle induces a mean slip velocity associated to an apparent translation in the bulk of the fluid. Using finite element simulation of 2D flows in a channel of 1.2 µm in height (Supplementary Fig. S3), we measured the flow velocity at a distance of 100 nm of the wall, i.e. for particles contacting the tip of the corrugations, and noticed an acceleration to an apparent slip length of ~20 nm, To investigate this effect further, we fitted the velocity distributions with the NVDA model including a slip velocity at the wall (see Supplementary Material). Note that the particle diameter was set to 200 nm and the channel height to that deduced from our calibration by profilometry (see legend of Fig. 4B). The slip velocity was plotted as a function of the shear rate at the wall for every set of data collected with rough hPDMS surfaces (colored data points in Fig. 4B). The graph was qualitatively fitted with a line, the slope of which defined a slip length of ~100 nm. This value was somewhat 5 times greater than our qualitative estimate, suggesting that the apparent slip could not account alone for our results. In another non-mutually exclusive direction, we suggest that anomalous transport properties may be related to the occurrence of surface-particle contacts. Using mm-scale flow cells with a rough surface obtained by adsorption of a monolayer of mm-scale particles, it has indeed been shown that the longitudinal velocity of particles travelling at the vicinity of the wall increased non linearly with the shear rate of the flow.27 This study proposed that the acceleration in particle motion was due to the transfer of momentum through interactions with


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the asperities of the surface and the subsequent flight over the surface. This mechanism is somewhat analogous with the combination of rolling and slipping undergone by colloids brought into contact. Note that such contacts break the fore-and-aft symmetry of the trajectories predicted for smooth spheres conveyed in a viscous fluid.12,28 The occurrence of particle-surface contacts associated to the roughness of the hPDMS layer could therefore lead to an apparent depletion of low velocity states in the particle velocity distribution, and therefore account for our data.

Conclusion Altogether we present a technology to fabricate shallow channels with a bottom wall with high roughness amplitude, which is composed of cracks with a fractal geometry. We then analyze the transport of particles in these microfluidic systems with the NVDA method. We analyze the particle velocity distribution, and demonstrate that its profile is consistent with a Poiseuille flow with smooth hPDMS surfaces, but departs from this “canonical” response with rough surfaces. Based on the analysis of the maximum and average particle velocity, we conclude that slippage is unlikely accounting for our results and suggest that particle-surface contacts and the associated transfer of momentum is a potential explanation. This mechanism of particle-surfaces transfer momentum has not been thoroughly documented in microfluidic systems, but several studies have been focused on colloid retention through porous materials with high roughness amplitude for groundwater contamination. Microfluidic technologies offer ideal solutions to build model “rock-on-a-chip” systems 29 dedicated to the characterization of confined transport as well as surface “trapping” with rough walls. Notably, surface trapping should be studied with the same chemistry and roughness parameters for the upper and lower walls of the channels in order to obtain results qualitatively comparable to those in porous materials. In another mutually-reinforcing direction, we suggest that the


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measurement of the average velocity of particles traveling in confined channels may find an unexpected application for minimally-invasive monitoring of microsystems’ aging, if mechanical constraints induce the formation of cracks. Our results also raise perspectives for separation science, because the degree of roughness of a shallow channel may provide a control parameter to enhance Field Flow Fractionation (FFF) technologies.2 A standard mode of transport for FFF separation combines transverse forces toward the channel walls together with longitudinal advection. Colloids then travel at the vicinity of surfaces, which are usually assumed to be smooth. We thus hypothesize that colloid migration could be finely tuned by tailoring the geometry and distribution of asperities to selectively immobilize (and hence sort) particles. These researches should be associated to fluid flow modeling at smaller length scales, because molecular dynamics simulations have uncovered complex fluid structures at the vicinity of rough walls with fractal geometries.30–32 The resulting data may shed light on the molecular origin of transverse forces away from the walls, which have been detected by FFF,33,34 but the physical origin of which remains controversial.35

Supplementary Information statement: Supplementary Video 1 of 200 nm particles traveling over a rough hMDPS surface; Model of transport in the presence of slippage at the walls; Structural characterization of crack patterns by image analysis of SEM; NVDA analysis of 200 nm particles traveling in rough channels of 900 1400, and 1950 nm in height; 2D COMSOL simulations of Poiseuille flows over rough surfaces and estimation of the apparent slip length for 200 nm particles.

Acknowledgements:


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The authors thank Prof. F. Charru for critical feedbacks on the manuscript and Dr. M. Fouet for critical reading. This work was partly supported by LAAS-CNRS micro and nanotechnologies platform, member of the French RENATECH network. We acknowledge funding

from ANR PolyTransFlow (13-BS09-0015).


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Bibliography (1) (2) (3) (4) (5) (6) (7)

(8)

(9) (10) (11) (12)

(13) (14) (15) (16)

(17) (18) (19)

(20)

Haeberle, S.; Zengerle, R. Microfluidic Platforms for Lab-on-a-Chip Applications. Lab on a Chip 2007, 7 (9), 1094. Giddings, J. C.; Yang, F. J.; Myers, M. N. Flow Field-Flow Fractionation: A Versatile New Separation Method. Science 1976, 193, 1244–1245. Sajeesh, P.; Sen, A. K. Particle Separation and Sorting in Microfluidic Devices: A Review. Microfluidics and nanofluidics 2014, 17 (1), 1–52. Ranchon, H.; Picot, V.; Bancaud, A. Metrology of Confined Flows Using Wide Field Nanoparticle Velocimetry. Sci. Rep. 2015, 5. Zettner, C. M.; Yoda, M. Particle Velocimetry Field Measurements in a near-Wall Flow Using Evanescent Wave Illumination. Exp Fluids 2003, 34, 115–121. Li, H.; Sadr, R.; Yoda, M. Multilayer Nano-Particle Image Velocimetry. Exp Fluids 2006, 41, 185–194. Li, Z.; D’eramo, L.; Monti, F.; Vayssade, A.-L.; Chollet, B.; Bresson, B.; Tran, Y.; Cloitre, M.; Tabeling, P. Slip Length Measurements Using µPIV and TIRF-Based Velocimetry. Israel Journal of Chemistry 2014, 54 (11–12), 1589–1601. Neto, C.; Evans, D. R.; Bonaccurso, E.; Butt, H.-J.; Craig, V. S. J. Boundary Slip in Newtonian Liquids: A Review of Experimental Studies. Reports on Progress in Physics 2005, 68 (12), 2859–2897. Joseph, P.; Tabeling, P. Direct Measurement of the Apparent Slip Length. Phys. Rev. E 2005, 71, 035303(R). Lee, C.; Choi, C.-H.; others. Structured Surfaces for a Giant Liquid Slip. Physical review letters 2008, 101 (6), 64501. Rothstein, J. P. Slip on Superhydrophobic Surfaces. Annual Review of Fluid Mechanics 2010, 42, 89–109. Davis, R. H.; Zhao, Y.; Galvin, K. P.; Wilson, H. J. Solid–solid Contacts due to Surface Roughness and Their Effects on Suspension Behaviour. Philosophical Transactions of the Royal Society of London A: Mathematical, Physical and Engineering Sciences 2003, 361 (1806), 871–894. Wilson, H. J.; Davis, R. H. The Viscosity of a Dilute Suspension of Rough Spheres. J Fluid Mech. 2000, pp 339–367. Zhao, Y.; Galvin, K. P.; Davis, R. H. Motion of a Sphere down a Rough Plane in a Viscous Fluid. International Journal of Multiphase Flow 2002, 28 (11), 1787–1800. Morales, V. L.; Gao, B.; Steenhuis, T. S. Grain Surface-Roughness Effects on Colloidal Retention in the Vadose Zone. Vadose Zone Journal 2009, 8 (1), 11–20. Bradford, S. A.; Torkzaban, S. Colloid Transport and Retention in Unsaturated Porous Media: A Review of Interface-, Collector-, and Pore-Scale Processes and Models. Vadose Zone Journal 2008, 7 (2), 667–681. Schmid, H.; Michel, B. Siloxane Polymers for High-Resolution, High-Accuracy Soft Lithography. Macromolecules 2000, 33, 3042–3049. Xia, Z. C.; Hutchinson, J. W. Crack Patterns in Thin Films. Journal of the Mechanics and Physics of Solids 2000, 48 (6–7), 1107–1131. Viero, Y.; He, Q.; Mazenq, L.; Ranchon, H.; Fourniols, J. Y.; Bancaud, A. Efficient Prototyping of Large-Scale Pdms and Silicon Nanofluidic Devices Using Pdms-Based Phase Shift Lithography. Microfluidics Nanofluidics 2012, 12, 465–473. Reisner, W.; Beech, J. P.; Larsen, N. B.; Flyvbjerg, H.; Kristensen, A.; Tegenfeldt, J. O. Nanoconfinement-Enhanced Conformational Response of Single DNA Molecules to Changes in Ionic Environment. Physical Review Letters 2007, 99, 58302. 17 / 18 ACS Paragon Plus Environment

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(21) Li, J.; Dozier, A. K.; Li, Y.; Yang, F.; Cheng, Y.-T. Crack Pattern Formation in Thin Film Lithium-Ion Battery Electrodes. Journal of The Electrochemical Society 2011, 158 (6), A689–A694. (22) Shi, D.; Jiang, J.; Tian, E.; Lung, C. Perimeter-Area Relation and Fractal Dimension of Fracture Surfaces. J Mater Sci Technol. 1997, pp 416–420. (23) Tabeling, P. A Brief Introduction to Slippage, Droplets and Mixing in Microfluidic Systems. Lab Chip 2009, 9 (17), 2428–2436. (24) Kandlikar, S. G.; Schmitt, D.; Carrano, A. L.; Taylor, J. B. Characterization of Surface Roughness Effects on Pressure Drop in Single-Phase Flow in Minichannels. Physics of Fluids (1994-present) 2005, 17 (10), 100606. (25) Panzer, P.; Liu, M.; Einzel, D. The Effects of Boundary Curvature on Hydrodynamic Fluid Flow: Calculation of Slip Lengths. International Journal of Modern Physics B 1992, 6 (20), 3251–3278. (26) Niavarani, A.; Priezjev, N. V. The Effective Slip Length and Vortex Formation in Laminar Flow over a Rough Surface. Physics of Fluids 2009, 21 (5), 52105. (27) Charru, F.; Larrieu, E.; Dupont, J.-B.; Zenit, R. Motion of a Particle near a Rough Wall in a Viscous Shear Flow. Journal of Fluid Mechanics 2007, 570, 431–453. (28) Parsi, F.; Gadala-Maria, F. Fore-and-Aft Asymmetry in a Concentrated Suspension of Solid Spheres. Journal of Rheology 1987, 31 (8), 725–732. (29) He, K.; Xu, L.; Gao, Y.; Yin, X.; Neeves, K. B. Evaluation of Surfactant Performance in Fracturing Fluids for Enhanced Well Productivity in Unconventional Reservoirs Using Rock-on-a-Chip Approach. Journal of Petroleum Science and Engineering 2015, 135, 531–541. (30) Papanikolaou, M.; Frank, M.; Drikakis, D. Nanoflow over a Fractal Surface. Physics of Fluids 2016, 28 (8), 82001. (31) Papanikolaou, M.; Frank, M.; Drikakis, D. Effects of Surface Roughness on Shear Viscosity. Physical Review E 2017, 95 (3). (32) Kalweit, M.; Drikakis, D. Multiscale Methods for Micro/nano Flows and Materials. Journal of Computational and Theoretical Nanoscience 2008, 5 (9), 1923–1938. (33) Williams, P. S.; Koch, T.; Giddings, J. Characterization of near-Wall Hydrodynamic Lift Forces Using Sedimentation Field-Flow Fractionation. Chem Eng Commun 1992, 111, 121–147. (34) Williams, P.; Moon, M. H.; Giddings, J. Influence of Accumulation Wall and Carrier Solution Composition on Lift Force in Sedimentation/steric Field-Flow Fractionation. Colloids and Surfaces A 1996, 113, 215–228. (35) Cevheri, N.; Yoda, M. Lift Forces on Colloidal Particles in Combined Electroosmotic and Poiseuille Flow. Langmuir 2014, 30 (46), 13771–13780.


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Figure 2 1 A 2 3 4 5 6 7 8 9 10 11 12 13 14 15 B 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 C 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


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