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Flow of power-law liquids in a Hele-Shaw cell driven by non-uniform electro-osmotic slip in the case of strong depletion

Published online by Cambridge University Press:  18 October 2016

Evgeniy Boyko ,
Moran Bercovici  and
Amir D. Gat
Evgeniy Boyko
Affiliation:
Faculty of Mechanical Engineering, Technion – Israel Institute of Technology, Haifa 3200003, Israel
Moran Bercovici*
Affiliation:
Faculty of Mechanical Engineering, Technion – Israel Institute of Technology, Haifa 3200003, Israel
Amir D. Gat*
Affiliation:
Faculty of Mechanical Engineering, Technion – Israel Institute of Technology, Haifa 3200003, Israel
*
†Email addresses for correspondence: [email protected], [email protected]
†Email addresses for correspondence: [email protected], [email protected]
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Abstract

We analyse flow of non-Newtonian fluids in a Hele-Shaw cell, subjected to spatially non-uniform electro-osmotic slip. Motivated by their potential use for increasing the characteristic pressure fields, we specifically focus on power-law fluids with wall depletion properties. We derive a $p$-Poisson equation governing the pressure field, as well as a set of linearized equations representing its asymptotic approximation for weakly non-Newtonian behaviour. To investigate the effect of non-Newtonian properties on the resulting fluidic pressure and velocity, we consider several configurations in one and two dimensions, and calculate both exact and approximate solutions. We show that the asymptotic approximation is in good agreement with exact solutions even for fluids with significant non-Newtonian behaviour, allowing its use in the analysis and design of microfluidic systems involving electrokinetic transport of such fluids.

JFM classification

Low-Reynolds-number flows: Hele-Shaw flows Micro-/Nano-fluid dynamics: Microfluidics Non-Newtonian Flows: Non-Newtonian Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 807 , 25 November 2016 , pp. 235 - 257
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Copyright
© 2016 Cambridge University Press 

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References

Abramowitz, M. & Stegun, I. A. 1964 Handbook of Mathematical Functions. Dover.Google Scholar
Afonso, A. M., Alves, M. A. & Pinho, F. T. 2009 Analytical solution of mixed electro-osmotic/pressure driven flows of viscoelastic fluids in microchannels. J. Non-Newtonian Fluid Mech. 159 (1), 50–63.CrossRefGoogle Scholar
Afonso, A. M., Alves, M. A. & Pinho, F. T. 2011 Electro-osmotic flow of viscoelastic fluids in microchannels under asymmetric zeta potentials. J. Engng Maths 71 (1), 15–30.CrossRefGoogle Scholar
Afonso, A. M., Alves, M. A. & Pinho, F. T. 2013 Analytical solution of two-fluid electro-osmotic flows of viscoelastic fluids. J. Colloid Interface Sci. 395, 277–286.CrossRefGoogle ScholarPubMed
Ajdari, A. 1995 Electro-osmosis on inhomogeneously charged surfaces. Phys. Rev. Lett. 75 (4), 755–759.CrossRefGoogle ScholarPubMed
Ajdari, A. 1996 Generation of transverse fluid currents and forces by an electric field: electro-osmosis on charge-modulated and undulated surfaces. Phys. Rev. E 53 (5), 4996–5005.Google ScholarPubMed
Ajdari, A. 2001 Transverse electrokinetic and microfluidic effects in micropatterned channels: lubrication analysis for slab geometries. Phys. Rev. E 65 (1), 016301.Google ScholarPubMed
Anderson, J. L. 1989 Colloid transport by interfacial forces. Annu. Rev. Fluid Mech. 21 (1), 61–99.CrossRefGoogle Scholar
Anderson, J. L. & Idol, W. K. 1985 Electroosmosis through pores with nonuniformly charged walls. Chem. Engng Commun. 38 (3–6), 93–106.CrossRefGoogle Scholar
Aronsson, G. & Janfalk, U. 1992 On Hele-Shaw flow of power-law fluids. Eur. J. Appl. Maths 3 (04), 343–366.CrossRefGoogle Scholar
Babaie, A., Sadeghi, A. & Saidi, M. H. 2011 Combined electroosmotically and pressure driven flow of power-law fluids in a slit microchannel. J. Non-Newtonian Fluid Mech. 166 (14), 792–798.CrossRefGoogle Scholar
Barnes, H. A. 1995 A review of the slip (wall depletion) of polymer solutions, emulsions and particle suspensions in viscometers: its cause, character, and cure. J. Non-Newtonian Fluid Mech. 56 (3), 221–251.CrossRefGoogle Scholar
Berli, C. L. A. 2010 Output pressure and efficiency of electrokinetic pumping of non-Newtonian fluids. Microfluid. Nanofluid. 8 (2), 197–207.CrossRefGoogle Scholar
Berli, C. L. A. & Olivares, M. L. 2008 Electrokinetic flow of non-Newtonian fluids in microchannels. J. Colloid Interface Sci. 320 (2), 582–589.CrossRefGoogle ScholarPubMed
Bird, R. B., Armstrong, R. C. & Hassager, O. 1987 Dynamics of Polymeric Liquids, volume 1: Fluid Mechanics, 2nd edn. John Wiley.Google Scholar
Boyko, E., Rubin, S., Gat, A. D. & Bercovici, M. 2015 Flow patterning in Hele-Shaw configurations using non-uniform electro-osmotic slip. Phys. Fluids 27 (10), 102001.CrossRefGoogle Scholar
Brotherton, C. M. & Davis, R. H. 2004 Electroosmotic flow in channels with step changes in zeta potential and cross section. J. Colloid Interface Sci. 270 (1), 242–246.CrossRefGoogle ScholarPubMed
Das, S. & Chakraborty, S. 2006 Analytical solutions for velocity, temperature and concentration distribution in electroosmotic microchannel flows of a non-Newtonian bio-fluid. Anal. Chim. Acta 559 (1), 15–24.CrossRefGoogle Scholar
Derjaguin, B. V., Dukhin, S. S. & Korotkova, A. A. 1961 Diffusiophoresis in electrolyte solutions and its role in the mechanism of film formation from rubber latexes by the method of ionic deposition. Kolloidn. Z. 23 (1), 53.Google Scholar
Derjaguin, B. V., Dukhin, S. S. & Korotkova, A. A. 1993 Diffusiophoresis in electrolyte solutions and its role in the mechanism of the formation of films from caoutchouc latexes by the ionic deposition method. Prog. Surf. Sci. 43 (1), 153–158.CrossRefGoogle Scholar
Dhinakaran, S., Afonso, A. M., Alves, M. A. & Pinho, F. T. 2010 Steady viscoelastic fluid flow between parallel plates under electro-osmotic forces: Phan–Thien–Tanner model. J. Colloid Interface Sci. 344 (2), 513–520.CrossRefGoogle ScholarPubMed
Erickson, D. & Li, D. 2002 Influence of surface heterogeneity on electrokinetically driven microfluidic mixing. Langmuir 18 (5), 1883–1892.CrossRefGoogle Scholar
Erickson, D. & Li, D. 2003 Three-dimensional structure of electroosmotic flow over heterogeneous surfaces. J. Phys. Chem. Ref. Data 107 (44), 12212–12220.CrossRefGoogle Scholar
Ghannam, M. T. & Esmail, M. N. 1997 Rheological properties of carboxymethyl cellulose. J. Appl. Polym. Sci. 64 (2), 289–301.3.0.CO;2-N>CrossRefGoogle Scholar
Ghosal, S. 2002 Lubrication theory for electro-osmotic flow in a microfluidic channel of slowly varying cross-section and wall charge. J. Fluid Mech. 459, 103–128.CrossRefGoogle Scholar
Ghosh, U. & Chakraborty, S. 2015 Electroosmosis of viscoelastic fluids over charge modulated surfaces in narrow confinements. Phys. Fluids 27 (6), 062004.CrossRefGoogle Scholar
Huang, Y., Chen, J., Wong, T. & Liow, J. 2016 Experimental and theoretical investigations of non-Newtonian electro-osmotic driven flow in rectangular microchannels. Soft Matt. 12 (29), 6206–6213.CrossRefGoogle ScholarPubMed
Hunter, R. J. 2000 Foundations of Colloid Science. Oxford University Press.Google Scholar
Irgens, F. 2014 Rheology and Non-Newtonian Fluids. Springer.CrossRefGoogle Scholar
Khair, A. S. & Squires, T. M. 2008a Fundamental aspects of concentration polarization arising from nonuniform electrokinetic transport. Phys. Fluids 20 (8), 087102.Google Scholar
Khair, A. S. & Squires, T. M. 2008b Surprising consequences of ion conservation in electro-osmosis over a surface charge discontinuity. J. Fluid Mech. 615, 323–334.CrossRefGoogle Scholar
Kim, J.-Y., Song, J.-Y., Lee, E.-J. & Park, S.-K. 2003 Rheological properties and microstructures of carbopol gel network system. Colloid Polym. Sci. 281 (7), 614–623.CrossRefGoogle Scholar
Lin, C.-X. & Ko, S.-Y. 1995 Effects of temperature and concentration on the steady shear properties of aqueous solutions of carbopol and CMC. Intl Commun. Heat Mass Transfer 22 (2), 157–166.CrossRefGoogle Scholar
Lyklema, J. 1995 Fundamentals of Interface and Colloid Science, volume II: Solid–Liquid Interfaces. Academic.Google Scholar
Ng, C. & Qi, C. 2014 Electroosmotic flow of a power-law fluid in a non-uniform microchannel. J. Non-Newtonian Fluid Mech. 208, 118–125.CrossRefGoogle Scholar
Olivares, M. L., Vera-Candioti, L. & Berli, C. L. A. 2009 The EOF of polymer solutions. Electrophoresis 30 (5), 921–928.CrossRefGoogle ScholarPubMed
Paul, P. H.2008 Electrokinetic device employing a non-Newtonian liquid. US Patent, US7429317.Google Scholar
Prieve, D. C., Anderson, J. L., Ebel, J. P. & Lowell, M. E. 1984 Motion of a particle generated by chemical gradients. Part 2. Electrolytes. J. Fluid Mech. 148, 247–269.CrossRefGoogle Scholar
Qi, C. & Ng, C. 2015 Electroosmotic flow of a power-law fluid in a slit microchannel with gradually varying channel height and wall potential. Eur. J. Mech. (B/Fluids) 52, 160–168.CrossRefGoogle Scholar
Qian, S. & Bau, H. H. 2002 A chaotic electroosmotic stirrer. Anal. Chem. 74 (15), 3616–3625.CrossRefGoogle ScholarPubMed
Roberts, G. P. & Barnes, H. A. 2001 New measurements of the flow-curves for carbopol dispersions without slip artefacts. Rheol. Acta 40 (5), 499–503.CrossRefGoogle Scholar
Ross, A. B., Wilson, S. K. & Duffy, B. R. 1999 Blade coating of a power-law fluid. Phys. Fluids 11 (5), 958–970.CrossRefGoogle Scholar
Rubin, S., Tulchinsky, A., Gat, A. & Bercovici, M.2016 Elastic deformations driven by non-uniform lubrication flows. arXiv:1607.02451.CrossRefGoogle Scholar
Schnitzer, O. & Yariv, E. 2012 Macroscale description of electrokinetic flows at large zeta potentials: nonlinear surface conduction. Phys. Rev. E 86 (2), 021503.Google ScholarPubMed
Sousa, J. J., Afonso, A. M., Pinho, F. T. & Alves, M. A. 2011 Effect of the skimming layer on electroosmotic-Poiseuille flows of viscoelastic fluids. Microfluid. Nanofluid. 10 (1), 107–122.CrossRefGoogle Scholar
Stroock, A. D., Weck, M., Chiu, D. T., Huck, W. T. S., Kenis, P. J. A., Ismagilov, R. F. & Whitesides, G. M. 2000 Patterning electro-osmotic flow with patterned surface charge. Phys. Rev. Lett. 84 (15), 3314.CrossRefGoogle ScholarPubMed
Tang, G. H., Li, X. F., He, Y. L. & Tao, W. Q. 2009 Electroosmotic flow of non-Newtonian fluid in microchannels. J. Non-Newtonian Fluid Mech. 157 (1), 133–137.CrossRefGoogle Scholar
Vakili, M. A., Sadeghi, A., Saidi, M. H. & Mozafari, A. A. 2012 Electrokinetically driven fluidic transport of power-law fluids in rectangular microchannels. Colloids Surf. A 414, 440–456.CrossRefGoogle Scholar
Vasu, N. & De, S. 2010 Electroosmotic flow of power-law fluids at high zeta potentials. Colloids Surf. A 368 (1), 44–52.CrossRefGoogle Scholar
Yariv, E. 2004 Electro-osmotic flow near a surface charge discontinuity. J. Fluid Mech. 521, 181–189.CrossRefGoogle Scholar
Zhang, J., He, G. & Liu, F. 2006 Electroosmotic flow and mixing in heterogeneous microchannels. Phys. Rev. E 73 (5), 056305.Google ScholarPubMed
Zhao, C. & Yang, C. 2010 Nonlinear Smoluchowski velocity for electroosmosis of power-law fluids over a surface with arbitrary zeta potentials. Electrophoresis 31 (5), 973–979.CrossRefGoogle Scholar
Zhao, C. & Yang, C. 2011 An exact solution for electroosmosis of non-Newtonian fluids in microchannels. J. Non-Newtonian Fluid Mech. 166 (17), 1076–1079.CrossRefGoogle Scholar
Zhao, C. & Yang, C. 2013a Electrokinetics of non-Newtonian fluids: a review. Adv. Colloid Interface Sci. 201, 94–108.CrossRefGoogle ScholarPubMed
Zhao, C. & Yang, C. 2013b Electroosmotic flows of non-Newtonian power-law fluids in a cylindrical microchannel. Electrophoresis 34 (5), 662–667.CrossRefGoogle Scholar
Zhao, C., Zholkovskij, E., Masliyah, J. H. & Yang, C. 2008 Analysis of electroosmotic flow of power-law fluids in a slit microchannel. J. Colloid Interface Sci. 326 (2), 503–510.CrossRefGoogle Scholar