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Electro-osmosis of superimposed fluids in the presence of modulated charged surfaces in narrow confinements

Published online by Cambridge University Press:  10 July 2015

Shubhadeep Mandal ,
Uddipta Ghosh ,
Aditya Bandopadhyay  and
Suman Chakraborty
Shubhadeep Mandal
Affiliation:
Department of Mechanical Engineering, Indian Institute of Technology Kharagpur, Kharagpur, West Bengal - 721302, India
Uddipta Ghosh
Affiliation:
Department of Mechanical Engineering, Indian Institute of Technology Kharagpur, Kharagpur, West Bengal - 721302, India
Aditya Bandopadhyay
Affiliation:
Advanced Technology Development Center, Indian Institute of Technology Kharagpur, Kharagpur, West Bengal - 721302, India
Suman Chakraborty*
Affiliation:
Department of Mechanical Engineering, Indian Institute of Technology Kharagpur, Kharagpur, West Bengal - 721302, India Advanced Technology Development Center, Indian Institute of Technology Kharagpur, Kharagpur, West Bengal - 721302, India
*
†Email address for correspondence: suman@mech.iitkgp.ernet.in
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Abstract

In the present study, we attempt to analyse the electro-osmotic flow of two superimposed fluids through narrow confinements in the presence of axially modulated surface charges. We attempt to solve for the flow structure as well as the interface deformation by both analytical and numerical techniques. Approximate analytical solutions are obtained through asymptotic analysis for low deformations, whereas numerical solutions are obtained by applying the phase field formalism; the numerical solutions are obtained for small as well as large interfacial deformations. The analytical solutions are derived only for the transient deformation of the interface, neglecting the transience in the flow, i.e. the flow is assumed to be quasisteady. The numerical solutions, however, are derived including the effects of inertia and transients in the flow. We attempt to compare our analytical and numerical results and explore the effects of several physico-chemical parameters on the deformation of the interface as well as the nature of the flow. Our analysis reveals that parameters such as the modulation wavelength, surface tension (described through the capillary number), viscosity ratio, permittivity ratio and extent of asymmetry in the potential on the two walls are the major contributors to the deformation and the resulting flow features.

JFM classification

Micro-/Nano-fluid dynamics: Micro-/Nano-fluid dynamics
Type
Papers
Information
Journal of Fluid Mechanics , Volume 776 , 10 August 2015 , pp. 390 - 429
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Copyright
© 2015 Cambridge University Press 

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References

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.Google Scholar
Ajdari, A. 1995 Electro-osmosis on inhomogeneously charged surfaces. Phys. Rev. Lett. 75 (4), 755–758.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 Scholar
Ajdari, A. 2001 Transverse electrokinetic and microfluidic effects in micropatterned channels: lubrication analysis for slab geometries. Phys. Rev. E 65 (1), 016301.Google Scholar
Anderson, D. M., McFadden, G. B. & Wheeler, A. A. 1998 Diffuse-interface methods in fluid mechanics. Annu. Rev. Fluid Mech. 30 (1), 139–165.Google Scholar
Badalassi, V. E., Ceniceros, H. D. & Banerjee, S. 2003 Computation of multiphase systems with phase field models. J. Comput. Phys. 190 (2), 371–397.Google Scholar
Bahga, S. S., Vinogradova, O. I. & Bazant, M. Z. 2010 Anisotropic electro-osmotic flow over super-hydrophobic surfaces. J. Fluid Mech. 644, 245–255.Google Scholar
Bandyopadhyay, D. & Sharma, A. 2007 Electric field induced instabilities in thin confined bilayers. J. Colloid Interface Sci. 311 (2), 595–608.Google Scholar
Brask, A., Kutter, J. P. & Bruus, H. 2005 Long-term stable electroosmotic pump with ion exchange membranes. Lab on a Chip 5 (7), 730–738.CrossRefGoogle ScholarPubMed
Brust, M., Schaefer, C., Doerr, R., Pan, L., Garcia, M., Arratia, P. & Wagner, C. 2013 Rheology of human blood plasma: viscoelastic versus Newtonian behavior. Phys. Rev. Lett. 110 (7), 078305.Google Scholar
Chakraborty, S. 2007 Order parameter modeling of fluid dynamics in narrow confinements subjected to hydrophobic interactions. Phys. Rev. Lett. 99 (9), 094504.Google Scholar
Chakraborty, S. 2008 Order parameter description of electrochemical–hydrodynamic interactions in nanochannels. Phys. Rev. Lett. 101 (18), 184501.CrossRefGoogle ScholarPubMed
Chan, P. C.-H. & Leal, L. G. 1979 The motion of a deformable drop in a second-order fluid. J. Fluid Mech. 92 (01), 131–170.CrossRefGoogle Scholar
Chang, C.-C. & Yang, R.-J. 2008 Chaotic mixing in a microchannel utilizing periodically switching electro-osmotic recirculating rolls. Phys. Rev. E 77 (5), 056311.Google Scholar
Chaudhury, K., Ghosh, U. & Chakraborty, S. 2013 Substrate wettability induced alterations in convective heat transfer characteristics in microchannel flows: an order parameter approach. Intl J. Heat Mass Transfer 67, 1083–1095.Google Scholar
Chen, C.-K. & Cho, C.-C. 2007 Electrokinetically-driven flow mixing in microchannels with wavy surface. J. Colloid Interface Sci. 312 (2), 470–480.Google Scholar
Choi, W., Sharma, A., Qian, S., Lim, G. & Joo, S. W. 2011 On steady two-fluid electroosmotic flow with full interfacial electrostatics. J. Colloid Interface Sci. 357 (2), 521–526.Google Scholar
Das, S., Dubsky, P., van den Berg, A. & Eijkel, J. C. T. 2012 Concentration polarization in translocation of DNA through nanopores and nanochannels. Phys. Rev. Lett. 108 (13), 138101.Google Scholar
Dhar, J., Ghosh, U. & Chakraborty, S. 2014 Alterations in streaming potential in presence of time periodic pressure-driven flow of a power law fluid in narrow confinements with non-electrostatic ion–ion interactions. Electrophoresis 35 (5), 662–669.Google Scholar
Ding, H., Gilani, M. N. H. & Spelt, P. D. M. 2010 Sliding, pinch-off and detachment of a droplet on a wall in shear flow. J. Fluid Mech. 644, 217–244.Google Scholar
Esmaeeli, A. & Reddy, M. N. 2011 The electrohydrodynamics of superimposed fluids subjected to a non-uniform transverse electric field. Intl J. Multiphase Flow 37 (10), 1331–1347.Google Scholar
Gambhire, P. & Thaokar, R. 2014 Electrokinetic model for electric-field-induced interfacial instabilities. Phys. Rev. E 89 (3), 032409.Google Scholar
Gambhire, P. & Thaokar, R. M. 2010 Electrohydrodynamic instabilities at interfaces subjected to alternating electric field. Phys. Fluids 22 (6), 064103.Google Scholar
Gao, Y., Wang, C., Wong, T. N., Yang, C., Nguyen, N.-T. & Ooi, K. T. 2007 Electro-osmotic control of the interface position of two-liquid flow through a microchannel. J. Micromech. Microengng 17 (2), 358–366.CrossRefGoogle Scholar
Gao, Y., Wong, T. N., Yang, C. & Ooi, K. T. 2005 Transient two-liquid electroosmotic flow with electric charges at the interface. Colloids Surf. A 266 (1–3), 117–128.CrossRefGoogle Scholar
Ghosh, U. & Chakraborty, S. 2012 Patterned-wettability-induced alteration of electro-osmosis over charge-modulated surfaces in narrow confinements. Phys. Rev. E 85 (4), 046304.Google Scholar
Ghosh, U. & Chakraborty, S. 2013 Electrokinetics over charge-modulated surfaces in the presence of patterned wettability: role of the anisotropic streaming potential. Phys. Rev. E 88 (3), 033001.Google Scholar
Haiwang, L., Wong, T. N. & Nguyen, N.-T. 2010 Time-dependent model of mixed electroosmotic/pressure-driven three immiscible fluids in a rectangular microchannel. Intl J. Heat Mass Transfer 53 (4), 772–785.Google Scholar
Israelachvili, J. 2011 Intermolecular and Surface Forces, 3rd edn. Academic.Google Scholar
Jacqmin, D. 1999 Calculation of two-phase Navier–Stokes flows using phase-field modeling. J. Comput. Phys. 155 (1), 96–127.Google Scholar
Leal, L. G. 2007 Advanced Transport Phenomena. Cambridge University Press.Google Scholar
Li, F., Yin, X.-Y. & Yin, X.-Z. 2009a Transient growth in a two-fluid channel flow under normal electric field. Phys. Fluids 21 (9), 094105.Google Scholar
Li, H., Wong, T. N. & Nguyen, N.-T. 2009b Electroosmotic control of width and position of liquid streams in hydrodynamic focusing. Microfluid. Nanofluid. 7 (4), 489–497.CrossRefGoogle Scholar
Li, H., Wong, T. N. & Nguyen, N.-T. 2010a A tunable optofluidic lens based on combined effect of hydrodynamics and electroosmosis. Microfluid. Nanofluid. 10 (5), 1033–1043.Google Scholar
Li, H., Wong, T. N. & Nguyen, N.-T. 2010b Microfluidic switch based on combined effect of hydrodynamics and electroosmosis. Microfluid. Nanofluid. 10 (5), 965–976.Google Scholar
Mandal, S., Chaudhury, K. & Chakraborty, S. 2014 Transient dynamics of confined liquid drops in a uniform electric field. Phys. Rev. E 89 (5), 053020.Google Scholar
Mayur, M., Amiroudine, S., Lasseux, D. & Chakraborty, S. 2013 Maxwell stress-induced flow control of a free surface electro-osmotic flow in a rectangular microchannel. Microfluid. Nanofluid. 16 (4), 721–728.Google Scholar
Melcher, J. R. & Taylor, G. I. 1969 Electrohydrodynamics: a review of the role of interfacial shear stresses. Annu. Rev. Fluid Mech. 1 (1), 111–146.Google Scholar
Mondal, P. K., DasGupta, D. & Chakraborty, S. 2014a Interfacial dynamics of two immiscible fluids in spatially periodic porous media: the role of substrate wettability. Phys. Rev. E 90 (1), 013003.Google Scholar
Mondal, P. K., Ghosh, U., Bandopadhyay, A., DasGupta, D. & Chakraborty, S. 2013 Electric-field-driven contact-line dynamics of two immiscible fluids over chemically patterned surfaces in narrow confinements. Phys. Rev. E 88 (2), 023022.Google Scholar
Mondal, P. K., Ghosh, U., Bandopadhyay, A., DasGupta, D. & Chakraborty, S. 2014b Pulsating electric field modulated contact line dynamics of immiscible binary systems in narrow confinements under an electrical double layer phenomenon. Soft Matt. 10 (42), 8512–8523.Google Scholar
Mortensen, N., Olesen, L., Belmon, L. & Bruus, H. 2005 Electrohydrodynamics of binary electrolytes driven by modulated surface potentials. Phys. Rev. E 71 (5), 056306.Google Scholar
Ng, C.-O. & Chu, H. C. W. 2011 Electrokinetic flows through a parallel-plate channel with slipping stripes on walls. Phys. Fluids 23 (10), 102002.Google Scholar
Ozen, O., Aubry, N., Papageorgiou, D. T. & Petropoulos, P. G. 2006 Electrohydrodynamic linear stability of two immiscible fluids in channel flow. Electrochim. Acta 51 (25), 5316–5323.Google Scholar
Qian, T., Wang, X.-P. & Sheng, P. 2003 Molecular scale contact line hydrodynamics of immiscible flows. Phys. Rev. E 68 (1), 016306.Google Scholar
Ramachandran, A. & Leal, L. G. 2012 The effect of interfacial slip on the rheology of a dilute emulsion of drops for small capillary numbers. J. Rheol. 56 (6), 1555–1587.Google Scholar
Schäffer, E., Thurn-Albrecht, T., Russell, T. & Steiner, U. 2000 Electrically induced structure formation and pattern transfer. Nature 403 (6772), 874–877.CrossRefGoogle ScholarPubMed
Schäffer, E., Thurn-Albrecht, T., Russell, T. P. & Steiner, U. 2001 Electrohydrodynamic instabilities in polymer films. Europhys. Lett. 53 (4), 518–524.Google Scholar
Sibley, D. N., Nold, A. & Kalliadasis, S. 2013 Unifying binary fluid diffuse-interface models in the sharp-interface limit. J. Fluid Mech. 736, 5–43.Google Scholar
Squires, T. M. & Bazant, M. Z. 2004 Induced-charge electro-osmosis. J. Fluid Mech. 509, 217–252.Google Scholar
Stone, H. A., Stroock, A. D. & Ajdari, A. 2004 Engineering flows in small devices. Annu. Rev. Fluid Mech. 36 (1), 381–411.Google Scholar
Subramanian, R. S. & Balasubramaniam, R. 2005 The Motion of Bubbles and Drops in Reduced Gravity. Cambridge University Press.Google Scholar
Sugioka, H. 2010 Chaotic mixer using electro-osmosis at finite Péclet number. Phys. Rev. E 81 (3), 036306.Google Scholar
Than, P., Preziosi, L., Joseph, D. D. & Arney, M. 1988 Measurement of interfacial tension between immiscible liquids with the spinning rod tensiometer. J. Colloid Interface Sci. 124 (2), 552–559.Google Scholar
Thaokar, R. M. & Deshmukh, S. D. 2010 Rayleigh instability of charged drops and vesicles in the presence of counterions. Phys. Fluids 22 (3), 034107.Google Scholar
Thaokar, R. M. & Kumaran, V. 2005 Electrohydrodynamic instability of the interface between two fluids confined in a channel. Phys. Fluids 17 (8), 084104.Google Scholar
Tomar, G., Shankar, V., Sharma, A. & Biswas, G. 2007 Electrohydrodynamic instability of a confined viscoelastic liquid film. J. Non-Newtonian Fluid Mech. 143 (2–3), 120–130.CrossRefGoogle Scholar
Tseluiko, D., Blyth, M. G., Papageorgiou, D. T. & Vanden-Broeck, J.-M. 2008a Effect of an electric field on film flow down a corrugated wall at zero Reynolds number. Phys. Fluids 20 (4), 042103–042121.Google Scholar
Tseluiko, D., Blyth, M. G., Papageorgiou, D. T. & Vanden-Broeck, J.-M. 2008b Electrified viscous thin film flow over topography. J. Fluid Mech. 597, 449–475.Google Scholar
Tseluiko, D. & Papageorgiou, D. T. 2006 Wave evolution on electrified falling films. J. Fluid Mech. 556, 361–386.Google Scholar
Uguz, A. K. & Aubry, N. 2008 Quantifying the linear stability of a flowing electrified two-fluid layer in a channel for fast electric times for normal and parallel electric fields. Phys. Fluids 20 (9), 092103.Google Scholar
Veremieiev, S., Thompson, H. M., Scholle, M., Lee, Y. C. & Gaskell, P. H. 2012 Electrified thin film flow at finite Reynolds number on planar substrates featuring topography. Intl J. Multiphase Flow 44, 48–69.Google Scholar
Verma, R., Sharma, A., Kargupta, K. & Bhaumik, J. 2005 Electric field induced instability and pattern formation in thin liquid films. Langmuir 21 (8), 3710–3721.CrossRefGoogle ScholarPubMed
Voicu, N. E., Harkema, S. & Steiner, U. 2006 Electric-field-induced pattern morphologies in thin liquid films. Adv. Funct. Mater. 16 (7), 926–934.Google Scholar
Wang, C., Gao, Y., Nguyen, N.-T., Wong, T. N., Yang, C. & Ooi, K. T. 2005 Interface control of pressure-driven two-fluid flow in microchannels using electroosmosis. J. Micromech. Microengng 15 (12), 2289–2297.Google Scholar
Wang, X.-P., Qian, T. & Sheng, P. 2008 Moving contact line on chemically patterned surfaces. J. Fluid Mech. 605, 59–78.Google Scholar
Watanabe, M., Shirai, H. & Hirai, T. 2003 Liquid–liquid two-layer electrohydrodynamic flow system. Sensors Actuators B 94 (3), 267–270.Google Scholar
Wu, N. & Russel, W. B. 2005 Dynamics of the formation of polymeric microstructures induced by electrohydrodynamic instability. Appl. Phys. Lett. 86 (24), 241912.Google Scholar
Wu, N. & Russel, W. B. 2009 Micro- and nano-patterns created via electrohydrodynamic instabilities. Nanotoday 4 (2), 180–192.Google Scholar
Yeoh, H. K., Xu, Q. & Basaran, O. A. 2007 Equilibrium shapes and stability of a liquid film subjected to a non-uniform electric field. Phys. Fluids 19 (11), 114111.Google Scholar
Yue, P., Feng, J. J., Liu, C. & Shen, J. 2004 A diffuse-interface method for simulating two-phase flows of complex fluids. J. Fluid Mech. 515, 293–317.Google Scholar
Zhang, J., He, G. & Liu, F. 2006 Electro-osmotic flow and mixing in heterogeneous microchannels. Phys. Rev. E 73 (5), 056305.Google Scholar
Zhang, J., Zahn, J. D. & Lin, H. 2011 A general analysis for the electrohydrodynamic instability of stratified immiscible fluids. J. Fluid Mech. 681, 293–310.Google Scholar