Skip to main content Accessibility help

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

  • Shubhadeep Mandal (a1), Uddipta Ghosh (a1), Aditya Bandopadhyay (a2) and Suman Chakraborty (a1) (a2)


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.


Corresponding author

Email address for correspondence:


Hide All
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, 277286.
Ajdari, A. 1995 Electro-osmosis on inhomogeneously charged surfaces. Phys. Rev. Lett. 75 (4), 755758.
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), 49965005.
Ajdari, A. 2001 Transverse electrokinetic and microfluidic effects in micropatterned channels: lubrication analysis for slab geometries. Phys. Rev. E 65 (1), 016301.
Anderson, D. M., McFadden, G. B. & Wheeler, A. A. 1998 Diffuse-interface methods in fluid mechanics. Annu. Rev. Fluid Mech. 30 (1), 139165.
Badalassi, V. E., Ceniceros, H. D. & Banerjee, S. 2003 Computation of multiphase systems with phase field models. J. Comput. Phys. 190 (2), 371397.
Bahga, S. S., Vinogradova, O. I. & Bazant, M. Z. 2010 Anisotropic electro-osmotic flow over super-hydrophobic surfaces. J. Fluid Mech. 644, 245255.
Bandyopadhyay, D. & Sharma, A. 2007 Electric field induced instabilities in thin confined bilayers. J. Colloid Interface Sci. 311 (2), 595608.
Brask, A., Kutter, J. P. & Bruus, H. 2005 Long-term stable electroosmotic pump with ion exchange membranes. Lab on a Chip 5 (7), 730738.
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.
Chakraborty, S. 2007 Order parameter modeling of fluid dynamics in narrow confinements subjected to hydrophobic interactions. Phys. Rev. Lett. 99 (9), 094504.
Chakraborty, S. 2008 Order parameter description of electrochemical–hydrodynamic interactions in nanochannels. Phys. Rev. Lett. 101 (18), 184501.
Chan, P. C.-H. & Leal, L. G. 1979 The motion of a deformable drop in a second-order fluid. J. Fluid Mech. 92 (01), 131170.
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.
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, 10831095.
Chen, C.-K. & Cho, C.-C. 2007 Electrokinetically-driven flow mixing in microchannels with wavy surface. J. Colloid Interface Sci. 312 (2), 470480.
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), 521526.
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.
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), 662669.
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, 217244.
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), 13311347.
Gambhire, P. & Thaokar, R. 2014 Electrokinetic model for electric-field-induced interfacial instabilities. Phys. Rev. E 89 (3), 032409.
Gambhire, P. & Thaokar, R. M. 2010 Electrohydrodynamic instabilities at interfaces subjected to alternating electric field. Phys. Fluids 22 (6), 064103.
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), 358366.
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), 117128.
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.
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.
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), 772785.
Israelachvili, J. 2011 Intermolecular and Surface Forces, 3rd edn. Academic.
Jacqmin, D. 1999 Calculation of two-phase Navier–Stokes flows using phase-field modeling. J. Comput. Phys. 155 (1), 96127.
Leal, L. G. 2007 Advanced Transport Phenomena. Cambridge University Press.
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.
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), 489497.
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), 10331043.
Li, H., Wong, T. N. & Nguyen, N.-T. 2010b Microfluidic switch based on combined effect of hydrodynamics and electroosmosis. Microfluid. Nanofluid. 10 (5), 965976.
Mandal, S., Chaudhury, K. & Chakraborty, S. 2014 Transient dynamics of confined liquid drops in a uniform electric field. Phys. Rev. E 89 (5), 053020.
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), 721728.
Melcher, J. R. & Taylor, G. I. 1969 Electrohydrodynamics: a review of the role of interfacial shear stresses. Annu. Rev. Fluid Mech. 1 (1), 111146.
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.
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.
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), 85128523.
Mortensen, N., Olesen, L., Belmon, L. & Bruus, H. 2005 Electrohydrodynamics of binary electrolytes driven by modulated surface potentials. Phys. Rev. E 71 (5), 056306.
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.
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), 53165323.
Qian, T., Wang, X.-P. & Sheng, P. 2003 Molecular scale contact line hydrodynamics of immiscible flows. Phys. Rev. E 68 (1), 016306.
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), 15551587.
Schäffer, E., Thurn-Albrecht, T., Russell, T. & Steiner, U. 2000 Electrically induced structure formation and pattern transfer. Nature 403 (6772), 874877.
Schäffer, E., Thurn-Albrecht, T., Russell, T. P. & Steiner, U. 2001 Electrohydrodynamic instabilities in polymer films. Europhys. Lett. 53 (4), 518524.
Sibley, D. N., Nold, A. & Kalliadasis, S. 2013 Unifying binary fluid diffuse-interface models in the sharp-interface limit. J. Fluid Mech. 736, 543.
Squires, T. M. & Bazant, M. Z. 2004 Induced-charge electro-osmosis. J. Fluid Mech. 509, 217252.
Stone, H. A., Stroock, A. D. & Ajdari, A. 2004 Engineering flows in small devices. Annu. Rev. Fluid Mech. 36 (1), 381411.
Subramanian, R. S. & Balasubramaniam, R. 2005 The Motion of Bubbles and Drops in Reduced Gravity. Cambridge University Press.
Sugioka, H. 2010 Chaotic mixer using electro-osmosis at finite Péclet number. Phys. Rev. E 81 (3), 036306.
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), 552559.
Thaokar, R. M. & Deshmukh, S. D. 2010 Rayleigh instability of charged drops and vesicles in the presence of counterions. Phys. Fluids 22 (3), 034107.
Thaokar, R. M. & Kumaran, V. 2005 Electrohydrodynamic instability of the interface between two fluids confined in a channel. Phys. Fluids 17 (8), 084104.
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), 120130.
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), 042103042121.
Tseluiko, D., Blyth, M. G., Papageorgiou, D. T. & Vanden-Broeck, J.-M. 2008b Electrified viscous thin film flow over topography. J. Fluid Mech. 597, 449475.
Tseluiko, D. & Papageorgiou, D. T. 2006 Wave evolution on electrified falling films. J. Fluid Mech. 556, 361386.
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.
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, 4869.
Verma, R., Sharma, A., Kargupta, K. & Bhaumik, J. 2005 Electric field induced instability and pattern formation in thin liquid films. Langmuir 21 (8), 37103721.
Voicu, N. E., Harkema, S. & Steiner, U. 2006 Electric-field-induced pattern morphologies in thin liquid films. Adv. Funct. Mater. 16 (7), 926934.
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), 22892297.
Wang, X.-P., Qian, T. & Sheng, P. 2008 Moving contact line on chemically patterned surfaces. J. Fluid Mech. 605, 5978.
Watanabe, M., Shirai, H. & Hirai, T. 2003 Liquid–liquid two-layer electrohydrodynamic flow system. Sensors Actuators B 94 (3), 267270.
Wu, N. & Russel, W. B. 2005 Dynamics of the formation of polymeric microstructures induced by electrohydrodynamic instability. Appl. Phys. Lett. 86 (24), 241912.
Wu, N. & Russel, W. B. 2009 Micro- and nano-patterns created via electrohydrodynamic instabilities. Nanotoday 4 (2), 180192.
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.
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, 293317.
Zhang, J., He, G. & Liu, F. 2006 Electro-osmotic flow and mixing in heterogeneous microchannels. Phys. Rev. E 73 (5), 056305.
Zhang, J., Zahn, J. D. & Lin, H. 2011 A general analysis for the electrohydrodynamic instability of stratified immiscible fluids. J. Fluid Mech. 681, 293310.
MathJax is a JavaScript display engine for mathematics. For more information see

JFM classification


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed