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Lubrication theory for electro-osmotic flow in a slit microchannel with the Phan-Thien and Tanner model

Published online by Cambridge University Press:  28 March 2013

O. Bautista ,
S. Sánchez ,
J. C. Arcos  and
F. Méndez
O. Bautista*
Affiliation:
ESIME Azcapotzalco, Instituto Politécnico Nacional, Av. de las Granjas No. 682, Col. Santa Catarina, Del. Azcapotzalco, México, D. F. 02250, Mexico
S. Sánchez
Affiliation:
Departamento de Termofluidos, Facultad de Ingeniería, UNAM México, D. F. 04510, Mexico
J. C. Arcos
Affiliation:
ESIME Azcapotzalco, Instituto Politécnico Nacional, Av. de las Granjas No. 682, Col. Santa Catarina, Del. Azcapotzalco, México, D. F. 02250, Mexico
F. Méndez
Affiliation:
Departamento de Termofluidos, Facultad de Ingeniería, UNAM México, D. F. 04510, Mexico
*
†Email address for correspondence: obautista@ipn.mx
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Abstract

In this work the purely electro-osmotic flow of a viscoelastic liquid, which obeys the simplified Phan-Thien–Tanner (sPTT) constitutive equation, is solved numerically and asymptotically by using the lubrication approximation. The analysis includes Joule heating effects caused by an imposed electric field, where the viscosity function, relaxation time and electrical conductivity of the liquid are assumed to be temperature-dependent. Owing to Joule heating effects, temperature gradients in the liquid make the fluid properties change within the microchannel, altering the electric potential and flow fields. A consequence of the above is the appearance of an induced pressure gradient along the microchannel, which in turn modifies the normal plug-like electro-osmotic velocity profiles. In addition, it is pointed out that, depending on the fluid rheology and the used values of the dimensionless parameters, the velocity, temperature and pressure profiles in the fluid are substantially modified. Also, the finite thermal conductivity of the microchannel wall was considered in the analysis. The dimensionless temperature profiles in the fluid and the microchannel wall are obtained as function of the dimensionless parameters involved in the analysis, and the interactions between the coupled momentum, thermal energy and potential electric equations are examined in detail. A comparison between the numerical predictions and the asymptotic solutions was made, and reasonable agreement was found.

JFM classification

Low-Reynolds-number flows: Lubrication theory Micro-/Nano-fluid dynamics: Microfluidics Non-Newtonian Flows: Non-Newtonian Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 722 , 10 May 2013 , pp. 496 - 532
Copyright
©2013 Cambridge University Press

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References

Adjari, A. 1995 Electro-osmosis on inhomogenously charged surfaces. Phys. Rev. Lett. 4, 755–759.Google Scholar
Adjari, 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, 4996–5005.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, 50–63.Google Scholar
Afonso, A. M., Alves, M. A. & Pinho, F. T. 2010 Electro-osmotic flow of viscoelastic fluids in microchannels under asymmetric zeta potentials. J. Engng Maths 1–16.Google Scholar
Anderson, J. L. & Idol, W. K. 1985 Electroosmosis through pores with nonuniformly charged walls. Chem. Engng Commun. 38, 93–106.CrossRefGoogle Scholar
Babaie, A., Saidi, M. H. & Sadeghi, A. 2012 Electroosmotic flow of power-law fluids with temperature dependent properties. J. Non-Newtonian Fluid Mech. 185–186, 49–57.CrossRefGoogle Scholar
Berli, C. L. A. & Olivares, M. L. 2008 Electrokinetic flow of non-Newtonian fluids in microchannels. J. Colloid Interface Sci. 320, 582–589.CrossRefGoogle ScholarPubMed
Bruus, H. 2008 Theoretical Microfluidics. Oxford University Press.Google Scholar
Chakraborty, S. 2007 Electroosmotically driven capillary transport of typical non-Newtonian biofluids in rectangular microchannels. Anal. Chim. Acta 605, 175–184.CrossRefGoogle ScholarPubMed
Chen, C.-H. 2011 Electro-osmotic heat transfer of non-Newtonian fluid flow in microchannels. Trans. ASME: J. Heat Transfer 133, 1–10.CrossRefGoogle Scholar
Chen, C.-H., Lin, H., Lele, S. K. & Santiago, J. G. 2005 Convective and absolute electrokinetic instability with conductivity gradients. J. Fluid Mech. 524, 263–303.Google Scholar
Coelho, P. M., Alves, M. A. & Pinho, F. T. 2012 Forced convection in electro-osmotic/poiseuille micro-channel flows of viscoelastic fluids: fully developed flow with imposed wall heat flux. Microfluid Nanofluid 12, 431–449.Google Scholar
Denn, M. M. 2008 Polymer Melt Processing. Foundations in Fluid Mechanics and Heat Transfer, Cambridge University Press.CrossRefGoogle Scholar
Escandón, J. P., Bautista, O., Méndez, F. & Bautista, E. 2011 Theoretical conjugate heat transfer analysis in a parallel flat plate microchannel under electro-osmotic and pressure forces with a Phan-Thien–Tanner fluid. Intl J. Therm. Sci. 50, 1022–1030.Google 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
Ghosal, S. 2004 Fluid mechanics of electroosmotic flow and its effect on band broadening in capillary electrophoresis. Electrophoresis 25, 214–228.CrossRefGoogle ScholarPubMed
Herr, A. E., Molho, J. I., Santiago, J. G., Mungal, M. G. & Kenny, T. W. 2000 Electroosmotic capillary flow with nonuniform zeta potential. Analyt. Chem. 72, 1053–1057.Google Scholar
Huang, K.-D. & Yang, R.-J. 2006 Numerical modeling of the Joule heating effect on electrokinetic flow focusing. Electrophoresis 27, 1957–1966.Google Scholar
Karniadakis, G., Beskok, A. & Aluru, N. 2005 Microflows and Nanoflows. Springer.Google Scholar
Kirby, B. J. & Hasselbrink, E. F. 2004 Zeta potential of microfluidic substrates: 1. Theory, experimental techniques, and effects on separations. Electrophoresis 25, 187–202.CrossRefGoogle ScholarPubMed
Li, D. (Ed.) 2008 Encyclopedia of Microfluidics and Nanofluidics, vol. XXXIII. Springer.CrossRefGoogle Scholar
Lin, H., Storey, B. D., Oddy, M. H., Chen, C.-H. & Santiago, J. G. 2004 Instability of electrokinetic microchannel flows with conductivity gradients. Phys. Fluids 16, 1922–1935.CrossRefGoogle Scholar
Lin, H., Storey, B. D. & Santiago, J. G. 2008 A depth-averaged electrokinetic flow model for shallow microchannels. J. Fluid Mech. 608, 43–70.CrossRefGoogle Scholar
Mallinson, G. D. & de Vahl Davis, G. 1973 The method of the false transient for the solution of couple elliptic equations. J. Comput. Phys. 12, 435–461.CrossRefGoogle Scholar
Maranzana, G., Perry, I. & Maillet, D. 2004 Mini and micro-channels: influence of axial conduction in the walls. Intl J. Heat Mass Transfer 47, 3993–4004.CrossRefGoogle Scholar
Masliyah, J. & Bhattacharjee, S. 2006 Electrokinetic and Colloid Transport Phenomena. Wiley-Interscience.Google Scholar
Northrop, P. W. C., Ramachandran, P. A., Schiesser, W. E. & Subramanian, V. R. 2013 A robust false transient method of lines for elliptic partial differential equations. Chem. Engng Sci. 90, 32–39.Google Scholar
Park, H. M. & Lee, W. M. 2008 Helmholtz–Smoluchowski velocity for viscoelastic electroosmotic flows. J. Colloid Interface Sci. 317, 631–636.CrossRefGoogle ScholarPubMed
Patankar, S. V. 1980 Numerical Heat Transfer and Fluid Flow. Hemisphere.Google Scholar
Phan-Thien, N. & Tanner, R. I. 1977 A new constitutive equation derived from network theory. J. Non-Newtonian Fluid Mech. 2, 353–365.CrossRefGoogle Scholar
Probstein, R. F. 1994 Physicochemical Hydrodynamics. John Wiley and Sons.Google Scholar
Reuss, F. F. 1809 Sur un nouvel effet de l’électricitè galvanique. Mémoires de la Socité Impériale des Naturalistes de Moscou, vol. 2. pp. 327–337.Google Scholar
Sadeghi, A., Saidi, M. H. & Mozafari, A. A. 2011 Heat transfer due to electroosmotic flow of viscoelastic fluids in a slit microchannel. Intl J. Heat Mass Transfer 54, 4069–4077.Google Scholar
Saville, D. A. 1977 Electrokinetic effects with small particles. Annu. Rev. Fluid Mech. 9, 321–337.CrossRefGoogle Scholar
Sounart, T. L. & Baygents, J. C. 2007 Lubrication theory for electro-osmotic flow in a non-uniform electrolyte. J. Fluid Mech. 576, 139–172.Google Scholar
Stone, H. A., Stroock, A. D. & Ajdari, A. 2004 Engineering flows in small devices: microfluidics toward a lab-on-a-chip. Annu. Rev. Biophys. Biomol. Struct. 36, 381–441.Google Scholar
Tang, G., Yan, D., Yang, C., Gong, H., Chai, C. & Lam, Y. 2007 Joule heating and its effects on electrokinetic transport of solutes in rectangular microchannels. Sensors Actuators A 139, 221–232.CrossRefGoogle Scholar
Tang, G., Yang, C., Chai, J. & Gong, H. 2004 Joule heating effect on electroosmotic flow and mass species transport in a microcapillary. Intl J. Heat Mass Transfer 47, 215–227.Google Scholar
Tannehill, J., Anderson, D. & Pletcher, R. 1997 Computational Fluid Mechanics and Heat Transfer. Taylor & Francis.Google Scholar
Tanner, R. I. 2002 Engineering Rehology. Oxford University Press.Google Scholar
Xuan, X. 2008 Joule heating in electrokinetic flow. Electrophoresis 298, 33–43.Google Scholar
Xuan, X. & Li, D. 2005 Analytical study of Joule heating effects on electrokinetic transportation in capillary electrophoresis. J. Chromatogr. A 1064, 227–237.CrossRefGoogle ScholarPubMed
Xuan, X., Sinton, D. & Li, D. 2004a Thermal end effects on electroosmotic flow in a capillary. Intl J. Heat Mass Transfer 47, 3145–3157.Google Scholar
Xuan, X., Xu, B., Sinton, D. & Li, D. 2004b Electroosmotic flow with joule heating effects. Lab on a chip 4, 230–236.CrossRefGoogle ScholarPubMed
Zhao, C. & Yang, C. 2011 Electro-osmotic mobility of non-Newtonian fluids. Biomicrofluidics 5, 1–8.CrossRefGoogle ScholarPubMed
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, 503–510.Google Scholar