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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: [email protected]
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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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