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A depth-averaged electrokinetic flow model for shallow microchannels

Published online by Cambridge University Press:  11 July 2008

HAO LIN ,
BRIAN D. STOREY  and
JUAN G. SANTIAGO
HAO LIN
Affiliation:
Mechanical Engineering Department, Stanford University, Stanford, CA 94305, USA
BRIAN D. STOREY
Affiliation:
Franklin W. Olin College of Engineering, Needham, MA 02492, USA
JUAN G. SANTIAGO
Affiliation:
Mechanical Engineering Department, Stanford University, Stanford, CA 94305, USA
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Abstract

Electrokinetic flows with heterogeneous conductivity configuration occur widely in microfluidic applications such as sample stacking and multidimensional assays. Electromechanical coupling in these flows may lead to complex flow phenomena, such as sample dispersion due to electro-osmotic velocity mismatch, and electrokinetic instability (EKI). In this work we develop a generalized electrokinetic model suitable for the study of microchannel flows with conductivity gradients and shallow-channel geometry. An asymptotic analysis is performed with the channel depth-to-width ratio as a smallness parameter, and the three-dimensional equations are reduced to a set of depth-averaged equations governing in-plane flow dynamics. The momentum equation uses a Darcy–Brinkman–Forchheimer-type formulation, and the convective–diffusive transport of the conductivity field in the depth direction manifests itself as a dispersion effect on the in-plane conductivity field. The validity of the model is assessed by comparing the numerical results with full three-dimensional direct numerical simulations, and experimental data. The depth-averaged equations provide the accuracy of three-dimensional modelling with a convenient two-dimensional equation set applicable to a wide class of microfluidic devices.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 608 , 10 August 2008 , pp. 43 - 70
Copyright
Copyright © Cambridge University Press 2008

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