Abstract
In this paper, a coordinate transformation method (CTM) is employed to numerically solve the Poisson–Nernst–Planck (PNP) equation and Navier–Stokes (NS) equations for studying the traveling-wave electroosmotic flow (TWEF) in a two-dimensional microchannel. Numerical solutions indicate that the numerical solutions of TWEF with and without the coordinate transformation are in good agreement, while CTM effectively improves stability and convergence rate of the numerical solution, and saves computational cost. It is found that the averaged flow velocity of TWEF in a micro-channel strongly depends on frequency of the electric field. Flow rate achieves a maximum around the charge frequency of the electric double layer. The approximate solutions of TWEF with slip boundary conditions are also presented for comparison. It is shown that the NS solution with slip boundary conditions agree well with those of complete PNP-NS equations in the cases of small ratios of Electric double layer(EDL) thickness to channel depth(λD/H). The NS solution with slip boundary conditions over-estimates the electroosmotic flow velocity as this ratio(λD/H) is large.
Highlights
Microfluidics has emerged as a new area of multiphysical research associated with fluid mechanics, biology, chemistry and electricity [1]
Numerical solutions indicate that the numerical solutions of traveling-wave electroosmotic flow (TWEF) with and without the coordinate transformation are in good agreement, while coordinate transformation method (CTM) effectively improves stability and convergence rate of the numerical solution, and saves computational cost
It is found that the averaged flow velocity of TWEF in a microchannel strongly depends on frequency of the electric field
Summary
Microfluidics has emerged as a new area of multiphysical research associated with fluid mechanics, biology, chemistry and electricity [1]. There is an excess of counter-ions over co-ions in a thin liquid layer near the solid wall This thin and charged liquid layer is called the Electric double layer (EDL) [3,4]. Electroosmosis (EOF) is the charged liquid flow relative to the stationary wall surface under an electric field applied at a tangent to the wall. Ramos [13,14,15,16] found directional flow rates of electroosmotic flows in a microchannel driven by traveling wave electrical fields. Difficult because of the locally high gradient near the solid wall and multiphysical interactions of fluid flow, electricity and ion migration. The objective of this study is to use CTM for numerical investigation of TWEF behaviors based on complete electrokinetic equations and to make comparison with approximate NS solutions with slip boundary conditions
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