An Exact Solution for Power-Law Fluids in a Slit Microchannel with Different Zeta Potentials under Electroosmotic Forces

Abstract

Electroosmotic flow (EOF) is one of the most important techniques in a microfluidic system. Many microfluidic devices are made from a combination of different materials, and thus asymmetric electrochemical boundary conditions should be applied for the reasonable analysis of the EOF. In this study, the EOF of power-law fluids in a slit microchannel with different zeta potentials at the top and bottom walls are studied analytically. The flow is assumed to be steady, fully developed, and unidirectional with no applied pressure. The continuity equation, the Cauchy momentum equation, and the linearized Poisson-Boltzmann equation are solved for the velocity field. The exact solutions of the velocity distribution are obtained in terms of the Appell's first hypergeometric functions. The velocity distributions are investigated and discussed as a function of the fluid behavior index, Debye length, and the difference in the zeta potential between the top and bottom.

Keywords: Asymmetric zeta potential; Electroosmosis; Non-Newtonian fluid; Power-law fluid.

Figure 1

Schematic diagram of electroosmotic flow in a slit microchannel.

Figure 2

Dimensionless velocity distributions u/u_s for different values of the fluid behavior index n under κH = 15. (a) Symmetric zeta potentials (ψ_t/ψ_b = 1). (b) Asymmetric zeta potentials (ψ_t/ψ_b = 1.5).

Figure 3

Dimensionless velocity distributions u/u_s for different values of κH under ψ_t/ψ_b = 1.5. (a) Shear thinning fluid (n = 0.8). (b) Shear thickening fluid (n = 1.2).

Figure 4

Dimensionless velocity distributions u/u_s as a function of the dimensionless zeta potential difference R. The values −2/3, −1/3, 0, 1/3, and 2/3 of R, correspond to 0.2, 0.5, 1.0, 2.0, and 5.0 of the zeta potential ratio (ψ_t/ψ_b), respectively. (a) Shear thinning fluid (n = 0.8). (b) Shear thickening fluid (n = 1.2).