Effect of magnetic field on electroosmotic flow of viscoelastic fluids in a microchannel

Abstract

Electroosmotic flow is an efficient transportation technology driven by applying an external electric field across the microchannel, which has a great potential for future application. This work is presented to study the unsteady electroosmotic flow of viscoelastic fluids combined with a constant pressure gradient and a vertical magnetic field through a parallel plate microchannel. For the reason that the upper and bottom walls of the parallel plate microchannel in microfluidic devices can be made of different materials, this leads to different hydrophobic properties, asymmetric zeta wall potentials, and different slip boundary conditions. The Navier slip model with different slip coefficients at walls is considered. The generalized Maxwell fluid with fractional derivative is adopted for the constitutive equation of the fluid. The analytical and numerical solutions of velocity are derived by employing the integral transform method and finite difference method, respectively. Excellent agreement is found between the numerical solutions and analytical solutions. Finally, the effects of fractional parameter $\alpha$ , relaxation time $\lambda$ , slip coefficients $a$ and $b$ , the ratio of wall zeta potentials $R_{\xi }$ , Hartmann number $Ha$ , and electrical field strength parameter $S$ on velocity profiles are interpreted graphically in detail.

Keywords: Electroosmotic flow; Fractional calculus; Magnetohydrodynamic flow; Second-order implicit finite difference scheme; Viscoelastic fluids.