Periodic electromagnetic electroosmotic flow of Jeffrey fluid with slip boundary conditions between parallel plates at high zeta potential

Abstract

In contrast to the conventional Debye–Hückel approach to approximate the Poisson–Boltzmann equation, the case retains the nonlinear Poisson–Boltzmann equations to investigate the periodic electromagnetic electroosmotic flow of Jeffrey fluid under the boundary condition of slip between parallel plates at high zeta potentials. In this research, the interdependence of potential and slip is considered. By means of the nonlinear sliding dependence of the zeta potential, analytical solutions of the potential are obtained for arbitrary values of the potential. Thereafter, an analytic expression for the periodic electroosmotic velocity of Jeffrey fluid is given. Numerical calculation of the oscillatory flow rate is performed based on the obtained geopotential distribution. The notable consequence is that the Hartmann number can lead to oscillations, yet such oscillations strongly depend on factors such as the oscillatory Reynolds number, slip length, and zeta potential, and there are significant differences in the flow properties under different factors. In addition, the introduction of Jeffrey fluid into periodic electromagnetic electroosmotic flow under high zeta potentials may facilitate an understanding of the magnetohydrodynamic instability of Jeffrey fluid.