The effects of depletion layer for electro-osmotic flow of fractional second-grade viscoelastic fluid in a micro-rectangle channel

Abstract

Abstract This work investigates unsteady electro-osmotic flow of a fractional second-order viscoelastic fluid in a micro-rectangle channel with considering depletion effects. Due to the existence of depletion, there are depletion layer near the plate and bulk flow adjacent to depletion layer for the flow in the whole domain. In order to express the boundary conditions at the interface, we introduce Maxwell stress to describe the interaction between Newtonian fluid and viscoelastic fluid with fractional derivative. To ensure the validity of the semi-analytical solution obtained by Laplace transform, the numerical solutions are acquired by finite difference method and Grunwald-Letnikov approximation and both of them have a better agreement. The increasing viscosity of viscoelastic fluid leads to the increasing driving difficulty of fluid in non-depleted layer and the decreasing velocity amplitude at steady state. Moreover, the increasing interfacial zeta potential difference can promote the fluid flow, and the change of interface charge density makes the velocity at the interface change dramatically.