Rotating electro-osmotic flow of third grade fluids between two microparallel plates

Abstract

In this paper, a rotating electro-osmotic flow (EOF) of an incompressible third grade fluid between micro-parallel plates is considered. The analysis is based upon the modified Navier–Stokes (N–S) equation for a transport electrolyte in a rotating frame of reference. Within the framework of linearized Poisson–Boltzmann (P–B) equation, exact solutions of the electric potential distribution are given. The approximate analytical solutions of the velocity and the flow rate are achieved by using perturbation techniques under the assumption of small non-Newtonian parameter Λ. In addition, the finite difference method is used to obtain the numerical solutions. We compare the analytical solutions with the numerical solutions within admissible parameter range, and obtain a good agreement between these solutions. The influences of the Reynolds number Re, the dimensionless non-Newtonian parameter Λ, the dimensionless electro-kinetic width K on the rotating EOF velocity profiles and volume flow rate are investigated in detail. With the increasing Reynolds number Re and non-Newtonian parameter Λ, the velocity is decreasing. The large angular velocity has an obvious effect near the center core of the micro-channel and causes a reversal in the velocity direction.