Time periodic electro-osmotic flow through a microannulus

Abstract

Flow behavior of time periodic electro-osmosis in a cylindrical microannulus is investigated based on a linearized Poisson–Boltzmann equation and Navier–Stokes equation. An analytical solution of electro-osmotic flow (EOF) velocity distribution as functions of radial distance, periodic time and relevant parameters is derived. By numerical computations, the influences of the electrokinetic width K denoting the characteristic scale of the microannulus to Debye length, the wall zeta potential ratio β denoting the inner cylinder to the outer cylinder, the ratio α denoting of the annular inner radius to outer radius and the periodical EOF electric oscillating Reynolds number Re on velocity profiles are presented. Results show that when electric oscillating Reynolds number is low and the electrokinetic width K is large, the electro-osmotic velocity amplitude shows a square pluglike profile. When the Reynolds number is high, the driving effect of the electric force decreases immediately away from the two cylindrical walls. The parameter β affects the dimension and direction of the EOF velocity profiles within the electric double layer near the two cylindrical walls in a microannulus. Two limiting cases are discussed, i.e., the time periodical EOF approximately in parallel plate microchannel and circular microtube. These results are agreed qualitatively with those obtained by previously related researches. Furthermore, the instantaneous EOF velocity profiles within a period of a time cycle for different applied electric frequency f, electrokinetic width K, and zeta potential ratio β are illustrated.