Analysis of Time Periodic Electroosmotic Flows

Abstract

Abstract Analytical solutions of time periodic electroosmotic flow in two dimensional straight channels are obtained as a function of a nondimensional parameter k, which is based on the electric double layer (EDL) thickness, kinematic viscosity and the frequency of the externally applied electric field. A parametric study as a function of k reveals interesting physics, ranging from oscillatory “plug-like” flow in the quasi-steady state to flows analogous to the oscillating flat plate in unbounded flow domain (Stokes’ second problem). The latter case differs from Stokes’ second solution within the EDL, since the flow is driven with oscillatory electric field, rather than a moving surface. Utilization of the instantaneous Helmholtz Smoluchowski velocity as the slip boundary condition on the wall matches the bulk flow solution accurately, even for high, frequency excitations. Unlike the steady electroosmotic flows, the vorticity for time periodic electroosmotic flows is not confined in the EDL.