Analytical solution for transient electroosmotic flow in a rotating microchannel

Abstract

An analytical solution is developed for the unsteady flow of fluid through a parallel rotating plate microchannel, under the influence of electrokinetic force using the Debye–Hückel (DH) approximation. Transient Navier–Stokes equations are solved exactly in terms of the cosine Fourier series using the separation of variables method. The effects of frame rotation frequency and electroosmotic force on the fluid velocity and the flow rate distributions are investigated. The rotating system is found to have a damped oscillatory behavior. It is found that the period and the decay rate of the oscillations are independent of the DH parameter (κ). A time dependent structure of the boundary layer is observed at higher rotational frequencies. Furthermore, the rotation is shown to generate a secondary flow and a parameter is defined (β(t)) to examine the ratio of the flow in the y and x directions. It showed that both the angular velocity and the Debye–Hückel parameters are influential on the induced transient secondary flow in the y direction. At high values of the Debye–Hückel parameter and the rotation parameter the flow rates in the x and y directions are found to be identical. The analytical solution results are found to be in good agreement with the numerical method results and previously published work in this field.