Oscillatory electro-magneto-kinetics of confined-Stokes-second-problem micro-flows

Abstract

We semi-analytically investigate the electro-magneto-hydrodynamics of time periodic electroosmotic flow of a Newtonian electrolyte through microchannels with oscillating boundaries, resembling a confined-Stokes-second-problem type system. Herein, a constant orthogonal magnetic field and a constant transverse electric field have been used along with the driving time periodic electric field to have better control over mixing in the microchannel or to augment the pumping. The Poisson–Boltzmann equation has been solved with Debye–Hückel linearization for the thin electric double layer to obtain the electric potential distribution. We determine the flow field for low Hartmann number (Ha) cases by the regular perturbation method. Furthermore, Laplace transformation has been used to solve the flow field for each order in the obtained perturbation series. We have obtained the solution of flow field up to O(Ha) and found an excellent match with the complete numerical solution for our range of Ha. The dependence of flow field on dimensionless parameters, such as Ha, electrokinetic number (M), and Womersley number (Wo), has been discussed thoroughly, where Ha and M are functions of the strength of applied magnetic field and transverse electric field, respectively, and Wo is the function of Debye length, kinematic viscosity, and frequency of the time periodic electric field. Interestingly, for large values Wo, we find wave like motion in the flow field, which induces vorticity as well as better mixing caliber. Additionally, we find that the interplay between Ha and M controls the mixing and modifies the flow rate according to the need. Various combinations of such parameters have been discussed to promote mixing as well as pumping for such strongly coupled microfluidic phenomena.