Combined electromagnetohydrodynamic flow in a microparallel channel with slightly corrugated walls

Abstract

In this work a perturbation method is introduced to study the effect of wall roughness on the combined electromagnetohydrodynamic flow in a microparallel channel with slightly corrugated walls under the Debye–Hückel approximation. The driving force is the sum of the electro-osmotic and Lorentz forces. The wall corrugations are described by periodic sinusoidal waves with small amplitudes compared to the channel height. The perturbation solutions of velocity and electric potential are obtained. The results show that the velocity and potential distributions are significantly disturbed by the wall roughness. The mean velocity can be enhanced at long-wavelength corrugations when the phase difference between the wall corrugations is near π. The enhancement of the mean velocity increases with S which represents the strength of the electric field in the x-direction. The decreasing effect of wall roughness increases with the wavenumber and decreases with the phase difference and the normalized reciprocal thickness of the electric double layer. The phase difference of wall roughness becomes unimportant when the wavenumber or Hartmann number is larger than 3.