Transforming Navier‐stokes equation to a fourth order nonlinear differential equation for the study of electrolyte flow in a circular microchannel

Abstract

AbstractIn this paper, analytical solutions are derived for the study of steady‐state electrolyte flow in a circular microchannel under the simultaneous effects of an external electric field and uniform wall injection. The Navier‐Stokes equations containing an axial linear electric body force are transformed to a fourth‐order nonlinear differential equation and solved analytically using a series solution method. The most important results are presented and discussed in terms of radial Reynolds number and a fundamental non‐dimensional electric field parameter. The Electrical Double Layer theory is employed to model the effects of external electric field. Analytical relations are given for velocity profiles, exit flow rate, and total pressure drop in the microchannel. The results show that a high‐intensity electric field can completely reverse the velocity profile or make it more flat in the presence of wall injection. This electric effect can be used in practical applications to control the shear stress, heat, or mass transfer in microchannels or microelectromechanical systems. In addition, various graphs are presented showing simultaneous effects of electric field and wall injection of the same fluid on the flow physics.