Capillary Filling Dynamics of Electromagnetohydrodynamic Flow of Non-Newtonian Fluids

Abstract

In this work, we aim to develop a mathematical model for capillary filling dynamics of electromagnetohydrodynamic flow of non-Newtonian fluids. An axially applied electric field and a transverse magnetic field are considered to elucidate the electromagnetohydrodynamic transport through the microcapillary. Assuming a non-Newtonian power-law obeying fluids, we analyze the transient evolution of the electromagnetohydrodynamic capillary positions by considering the magnitude of the total force balance via finite volume-based numerical formalism. We have highlighted the various rheological regimes in the horizontal capillary through a scaling analysis. For the Newtonian fluids, corresponding inviscid linear Washburn regime is also analyzed and compared with the power-law obeying fluids. Furthermore, we have also derived closed-form analytical expressions for the electromagnetohydrodynamic velocity, pressure gradient, and transient evolution of the capillary positions by using couple stress parameter model to characterize the fluid rheological behaviors. We perform a comparison test of the coupled stress parameter model with the results from the literature for a similar set of fluid rheological parameters. The comparison results are found to be in good agreement.