Capillary filling under electro-osmotic effects in the presence of electromagneto-hydrodynamic effects

Abstract

We report various regimes of capillary filling dynamics under electromagneto-hydrodynamic interactions, in the presence of electrical double layer effects. Our chosen configuration considers an axial electric field and transverse magnetic field acting on an electrolyte. We demonstrate that for positive interfacial potential, the movement of the capillary front resembles capillary rise in a vertical channel under the action of gravity. We also evaluate the time taken by the capillary front to reach the final equilibrium position for positive interfacial potential and show that the presence of a transverse magnetic field delays the time of travel of the liquid front, thereby sustaining the capillary motion for a longer time. Our scaling estimates reveal that the initial linear regime starts, as well as ends, much earlier in the presence of electrical and magnetic body forces, as compared to the corresponding transients observed under pure surface tension driven flow. We further obtain a long time solution for the capillary imbibition for positive interfacial potential, and derive a scaling estimate of the capillary stopping time as a function of the applied magnetic field and an intrinsic length scale delineating electromechanical influences of the electrical double layer. Our findings are likely to offer alternative strategies of controlling dynamical features of capillary imbibition, by modulating the interplay between electromagnetic interactions, electrical double layer phenomena, and hydrodynamics over interfacial scales.