Numerical simulation of two-fluid flow of electrolyte solution with charged deforming interfaces

Abstract The authors’ volume-of-fluid based electrokinetic flow model for multiphase flow with fluid–fluid interfaces, recently extended by them to allow for interfacial charge, is refined and more comprehensively validated under dynamic conditions. Validation is performed using (i) an analytical solution for drop relaxation in the presence of ions and interfacial charge, and (ii) published experimental observations of the shape evolution of a critically charged water droplet in air, undergoing Rayleigh instability. Predictions based on two methods of representing the electrical force, in combination with two different numerical treatments of the interfacial charge, are compared. It is shown that the most accurate predictions, when there is interfacial charge, are obtained by using a “modified pressure” formulation (in which part of the Maxwell stress is incorporated into the pressure) in combination with a published treatment for solving the Poisson equation for the electrical potential that is similar to the Ghost Fluid Method; this is therefore the recommended model combination. The choice of method (modified pressure or standard formulation) is found to be unimportant when there is no interfacial charge. Finally, the recommended model is used to predict the steady state deformation of a hexadecane drop in an electrolyte solution during pressure-driven flow through a cylindrical microchannel, when both the channel wall and the drop interface carry electric charge. It is shown that, for low interfacial tension, electrokinetic forces can significantly enhance or reduce the drop deformation, compared with that of a drop with no interfacial charge, when the charges on the drop interface and channel wall are of the same or opposite sign, respectively.