On a Numerical Model for Free Surface Flows of a Conductive Liquid Under an Electrostatic Field

Abstract

In this paper, a numerical model is developed that can simulate the unsteady axisymmetric free-surface flow of a perfectly conductive liquid under an electrostatic field. The effect of the electrostatic field is modeled by a force distributed on the liquid free surface. Assuming the liquid as a perfect conductor makes it possible to reduce the general electromagnetic equations to electrostatic equations. The Navier–Stokes equations are solved to find the velocity and pressure fields. The free surface advection and reconstruction are performed based on the volume-of-fluid method using Youngs’ algorithm. To evaluate the effect of the electric field on the free surface, the electrostatic potential is first solved for the entire computational domain. Next, the electric field intensity and the surface density of the electric charge are calculated on the free surface after which the electric force can be determined. The computational method for treating this force is similar to that of the surface tension using the continuum surface force method. The developed model is validated by a comparison between the calculated results with those of the analytics as well as experiments for an electrowetting scenario.