A charge-conservative approach for simulating electrohydrodynamic two-phase flows using volume-of-fluid

In the present study we propose a charge-conservative scheme to solve twophase electrohydrodynamic (EHD) problems using the Volume-of-Fluid (VOF) method. EHD problems are usually simplified by assuming that the fluids involved are purely dielectric (insulators) or purely conducting. Gases can be considered as perfect insulators but pure dielectric liquids do not exist in nature and insulating liquids have to be approximated using the “Taylor– Melcher leaky dielectric model” [1, 2] in which a leakage of charge through the liquid due to ohmic conduction is allowed. It is also a customary assumption to neglect the convection of charge against the ohmic conduction. The scheme proposed in this article can deal with any EHD problem since it does not rely on any of the above simplifications. An unrestricted EHD solver requires not only to incorporate electric forces in the Navier-Stokes equations, but also to consider the charge migration due to both conduction and convection in the electric charge conservation equation [3]. The conducting or insulating nature of the fluids arise on their own as a result of their electric and fluid mechanical properties. The EHD solver has been built as an extension to Gerris, a Free Software solver for the solution of incompressible fluid motion using an adaptive VOF method on octree meshes developed by Popinet [4, 5]. ∗Corresponding author Email addresses: [email protected] (J. M. López-Herrera), [email protected] (S. Popinet), [email protected] ( M. A. Herrada) Preprint submitted to Journal of Computational Physics November 30, 2010