Application of Galerkin finite-element computations in studying electrohydrodynamic problems

In studying electrohydrodynamic problems, nonlinearly coupled equations for both fluid flows and electric variables are usually considered. Often deformable fluid interfaces are also involved, leading to challenging free-boundary problems. This paper presents a systematic computational approach, based on the Galerkin finite-element method, to solve nonlinear electrohydrodynamic problems even with free fluid interfaces. Examples include electric force effects on the upstream meniscus of a liquid coating bead where only electric normal stress at the fluid interface is important, nonlinear deformations of a leaky dielectric drop in an electric field where both normal and tangential electric stresses are present at the drop interface, and space-charge induced electrohydrodynamic flows due to corona discharge from a wire enclosed in a rectangular shield where electric body force appears in the bulk fluid.