Numerical modeling of an electrostatically driven liquid meniscus in the cone–jet mode

A numerical model has been developed for an electrostatically driven liquid meniscus for a dielectric fluid. The model is able to calculate the shape of the liquid cone and the resulting jet, the velocity fields inside the liquid cone–jet, the electric fields in and outside the cone–jet, and the surface charge density at the liquid surface. The mathematical formulas with proper boundary conditions for the relevant physical processes are described in detail. The equations of continuity, momentum and electric potential are solved numerically with an iterative procedure developed for the model. The results of the present model fit well with experimental observations of the cone shape and jet formation.