A mathematical model and an explicit finite difference iterative integration algorithm for two-dimensional laminar steady flow of an incompressible viscous electrically conducting but neutrally charged liquid containing electrically charged particles and exposed to an externally applied electrostatic field were developed. The system of governing electrohydrodynamic equations was derived from a combination of Maxwell's equations of electrodynamics and the Navier-Stokes equations. Numerical results demonstrate the existence of strong electrothermoconvective motion in the liquid during the solidification/melting and quantify its influence on the amount of accrued solid, deposition pattern of the electrically charged particles inside the accrued solid, and the melt/solid interface shape.
