Flows Inside and Around a Vaporizing/Condensing Drop Translating in an Electric Field

Abstract

The flow behavior inside and around a translating liquid drop that simultaneously experiences a large interfacial radial mass flux as a result of evaporation or condensation, and the influence of a uniform electric field is analyzed in this paper. The steady-state equations of continuity and momentum of both continuous and drop phases are transformed, by a perturbation technique, into a series of systems of linear partial differential equations which are then solved analytically. The flow structure and the drag force are computed to the first order in ε( =U∞R/ν), the perturbed parameter. Interfacial velocity profiles are represented by Legendre polynomials up to second order to accommodate the electric-field-induced shear stress. It is found that the presence of an electric field does not contribute to the total drag force, but greatly modifies the flow patterns. The droplet internal flow is dominated by the electric field such that the double loop Taylor flow appears at relatively high field strength. The outside flow is dominated by the interfacial mass flux and the recirculation zone only shows up for an evaporating drop under a negative electric field. The electric field also moves the dividing streamline toward to or away from the surface depending on the direction of the electric field and the velocity direction at the interface. Also the effects of an electric field on the flow field are more pronounced for a drop with outward interfacial mass flux because the electric field helps restore the strength of internal circulation weakened by the outward interfacial mass flux.