Numerical simulation of electrospraying in the cone-jet mode

Abstract

This article solves numerically the equations of the leaky-dielectric model applied to cone jets. The solution is a function of the properties of the fluid and its flow rate, universal in that it does not depend on the geometry and potential of the electrodes. This is made possible by the use of the potential field generated by a semi-infinite Taylor cone as a far-field boundary condition. The numerical solution yields the current emitted by the electrospray, which compares well with experimental data, and detailed information about the velocity, surface charge, electric field and the position of the free surface. These characteristics are generally inaccessible through experiments, and are needed to understand the relative importance of competing processes and the dominant physics. The simulations investigate the liquids tributyl phosphate and propylene carbonate (dielectric constants of 8.91 and 64.9 respectively), in a wide range of electrical conductivities and flow rates. The simulations show that the position of the surface, expressed in units of the characteristic length $r_{c}$, is largely invariant regardless of the physical properties and flow rates of the liquids. The surface charge falls below its equilibrium value along the transition from cone to jet, with a deficit that increases with the ratio between the electrical relaxation and flow residence times. Several characteristics of the cone jet are functions of the dielectric constant, which is consistent with the importance of charge relaxation effects (i.e. with the absence of surface charge equilibrium). The electric energy transferred to the transition region is largely transformed into viscous and ohmic dissipation, and conversion into kinetic energy only dominates once most of the current is fixed on the surface.