Modelling of Electrohydrodynamic Droplet Motion under the Influence of Strong Electric Fields

Abstract

This work focuses on the numerical study of electrohydrodynamic multiphase fluid flow problems. Liquid bodies experience deformations caused by strong external electric fields. These deformations can be used in industrial applications to accurately control the motion of single droplets. In the limiting case, strong electric fields can force atomisation of fine microdroplets from much larger liquid bulks. Due to differences in the electrical properties of the different fluid phases, the flow affects in turn the electric field distribution. The analysis of such coupled flows requires numerical modelling of the interdependent hydrodynamic and electrodynamic problems. Since most liquids exhibit some conductivity due to intrinsic ionic species and dissolved impurities, the electrodynamic problem must be modelled by an electroquasistatic model taking into account capacitive, resistive and convective electrical currents. This electroquasistatic problem is coupled to an incompressible fluid flow problem described by the Navier-Stokes equations. Both problems are solved on the same computational grid, using the finite volume method. The fluid-fluid interface is modelled using the volume of fluid method. The resulting diffuse interface captures the motion of the phase boundaries while efficiently handling topology changes. The motion of contact lines is furthermore modelled using a dynamic contact angle model including hysteresis effects. Pinned contact lines and stick-slip contact line motion in transient problems can therefore be represented. The developed solver is readily applicable to a large range of electrohydrodynamic flow problems. This work investigates electrohydrodynamic flows occurring in three technical applications. First, the dynamics of sessile droplets subjected to an AC electric field on the surface of an insulator are considered. The dynamics of the oscillating droplets are compared with experimental data. Partial discharge inception fields are then estimated for similar configurations. Secondly, the detachment dynamics of two liquids in an on-demand droplet generator, where droplet detachment is enforced by electric fields, are considered and compared to experimental data. The different conductivities of the liquids are shown to lead to substantially different detachment dynamics. Relevant parameters in the detachment dynamics are extracted from the simulations. Finally, transient electrosprays in the cone-jet mode are characterised for a number of liquids with different electromechanical properties. The charge-radius correlations of the first ejections are found to obey the scaling laws reported in the literature. Moreover, additional scaling laws are found for the subsequent ejections.