Capillary-dominated electrified jets of a viscous leaky dielectric liquid

The capillary-dominated regime of dynamics of electrified jets of a viscous leaky dielectric liquid is studied numerically. In this regime the effective force in the direction of an applied field due to tangential electric stresses is balanced by the gradient of liquid pressure governed by the surface-tension stresses. As is characteristic of this regime, the electric current and the characteristic jet radius are dependent on the surface-tension coefficient and not on viscosity. In the scope of this work, the conditions of the existence of this regime are determined. A qualitative order-of-magnitude analysis gives the power-law dependences of the jet radius and electric current on the parameters of the problem (conductivity, applied electric field, flow rate, and surface-tension coefficient). Numerical results are obtained for low conductive liquids for a large range of the dimensionless flow rate (capillary number, Ca). The order-of-magnitude estimations of electric current are in agreement with the numerical results given a small Ca. The corresponding numerically obtained jet shapes are discussed and explained.