Viscous potential flow analysis of capillary instability with radial electric field

Abstract

A linear analysis of capillary instability with radial electric field is carried out using viscous potential flow theory. In viscous potential flow, the viscous term in the Navier-Stokes equation vanishes as vorticity is zero but viscosity is not zero. Viscosity enters through normal stress balance in viscous potential flow theory and the tangential stresses are not considered. The effect of gravity and free surface charges at the interface are neglected. A dispersion relation is derived for the case of radially imposed electric field and stability is discussed in terms of various parameters such as Ohnesorge number, permittivity ratio, etc. A condition for neutral stability is obtained and it is given in terms of critical value of electric field. It is observed that the radial electric field has dual effect on the stability of the system corresponding to the values of conductivities and permittivities of the fluids.