Toroidal drop under electric field: arbitrary drop-to-ambient fluid viscosity ratio

Abstract

In the absence of external forces, a liquid toroidal drop freely suspended in another fluid shrinks towards its centre. It is shown that if the two phases are slightly conducting viscous incompressible fluids with the drop-to-ambient fluid ratios of electric conductivities, dielectric constants and viscosities to be 1/ R , Q and λ , respectively, then the toroidal drop with volume 4 π /3 and having major radius ρ can become almost stationary when subjected to a uniform electric field aligned with the drop’s axis of symmetry. In this case, Q and electric capillary number Ca E that defines the ratio of electric stress to surface tension, are functions of R , ρ and λ and are found analytically. Those functions are relatively insensitive to λ , and for ρ ≥3, they admit simple approximations, which coincide with those obtained recently for λ =1. Streamlines inside and outside the toroidal drop for the same R and ρ but different λ are qualitatively similar.