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

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 lambda, respectively, then the toroidal drop with volume 4 pi/3 and having major radius rho 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, rho and lambda and are found analytically. Those functions are relatively insensitive to lambda, and for rho >= 3, they admit simple approximations, which coincide with those obtained recently for lambda = 1. Streamlines inside and outside the toroidal drop for the same R and rho but different lambda are qualitatively similar.