@article {Zabarankin20160633,
author = {Zabarankin, Michael},
title = {Liquid toroidal drop under uniform electric field},
volume = {473},
number = {2202},
year = {2017},
doi = {10.1098/rspa.2016.0633},
publisher = {The Royal Society},
abstract = {The problem of a stationary liquid toroidal drop freely suspended in another fluid and subjected to an electric field uniform at infinity is addressed analytically. Taylor{\textquoteright}s discriminating function implies that, when the phases have equal viscosities and are assumed to be slightly conducting (leaky dielectrics), a spherical drop is stationary when Q=(2R2+3R+2)/(7R2), where R and Q are ratios of the phases{\textquoteright} electric conductivities and dielectric constants, respectively. This condition holds for any electric capillary number, CaE, that defines the ratio of electric stress to surface tension. Pairam and Fern{\'a}ndez-Nieves showed experimentally that, in the absence of external forces (CaE=0), a toroidal drop shrinks towards its centre, and, consequently, the drop can be stationary only for some CaE\>0. This work finds Q and CaE such that, under the presence of an electric field and with equal viscosities of the phases, a toroidal drop having major radius ρ and volume 4π/3 is qualitatively stationary{\textemdash}the normal velocity of the drop{\textquoteright}s interface is minute and the interface coincides visually with a streamline. The found Q and CaE depend on R and ρ, and for large ρ, e.g. ρ>=3, they have simple approximations: Q\~{}(R2+R+1)/(3R2) and CaE\~{}33πρ/2 (6~ln~ρ+2~ln[96π]-9)/(12~ln~ρ+4~ln[96π]-17) (R+1)2/(R-1)2.},
issn = {1364-5021},
URL = {http://rspa.royalsocietypublishing.org/content/473/2202/20160633},
eprint = {http://rspa.royalsocietypublishing.org/content/473/2202/20160633.full.pdf},
journal = {Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences}
}