TY - JOUR
T1 - Toroidal drop under electric field
T2 - arbitrary drop-to-ambient fluid viscosity ratio
AU - Zabarankin, Michael
N1 - Publisher Copyright:
© 2017 The Author(s) Published by the Royal Society. All rights reserved.
PY - 2017/9/1
Y1 - 2017/9/1
N2 - 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 4π/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 CaE 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.
AB - 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 4π/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 CaE 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.
KW - Analytical solution
KW - Electric field
KW - Stationary shape
KW - Stokes flow
KW - Toroidal drop
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U2 - 10.1098/rspa.2017.0379
DO - 10.1098/rspa.2017.0379
M3 - Article
AN - SCOPUS:85029910741
SN - 1364-5021
VL - 473
JO - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
JF - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
IS - 2205
M1 - 20170379
ER -