Electrohydrodynamics of a viscous drop with inertia

Document Type

Article

Publication Date

5-23-2016

Abstract

Most of the existing numerical and theoretical investigations on the electrohydrodynamics of a viscous drop have focused on the creeping Stokes flow regime, where nonlinear inertia effects are neglected. In this work we study the inertia effects on the electrodeformation of a viscous drop under a DC electric field using a novel second-order immersed interface method. The inertia effects are quantified by the Ohnesorge number Oh, and the electric field is characterized by an electric capillary number CaE. Below the critical CaE, small to moderate electric field strength gives rise to steady equilibrium drop shapes. We found that, at a fixed CaE, inertia effects induce larger deformation for an oblate drop than a prolate drop, consistent with previous results in the literature. Moreover, our simulations results indicate that inertia effects on the equilibrium drop deformation are dictated by the direction of normal electric stress on the drop interface: Larger drop deformation is found when the normal electric stress points outward, and smaller drop deformation is found otherwise. To our knowledge, such inertia effects on the equilibrium drop deformation has not been reported in the literature. Above the critical CaE, no steady equilibrium drop deformation can be found, and often the drop breaks up into a number of daughter droplets. In particular, our Navier-Stokes simulations show that, for the parameters we use, (1) daughter droplets are larger in the presence of inertia, (2) the drop deformation evolves more rapidly compared to creeping flow, and (3) complex distribution of electric stresses for drops with inertia effects. Our results suggest that normal electric pressure may be a useful tool in predicting drop pinch-off in oblate deformations.

Identifier

84971276067 (Scopus)

Publication Title

Physical Review E

External Full Text Location

https://doi.org/10.1103/PhysRevE.93.053114

e-ISSN

24700053

ISSN

24700045

Issue

5

Volume

93

Grant

1412789

Fund Ref

National Science Foundation

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