Electrohydrodynamic effects on the deformation and orientation of a liquid capsule in a linear flow

Abstract

The role of a uniform electric field on the deformation and orientation of a liquid capsule with a viscoelastic membrane is considered analytically in the small deformation limit. The capsule is freely suspended either in a quiescent fluid or in a shear flow. The viscoelasticity of the membrane is taken into account by the Kelvin–Voigt model and the electrohydrodynamic flow is analyzed on the basis of the leaky dielectric model. In this article, we consider three different prototype models of capsules; viz., a neo-Hookean (incompressible isotropic) membrane, a red blood cell-type (area-preserving) membrane, and an interfacial-tension droplet. The deformed capsule shape from its initial sphericity and its orientaion are determined from the linearized governing equations and boundary conditions in the limit of small deformations. The asymptotic theory shows that the degree of capsule deformation induced by a uniform electric field alone is independent of the surface viscosity of the capsule as well as the viscosity ratio between the two fluids inside and outside the capsule. Meanwhile, in the presence of an imposed shear flow, the degree of deformation depends on the surface viscosity with preserving still the independence of the viscosity ratio. For an illustrative purpose, experimental results for the role of a uniform electric field on the orientation of an interfacial-tension droplet in a shear flow are discussed briefly.