Electrohydrodynamics of a pair of liquid drops

Abstract

In this paper we consider the flow field generated by a uniform electrostatic field in and about a pair of identical liquid drops immersed in a conducting fluid. It is assumed that the undisturbed electric field is parallel to the line joining the centres of the two drops. The flow field is due to the tangential electric stress over the surfaces of the drops and here this stress and the flow field are expressed in terms of bispherical harmonics. When the distance between the centres of the drops is many drop diameters the tangential electric stress and the flow field in and about one drop are unaffected by the presence of the other drop, as expected. When the distance between the centres of the drops is of the order of two drop diameters there is a substantial modification in the tangential electric stress at the surfaces of the drops and in the induced flow field, especially in the region between the planes through the drop centres perpendicular to the undisturbed electric field.

Liquid toroidal drop in compressional flow with arbitrary drop-to-ambient fluid viscosity ratio

“…5 The second approach is less complex, because the kinematic condition is considerably simpler than the normal stress boundary condition and does not involve pressure. It was used for solving the two-phase Stokes flow problems for two liquid spheres and liquid spindle embedded in another fluid and subjected to a uniform electric field [30,31]. However, because it does not satisfy the normal stress boundary condition, it has two disadvantages: (i) it cannot be checked against the closed-form integral solutions for λ = 1 and (ii) it does not conform to quasi-stationary simulations of drop dynamics.…”

Electrohydrodynamic deformation and interaction of drop pairs

“…Use of the leaky dielectric model to analyse the two-drop problem has been made previously by Sozou (1975), who examined the situation in the limit that drop deformation was negligible and that there was no relative motion of the drops. These two stipulations left unanswered several fundamental questions regarding the electrically driven, temporal evolution of the microstructure of an emulsion.…”

“…Axisymmetric two-drop problem with an electric field aligned with the line of centres. Sozou (1975). The use of the integral equation representations for both the electric field and the viscous flow follows in the spirit of Sherwood (1988) who analysed the low-Reynolds-number deformation of an isolated drop in an electric field.…”

A ghost fluid, level set methodology for simulating multiphase electrohydrodynamic flows with application to liquid fuel injection

“…A number of researchers have explored the case of a suspended drop in a uniform electric field, including Taylor [10], Landau and Lifshitz [46], Cheng and Chaddock [47], Sozou [48], Baygents and Rivette [17,49], and Tomar et al [18]. For this case, the geometry and electric field alignment are identical to that for the dielectric drop in the preceding section, as shown in Fig.…”