Electrohydrodynamics of a compound drop

Abstract

The behavior of a compound drop, comprising two concentric fluid spheres, in a uniform electric field is studied analytically. The governing electrohydrodynamic equations are solved for Newtonian and immiscible fluids in the framework of leaky-dielectric theory and in the limit of small electric field strength and fluid inertia. A detailed analysis of the electric and flow fields is presented and it is shown that there will be four possible flow patterns in and around the globule, in terms of the direction of the external flow (pole-to-equator vs equator-to-pole) and the number of vortices (single-vortex vs double vortices) in the shell, and that the senses of the net electric shear stresses at the surfaces of the inner and the outer drops and their relative importance are the key parameters in setting these patterns. A circulation map is constructed, which is used to infer about the likelihood of the flow patterns and transition from one pattern to another for representative fluid systems. For small distortion from the spherical shape, the deformations of the inner and the outer drops are found using normal stress balances at the corresponding surfaces. It is shown that there will be four possible modes for the deformation of the compound drop, which are determined by the net normal electric and hydrodynamic stresses at the pertinent surfaces. The dynamic responses of the inner and the outer drops for representative fluid systems are studied using a deformation map, which characterizes the possibilities of the deformation modes and transition from one mode to another as a function of the fluid properties.

Electro-Hydrodynamics of Emulsion Droplets: Physical Insights to Applications

“…The foundation of the theory of a double-emulsion droplet under an electric field is that of a single-emulsion droplet as discussed in Section 3 . A more comprehensive coverage of the governing equations is not included in this review and can be found in literature [ 143 , 144 ]. An A/B/A type (core/shell/ambient) of a double-emulsion droplet has the same liquid in the core, and ambient, and is essentially a two-phase problem.…”

“…The dynamics of a double-emulsion droplet within a weak electric field or small deformation limit is extensively reported and well understood [ 33 , 67 , 93 , 94 , 143 , 144 , 145 , 146 , 147 , 148 , 149 , 150 , 151 ]. A/B/C types of a double-emulsion droplets can show four distinct modes of deformation of core/shell-shell/ambient, i.e., prolate-prolate (PP), prolate-oblate (PO), oblate-prolate (OP), and oblate-oblate (OO), which entirely depends on the ratio ( ) across each of the interface [ 67 , 93 , 143 ]. If , the interface deforms oblate and if , it deforms prolate.…”

“…Behjatian and Esmaeeli [ 143 ] studied the A/B/C type concentric emulsion analytically under a DC electric field using domain perturbation method and showed various free-charge distributions surrounding the interfaces depending on the relative magnitudes of and (See Figure 8 A). They also studied the deformation-time history of the double droplets under weak electric fields [ 93 ].…”

Numerical simulation of electrohydrodynamics of a compound drop based on the ternary phase field method

“…Six leaky dielectric systems from the study by Behjatian and Esmaeeli 13 are used in the small deformation simulations of the compound drop under weak electric field. The key physical properties of six leaky dielectric systems are extracted from Behjatian and Esmaeeli 13 and given in Table 1. For comparison, the definition of time scale of flow t is the same as that of Behjatian and Esmaeeli, 14 as listed as follows…”

“…It can be seen from Figure 5 that for system 3 ( Figure 5(c) compound drop for the other five systems is in good agreement with the analytical results of Behjatian and Esmaeeli. 13,14 The free charge distribution is further examined in order to find out the reason why a big error generates in the deformation simulation of system 3. Figure 6 shows the distribution of free charge and electric stress for systems 1-6.…”