Electrohydrodynamics of a concentric compound drop in an AC electric field

Abstract

The dynamics of a compound drop suspended in another immiscible fluid in the presence of an AC electric field is investigated experimentally and using analytical theory. A closed-form analytical expression for the mean deformation and amplitude of deformation at cyclical steady state is derived in the small deformation limit. Experiments were performed with 0.1M NaCl/castor oil compound drops suspended in highly viscous silicone oil. In this case, both the core and the shell deform into prolate spheroids. The effect of two independent variables was investigated, namely, the ratio of the core radius to the shell radius and the frequency (ω) of the applied AC field. In the limit of ω → 0, the present analytical model reduces to the DC electric field model for the compound drop. It was observed that the size of the core significantly affects the dynamics of the compound drop. The mean and the amplitude of deformation of the shell increase considerably with an increase in the radius ratio. Since the present model is valid for a small deviation from a spherical shape, an excellent quantitative agreement is found between analytical and experimental results at low deformation, whereas, at large deformation, the match is only qualitative. It was also observed that the relative phase difference between the core and the shell decreases with an increase in the radius ratio and frequency of the applied electric field.

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 ].…”

“…The extent of the deformation of the inner core droplet also depends on the electrical conductivity of the shell. Soni et al [ 144 ] extended the analytical analysis to an AC electric field. They showed that in the limit of zero frequency, their results reduced to those derived by Behjatian and Esmaelli [ 143 ].…”

Dilute dispersion of compound particles: deformation dynamics and rheology

“…Kim & Dabiri (2017) numerically investigated the time evolution of eccentric compound droplets subjected to a simple shear flow. The effects of inertia (Bazhlekov, Shopov & Zapryanov 1995), viscoelasticity (Zhou, Yue & Feng 2006), surfactant laden interfaces (Hamedi & Babadagli 2010;Xu et al 2013;Srinivasan & Shah 2014;Zhang et al 2015;Mandal, Ghosh & Chakraborty 2016), confinement (Song, Xu & Yang 2010) and electric field (Soni, Thaokar & Juvekar 2018;Santra, Das & Chakraborty 2020a;Santra et al 2020b) on compound drops have also been addressed and thus, the literature on compound drops is plentiful. However, the presence of three fluids and multiple deforming interfaces make the analysis of compound drops cumbersome.…”

Simulations of a weakly conducting droplet under the influence of an alternating electric field

“…The EHD of a droplet under the action of an applied direct electric field have been investigated by several researchers in the past considering perfect [11][12][13] and leaky dielectric media [3,14]. While the underlying physics under DC field have been addressed in details from deep-rooted theoretical [15], experimental [16] and numerical [3,[11][12][13][14][17][18][19][20] considerations, there is a compelling need to assess a possible straight forward extrapolation of identical inferences for alternating electric field as well [21]. In a recent study, Esmaeeli and Halim [22] provided extensive 1D numerical simulations for leaky dielectric systems, to predict that a droplet in an alternating electric field undergoes shape oscillations about the steady-state deformation observed under a root mean squared (rms) equivalent DC field, for all possible electrical conductivity (K r ) and permittivity (S) ratios.…”