Cross-stream migration of drops suspended in Poiseuille flow in the presence of an electric field

Abstract

The present study focuses on the cross-stream migration of a neutrally buoyant two-dimensional drop in a Poiseuille flow in a channel under the influence of an electric field. In the absence of an electric field, the important nondimensional parameters describing this problem are the viscosity ratio (λ) between the drop fluid and the surrounding medium, the ratio of drop diameter to channel height (a^{*}), and the capillary number (Ca). The influence of all these parameters on drop migration is investigated. It is observed that a large drop moves slowly as compared to a smaller drop, but attains a steady shape at the center line of the channel. The increase in value of the capillary number enhances the cross-stream migration rate, while the increase in viscosity ratio reduces the tendency of the drops to move towards the channel center line. The presence of an electric field introduces additional interfacial stresses at the drop interface, which in turn alters the dynamics observed in the absence of an electric field. Extensive computations are carried out to analyze the combined effect of the electric field and the shear flow on the cross-stream migration of the drop. The computational results for a perfect dielectric indicate that the droplet migration enhances in the presence of an electric field. The permittivity ratio (S) and the electric field strength (E) play major roles in drop migration and deformation. Computations using the leaky dielectric model also show that for certain combinations of electrical properties the drop undergoes immense elongation along the direction of the electric field. The conductivity ratio (R) is again a vital parameter in such a system of fluids. It is further observed that for certain conditions the leaky dielectric drops exhibit rotation together with translation.

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

“…The droplet and the surrounding medium are silicone oil and castor oil, respectively. The densities of both the fluids are equal to 980 kg/m 3 . The values of the viscosity of the silicone oil and castor oil are 54 and 65 P (nearly the same).…”

“…Electrically driven dynamics of a liquid droplet suspended in another medium has been a subject of intense research from several decades due to its relevance in industrial applications [1], microfluidics [2][3][4][5], biological systems [6] and natural phenomena such as electrification of rain, raindrops bursting in thunderstorms and electrification of the atmosphere [7][8][9]. Significant research efforts, therefore, have been directed to address various facets of the coupling between electromechanics and electrohydrodynamics over various spatial and temporal scales [10].…”

“…Reported research has revealed that the main electrical parameters that govern the shape evolution of a droplet under direct or alternating electric field are the electrical conductivity ratio and the permittivity ratio between the droplet and surrounding fluid. 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].…”

“…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.…”

Steady axial electric field may lead to controllable cross-stream migration of droplets in confined oscillatory microflows

“…Several reported studies pointed out that the migration characteristic of a droplet can be modulated by altering the deformability of the interface (Goldsmith & Mason 1962; Chaffey, Brenner & Mason 1965; Haber & Hetsroni 1971; Wohl & Rubinow 1974; Stan et al 2011; Mandal et al 2015 a ), fluid properties (Chan & Leal 1979; Mukherjee & Sarkar 2013, 2014; Hazra, Mitra & Sen 2019), flow inertia (Ho & Leal 1974; Mortazavi & Tryggvason 2000; Chen et al 2014) and the nature of flow (steady or oscillatory)(Graham & Higdon 2000 a , 2002; Chaudhury, Mandal & Chakraborty 2016). In addition to these factors, mutual interactions between electric forcing and domain confinement can also be used as a means of fine-tuning the modulation of the droplet's motion (Deshmukh & Thaokar 2012; Esmaeeli 2016; Zhang et al 2016; Brosseau & Vlahovska 2017; Nath et al 2018; Santra, Mandal & Chakraborty 2018 b , 2019 a ; Poddar et al 2019 a ).…”