Sedimentation of a surfactant-laden drop under the influence of an electric field

Abstract

The sedimentation of a surfactant-laden deformable viscous drop acted upon by an electric field is considered theoretically. The convection of surfactants in conjunction with the the combined effect electrohydrodynamic flow and sedimentation leads to a locally varying surface tension, which subsequently alters the drop dynamics via the interplay of Marangoni, Maxwell and hydrodynamic stresses. Assuming small capillary number and small electric Reynolds number, we employ a regular perturbation technique to solve the coupled system of governing equations. It is shown that when a leaky dielectric drop is sedimenting in another leaky dielectric fluid, Marangoni stress can oppose the electrohydrodynamic motion severely, thereby causing corresponding changes in internal flow pattern. Such effects further result in retardation of drop settling velocity, which would have otherwise increased due to the influence of charge convection. For highly mobile surfactants (high Péclet number limit), the drop surface becomes immobilized and the charge convection effect gets completely eliminated. For non-spherical drop shapes, the effect of Marangoni stress is overcome by the 'tip stretching' effect on the flow field. As a result, the drop deformation gets intensified with increment in sensitivity of surface tension to the local surfactant concentration. Consequently, for oblate type of deformation the elevated drag force causes further reduction in velocity. Owing to similar reasons, prolate drops experience lesser drag and settles faster than the surfactant-free case. In addition to this, with increased sensitivity of interfacial tension on the surfactant concentration, the asymmetric deformation about the equator gets suppressed. These findings may turn out to be of fundamental significance towards designing electrohydrodynamically actuated droplet based microfluidic systems that are intrinsically tunable by varying the surfactant concentration. *

Effect of surfactant on the settling of a drop towards a wall

“…The dynamics of a fluid drop in another immiscible fluid has been a topic of substantial research over many years owing to its large range of applications such as the science of colloids and emulsions (Meyyappan, Wilcox & Subramanian 1983;Zhang & Davis 1992), sedimentation (Rushton & Davies 1973;Haber & Hetsroni 1981;Poddar et al 2018), † Email address for correspondence: uddipta.ghosh@iitgn.ac.in early biomechanical modelling of cells (Hochmuth et al 1993;Tsai, Frank & Waugh 1993), to name but a few. A large number of studies have, therefore, been carried out focusing on various aspects of droplet motion (see for example, Hetsroni & Haber 1970;Haber & Hetsroni 1971;Rallison 1981;Acrivos 1983;Bentley & Leal 1986;Sherwood 1988;Subramanian & Balasubramanian 2001;Probstein 2005;Baroud, Gallaire & Dangla 2010;Lavrenteva, Rosenfeld & Nir 2011;Anna 2016), among which, settling of drops has received significant attention over the years (Vizika & Saville 1992;Ha & Yang 1995;Probstein 2005;Leal 2007;Poddar et al 2018), as attributable to its relevance in industrial applications, such as in crude-oil industries (Mhatre et al 2015;Mandal, Bandopadhyay & Chakraborty 2017a), various separation processes (Ptasinski & Kerkhof 1992) as well as in several other microfluidic applications. As such, various aspects of droplet sedimentation have been rigorously analysed over the years (Subramanian & Balasubramanian 2001;Anna 2016), which include dynamics of freely falling drops (Subramanian & Balasubramanian 2001;Probstein 2005;Leal 2007), influence of external electric fields on...…”

Electro-Hydrodynamics of Emulsion Droplets: Physical Insights to Applications

“…The high voltage is supplied across the electrodes and dynamics are captured by using cameras. In these studies, some authors have also introduced surfactants at the liquid-liquid interface [ 27 , 71 , 72 , 73 , 74 , 75 , 76 , 77 , 78 , 79 , 80 , 81 , 82 , 83 , 84 , 85 , 86 , 87 , 88 , 89 ]. A summary of the most prominent works related to droplet EHD are summarized in Table 1 .…”

“…The influence of interfacial properties on the droplet deformation and breakup under an electric field has also been a topic of profound interest for decades [ 27 , 71 , 72 , 73 , 74 , 75 , 76 , 77 , 78 , 79 , 80 , 81 , 82 , 83 , 84 , 85 , 86 , 87 ]. The surface-active molecules prompt to change in the interracial and rheological properties, leading to interfacial perturbations and breakups [ 23 , 71 , 136 , 137 , 138 ].…”

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

“…Motivated by the classical work of Taylor (1966), several studies have been reported on electrically modulated morpho-dynamics of droplets in an external flow (Hase, Watanabe & Yoshikawa 2006; Ristenpart et al 2009; Mhatre & Thaokar 2013; Zhang et al 2016; Brosseau & Vlahovska 2017; Poddar et al 2018, 2019 b ; Behera et al 2019; Santra et al 2018 b , 2019 a ; Santra, Das & Chakraborty 2020). Mandal, Bandopadhyay & Chakraborty (2016) studied the cross-stream migration of the droplet in unbounded plane Poiseuille flow under uniform electric field.…”