Influence of interfacial slip on the suspension rheology of a dilute emulsion of surfactant-laden deformable drops in linear flows

Abstract

The present study deals with the effect of interfacial slip on the deformation and emulsion rheology of a dilute suspension of droplets in a linear flow. The droplets are laden with surfactants that are bulk-insoluble and get transported only along the interface. An asymptotic approach is adopted for the present analysis in order to tackle the nonlinearity present due to deformation of droplets. The analysis is carried out under two different limiting scenarios namely: surface diffusion-dominated-surfactant transport and surface convection-dominated surfactant transport. For either of the limiting cases we look into the droplet dynamics for two commonly encountered bulk flows -uniaxial extensional and simple shear flow. Under the assumption of negligible fluid inertia in either phase, it is shown that slip at the droplet interface significantly affects the surfactant-induced Marangoni stress and hence droplet deformation and emulsion rheology. Presence of interfacial slip not only brings about a decrease in the droplet deformation but also reduces the effective viscosity of the emulsion. The fall in both droplet deformation and effective viscosity is found to be more severe for the limiting case of surface convection-dominated surfactant transport. For the case of an imposed simple shear flow, the normal stress differences generated due to droplet deformation are affected as well due to the presence of interfacial slip. † E-mail address for correspondence: suman@mech.iitkgp.ernet.in studies deals with the effect of interfacial slip on the droplet dynamics 9,30-32 . Ramachandran and Leal 9 studied the effect of interfacial slip on the rheology and dynamics of a dilute emulsion of droplets suspended in linear flows. They showed that increase in the slip at the interface reduces both the droplet deformation as well as the effective viscosity of the emulsion.Recently, Vlahovska et al. and Mandal et al. 12,14 investigated the effect of surfactants on the deformation characteristics as well as the emulsion rheology of a dilute suspension of droplets in linear flows. However, there is no study available in the literature that puts forward the effect of interfacial slip on the dynamics of a surfactant-laden droplet. Surfactants at the droplet surface bring in alterations in the interfacial rheology that promotes the presence of interfacial slip, which is quite realistic in any multiphase system and is found to possess a significant effect on droplet dynamics 9,31 . This is the prime objective of the present study. It is seen that interfacial slip induces a greater stability to the emulsion by reducing the droplet deformation brought about by the imposed linear flow. Also, it reduces the effective viscosity of the suspension. It is observed that there is a good match between our theoretical prediction and previously performed experiments when the effect of interfacial slip is taken into consideration in our analysis. For the limiting case of convection dominated surfactant transport, the influence of slip is found to be h...

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

“…As such, a large number of investigations on the effect of surface impurities on droplet motion have been carried out (Levich & Krylov 1969;Sadhal & Johnson 1983;Oguz & Sadhal 1988;Stone & Leal 1990;Cuenot, Magnaudet & Spennato 1997;Wang, Papageorgiou & Maldarelli 1999;Hanna & Vlahovska 2010), which includes, for instance, motion of compound drops with surfactants (Tsemakh, Lavrenteva & Nir 2004;Mandal et al 2016), settling of surfactant-laden drops and bubbles (Chen & Stebe 1996;Poddar et al 2018), motion of surfactant-laden drops in Poiseuille flow (Hanna & Vlahovska 2010;Pak, Feng & Stone 2014;Mandal, Bandopadhyay & Chakraborty 2015;Das et al 2017;Das, Mandal & Chakraborty 2018b), to name just a few. A number of studies have also been carried out (Vlahovska, Bławzdziewicz & Loewenberg 2002;Vlahovska, Loewenberg & Blawzdziewicz 2005;Pal 2011;Danov et al 2012;Mandal et al 2017b;Das, Bhattacharjee & Chakraborty 2018a;Sengupta, Walker & Khair 2018), to probe into the influence of surfactants on the bulk rheology of emulsions. These studies indicate that surface impurities might have multifold effects on the motion and deformation of drops and bubbles (Stone & Leal 1990;Tsemakh et al 2004;Vlahovska et al 2005).…”

“…2012; Mandal et al. 2017 b ; Das, Bhattacharjee & Chakraborty 2018 a ; Sengupta, Walker & Khair 2018), to probe into the influence of surfactants on the bulk rheology of emulsions. These studies indicate that surface impurities might have multifold effects on the motion and deformation of drops and bubbles (Stone & Leal 1990; Tsemakh et al.…”

Non-Stick Length of Polymer–Polymer Interfaces under Small-Amplitude Oscillatory Shear Measurement

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“…Issues of interest regarding the interface rheology of polymeric flows include the drag friction of a droplet [ 1 , 2 ], the coalescence kinetics of droplets in immiscible blends and emulsions [ 3 ], the viscosity reduction in polymer blends [ 4 , 5 ] and emulsions [ 6 ] by interfacial slip, multilayer melt flow in coextrusion processing [ 7 ], adhesion properties in relation to the effect of melt rheological processing [ 8 ], and the interface formation in multi-material 3D printing [ 9 ]. Understanding these phenomena requires the characterization of not only the bulk rheology of the components but also of the interface rheology.…”

Active compound particles in a quadratic flow: hydrodynamics and morphology

“…Nooranidoost and Kumar 31 modelled leukaemia cells as compound droplets with a viscoelastic shell material and analyzed their migratory dynamics in a constricted microcapillary. Moreover, a few theoretical [32][33][34] and numerical 35,36 studies analyzed the dynamics of compound droplets with an eccentrically located core in a confined background flow. Additionally, the effects of surfactant laden interfaces, 28,34,[37][38][39] confinement, 40 electric field, 41 etc., on passive compound droplets, have also been addressed.…”