Effects of non-uniform interfacial tension in small Reynolds number flow past a spherical liquid drop

Abstract

A singular perturbation solution is given for small Reynolds number flow past a spherical liquid drop. The interfacial tension required to maintain the drop in a spherical shape is calculated. When the interfacial tension gradient exceeds a critical value, a region of reversed flow occurs on the interface at the rear and the interior flow splits into two parts with reversed circulation at the rear. The magnitude of the interior fluid velocity is small, of order the Reynolds number. A thin transition layer attached to the drop at the rear occurs in the exterior flow. The effects could model the stagnant cap which forms as surfactant is added but the results apply however the variability in the interfacial tension might have been induced.

Swimming active droplet: A theoretical analysis

“…1 (b). For this geometry there exists a solution of the Stokes equation for the fluid flow field inside and outside of the droplet as well as the fluid velocity at the interface [35,36]. The solution at the interface is given in terms of the surface tension gradient: n+1 (z).…”

Marangoni flow at droplet interfaces: Three-dimensional solution and applications

“…In the proximity of the droplet interface, Marangoni flow is directed towards increasing surface tension. So far, there have been detailed studies of the flow field around active droplets, where the surface tension is axisymmet-ric σ = σ(θ) 38,39 . Formulas of the non-axisymmetric case have been mentioned in an extensive study of the rheology of emulsion drops and have been used to explain cross-streamline migration of emulsion droplets in Poiseuille flow [40][41][42] .…”

Hydrodynamics of an inertial active droplet

“…Surprisingly for , although the external stresslets enlarge due to inertial effect, which successively enhances the interfacial stress (see figure 2 b ), the migration velocity increases with . This is due to the existence of prominent counter rotating vortices of the interior flow in the direction of migration of the droplet (see figure 3 c ), which re-acclimate and retaliate the enhanced stress at finite (Mason & Moremedi 2011). In this regard, we note that the previous counteraction for is inconceivable for an equivalent solid squirmer (with ).…”

“…Wu et al (2009) have demonstrated kinematic separation of mixed bacteria streaming against a wall and shown that the larger bacteria have a faster rate than the smaller bacteria. However, there exist preferably a limited number of studies that have quantified the effects of convective inertia on the kinematics and energetics of swimming droplets (Li & Mao 2001; Mason & Moremedi 2011) which are potential artificial analogues of biological systems.…”

“…The velocity fields of a spherical droplet with a non-uniform interfacial tension up to first order in low Reynolds number flow was attempted by Mason & Moremedi (2011). Further, several studies have numerically investigated the Marangoni transport of droplets in presence of the convective effects of fluid inertia (Li & Mao 2001; Bäumler 2014; Blyth & Pozrikidis 2014; Shardt, Masoud & Stone 2016; Seric, Afkhami & Kondic 2018).…”