Influence of insoluble surfactant on the deformation and breakup of a bubble or thread in a viscous fluid

Abstract

The influence of surfactant on the breakup of a prestretched bubble in a quiescent viscous surrounding is studied by a combination of direct numerical simulation and the solution of a long-wave asymptotic model. The direct numerical simulations describe the evolution toward breakup of an inviscid bubble, while the effects of small but non-zero interior viscosity are readily included in the long-wave model for a fluid thread in the Stokes flow limit.The direct numerical simulations use a specific but realizable and representative initial bubble shape to compare the evolution toward breakup of a clean or surfactantfree bubble and a bubble that is coated with insoluble surfactant. A distinguishing feature of the evolution in the presence of surfactant is the interruption of bubble breakup by formation of a slender quasi-steady thread of the interior fluid. This forms because the decrease in surface area causes a decrease in the surface tension and capillary pressure, until at a small but non-zero radius, equilibrium occurs between the capillary pressure and interior fluid pressure.The long-wave asymptotic model, for a thread with periodic boundary conditions, explains the principal mechanism of the slender thread's formation and confirms, for example, the relatively minor role played by the Marangoni stress. The largetime evolution of the slender thread and the precise location of its breakup are, however, influenced by effects such as the Marangoni stress and surface diffusion of surfactant.

Dynamics of a viscous thread surrounded by another viscous fluid in a cylindrical tube under the action of a radial electric field: breakup and touchdown singularities

“…Recent and ongoing analytical studies concentrate on describing the pinching process asymptotically by utilizing the separation of radial and axial scales and mapping the dynamics to a class of self-similar solutions which are universal when inertia is present; notable studies include the work of Eggers (1993), Eggers & Dupont (1994), Papageorgiou (1995), Brenner et al (1996) for jets surrounded by a passive medium; Craster et al (2002), Craster et al (2003), Craster et al (2005), for surfactant-covered or compound jets; Conroy et al (2010), for core-annular arrangements in the presence of electrokinetic effects. Significant computational work has also been carried out with the aim of simulating the phenomena and evaluating the asymptotic theories (the latter are considerably less demanding numerically) -see Newhouse & Pozrikidis (1992), Pozrikidis (1999), Lister & Stone (1998), Sierou & Lister (2003), who simulate Stokes flows using boundary integral methods, and Ambravaneswaran et al (2002), Chen et al (2002), Notz et al (2001), Notz & Basaran (2004), Collins et al (2007), Hameed et al (2008) who compute the flow at arbitrary Reynolds number and in some instances include the effects of surfactants and electric fields -the extensions and novel aspects of the present work are outlined later.…”

A numerical investigation on the drainage of a surfactant-modified water droplet in paraffin oil

“…Till then, Marangoni convection was shown to be of first importance in a large variety of systems [15,16]. It was in particular shown to govern fingering [17], droplet break-up, coalescence [18][19][20] and drainage [21].…”

“…One challenge is the tracking of the free moving interfaces on which they adsorb/desorb. Another important difficulty is the necessity for the interfaces to remain as sharp as possible even for highly deformed geometries like in shear flows or in splashes [19,20] or rising bubbles [22][23][24][25][26]. Accounting for the effect of a surfactant is adding one more complexity level since a new set of equations describing the mass exchanges between surfactant adsorbed layers and bulk liquids have to be implemented.…”

A diffuse-interface approach for modelling transport, diffusion and adsorption/desorption of material quantities on a deformable interface

“…Surfactants are a classic example where the amphiphilic organic compounds may adsorb to and desorb from a liquid/liquid or liquid/gas interface and lower the surface tension on the interface. Thus, inhomogeneous distribution of surfactants produces Marangoni forces -tangential forces along the interface -that affect the dynamics; surfactants play important roles in vortex pair interaction (e.g., [86,34]), fingering (e.g., [84,63]) and drop break-up and coalescence (e.g., [35,36,48,32]). Other examples include biomembranes where transmembrane proteins play an important role in intraand extra-cellular dynamics (e.g., [46,2,51,29]), epitaxially grown thin films where adsorbing/desorbing adatoms affect the dynamics and coarsening of the thin film (e.g., [23,81,52]), and electrochemical dissolution of binary alloys where one component is removed selectively and dissolved in an electrolyte solution (e.g., [19,15]).…”

“…A level-set method for solving the surfactant equation was presented in [89], and later coupled to an external flow solver in [88]. An alternative approach tracking and approach was developed in [90,32], using the socalled Arbitrary Lagrangian-Eulerian (ALE) method. An immersed interface boundary method for interfacial flows with insoluble surfactants was recently developed in [47].…”