Surfactant spreading in a two-dimensional cavity and emergent contact-line singularities

We model the advective Marangoni spreading of insoluble surfactant at the free surface of a viscous fluid that is confined within a two-dimensional rectangular cavity. Interfacial deflections are assumed small, with contact lines pinned to the walls of the cavity, and inertia is neglected. Linearising the surfactant transport equation about the equilibrium state allows a modal decomposition of the dynamics, with eigenvalues corresponding to decay rates of perturbations. Computation of the family of mutually orthogonal two-dimensional eigenfunctions reveals singular flow structures near each contact line, resulting in spatially oscillatory patterns of shear stress and a pressure field that diverges logarithmically. These singularities at a stationary contact line are associated with dynamic compression of the surfactant monolayer. We show how they can be regularised by weak surface diffusion. Their existence highlights the need for careful treatment in computations of unsteady advection-dominated surfactant transport in confined domains.

Surfactant transport between foam films

Surfactant transport from foam film to foam film is an essential (yet poorly understood) aspect of the viscoplastic yielding behaviour of flowing foam. Recent experimental and modelling work by Bussonnière & Cantat (J. Fluid Mech., vol. 922, 2021, A25) has, however, helped to advance understanding of the relevant surfactant transport processes: the significance of that work is described herein.

Hydrodynamics and Interfacial Surfactant Transport in Vascular Gas Embolism

Vascular gas embolism - bubble entry into the blood circulation - is pervasive in medicine, including over 340,000 cardiac surgery patients in the US annually. The gas-liquid interface interacts directly with constituents in blood, including cells and proteins, and with the endothelial cells lining blood vessels to provoke a variety of undesired biological reactions. Surfactant therapy, a potential preventative approach, is based in fluid dynamics and transport mechanics. Herein we review literature relevant to understanding of the key gas-liquid interface interactions inciting injury at the molecular, organelle, cellular and tissue levels, including clot formation, cellular activation, and adhesion events. We review the fluid physics and transport dynamics of surfactant-based interventions to reduce tissue injury from gas embolism. In particular, we focus on experimental research and computational and numerical approaches which demonstrate how surface-active chemical based intervention, based on competition with blood-borne or cell surface-borne macromolecules for surface occupancy of gas-liquid interfaces, alters cellular mechanics, mechanosensing and signaling coupled to fluid stress exposures occurring in gas embolism. We include a new analytical approach for which an asymptotic solution to the Navier-Stokes equations coupled to the convection-diffusion interaction for a soluble surfactant provides additional insight regarding surfactant transport with a bubble in a non-Newtonian fluid.

Size dependent droplet interfacial tension and surfactant transport in liquid–liquid systems, with applications in shipboard oily bilgewater emulsions

Dynamic interfacial tension of droplets with surfactants is measured and investigated to understand bilgewater emulsion stability.

Drops with insoluble surfactant squeezing through interparticle constrictions

The interfacial behaviour of surfactant-laden drops squeezing through tight constrictions in a uniform far-field flow is modelled with respect to capillary number, drop-to-medium viscosity ratio and surfactant contamination. The surfactant is treated as insoluble and non-diffusive, and drop surface tension is related to surfactant concentration by a linear equation of state. The constriction is formed by three solid spheres held rigidly in space. A characteristic aspect of this confined and contaminated multiphase system is the rapid development of steep surfactant-concentration gradients during the onset of drop squeezing. The interplay between two physical effects of surfactant, namely the greater interface deformability due to decreased surface tension and interface immobilization due to Marangoni stresses, results in particularly rich drop-squeezing dynamics. A three-dimensional boundary-integral algorithm is used to describe drop hydrodynamics, and accurate treatment of close squeezing and trapped states is enabled by advanced singularity subtraction techniques. Surfactant transport and hydrodynamics are coupled via the surface convection equation (or convection–diffusion equation, if artificial diffusion is included), the interfacial stress balance and a solid-particle contribution based on the Hebeker representation. For extreme conditions, such as drop-to-medium viscosity ratios significantly less than unity, it is found that upwind-biased methods are the only stable approaches for modelling surfactant transport. Two distinct schemes, upwind finite volume and flow-biased least squares, are found to provide results in close agreement, indicating negligible numerical diffusion. Surfactant transport is enhanced by low drop-to-medium viscosity ratios, at which extremely sharp concentration gradients form during various stages of the squeezing process. The presence of surfactant, even at low degrees of contamination, significantly decreases the critical capillary number for droplet trapping, due to the accumulation of surfactant at the downwind pole of the drop and its subsequent elongation. Increasing the degree of contamination significantly affects surface mobility and further decreases the critical capillary number as well as drop squeezing times, up to a threshold above which the addition of surfactant negligibly affects squeezing dynamics.