Analysis of a model for surfactant transport around a foam meniscus

A model developed by Bussonnière & Cantat [1] is considered for film-to-film surfactant transport around a meniscus within a foam, with the transport rate dependent upon film-to-film tension difference. The model is applied to the case of a five-film device, in which motors are used to compress two peripheral films on one side of a central film and to stretch another two peripheral films on the central film's other side. Moreover, it is considered that large amounts of compression or stretch are imposed on peripheral films, and also that compression or stretch might be imposed at high velocities (relative to a characteristic velocity associated with physico-chemical properties of the foam films themselves). The actual strain that results on elements within each film might differ from the imposed strain, with the instantaneous film length coupled to the actual strain determining the amount of surfactant currently on each film (and hence also the amount of surfactant that has transferred either from or onto films). Quite distinct surfactant transport behaviour is predicted for the stretched film compared with the compressed one. In particular, when a film is stretched sufficiently at high enough velocity, surfactant flux onto it is predicted to become extremely 'plastic', increasing significantly.

Viscous froth model applied to the motion and topological transformations of two-dimensional bubbles in a channel: three-bubble case

The viscous froth model is used to predict rheological behaviour of a two-dimensional (2D) liquid-foam system. The model incorporates three physical phenomena: the viscous drag force, the pressure difference across foam films and the surface tension acting along them with curvature. In the so-called infinite staircase structure, the system does not undergo topological bubble neighbour-exchange transformations for any imposed driving back pressure. Bubbles then flow out of the channel of transport in the same order in which they entered it. By contrast, in a simple single bubble staircase or so-called lens system, topological transformations do occur for high enough imposed back pressures. The three-bubble case interpolates between the infinite staircase and simple staircase/lens. To determine at which driving pressures and at which velocities topological transformations might occur, and how the bubble areas influence their occurrence, steady-state propagating three-bubble solutions are obtained for a range of bubble sizes and imposed back pressures. As an imposed back pressure increases quasi-statically from equilibrium, complex dynamics are exhibited as the systems undergo either topological transformations, reach saddle-node bifurcation points, or asymptote to a geometrically invariant structure which ceases to change as the back pressure is further increased.

Micro-mechanical prediction of the effect of surfactant concentration and external friction on the visco-elasto-plastic response of an aqueous foam

We apply a combination of the Viscous Froth model and a surfactant transfer model [Zaccagnino et al., Phys. Rev. E, 2018, 98, 022801] to predict the rheological response of a two-dimensional dry aqueous foam. The model includes both the effect of friction between the foam and the boundaries of the container and also the dissipative effects on the film interfaces caused by surfactant motion. These dynamics are characterized by two free parameters: the Gibbs elasticity, relating surfactant concentration to interfacial tension, and the mobility of the surfactant molecules on the interfaces. We employ numerical simulations to evaluate the static shear modulus, yield stress and the storage and loss moduli of a foam and investigate the effect of our free parameters on these rheological properties.

Simulation of surfactant transport during the rheological relaxation of two-dimensional dry foams

We describe a numerical model to predict the rheology of two-dimensional dry foams. The model accurately describes soap film curvature and viscous friction with the walls, and includes the transport of surfactant within the films and across the vertices where films meet. It accommodates the changes in foam topology that occur when a foam flows and, in particular, accurately represents the relaxation of the foam following a topological change. The model is validated against experimental data, allowing the prediction of elastic and viscous parameters associated with different surfactant solutions.