Surfactant transport onto a foam film in the presence of surface viscosity has been simulated as a model for processes occurring during foam fractionation with reflux. A boundary condition is specified determining the velocity at the end of the film where it joins up with a Plateau border containing surfactant rich reflux material. The evolutions of surface velocity and surfactant surface concentration on the film are computed numerically using a finite difference method coupled with the material point method. Results are analysed both for low and high surface viscosities. Evolution is comparatively rapid when surface viscosity is low, but the larger the surface viscosity becomes, the slower the surface flow, and the lower the surfactant surface concentration on the film at any given time . For a large surface viscosity, the surface concentration of surfactant is maintained nearly uniform except at positions near the Plateau border where the velocity and surfactant concentration fields need to adjust to satisfy the boundary condition at the end of the film. The boundary condition imposed at the end of the film implies also that a drier foam (i.e. smaller radius of curvature of the Plateau border) leads to less surfactant transport onto the films. Moreover, the shorter the film length is, also the shorter the characteristic time for surfactant transport onto the film surface. Thinner films however give longer characteristic times for surfactant transport

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The viscous froth model for two-dimensional (2D) dissipative foam rheology is combined with Marangoni-driven surfactant redistribution on a foam film. The model is used to study the flow of a 2D foam system consisting of one bubble partially filling a constricted channel and a single spanning film connecting it to the opposite channel wall. Gradients of surface tension arising from film deformation induce tangential flow that redistributes surfactant along the film. This redistribution, and the consequent changes in film tension, inhibit the structure from undergoing a foam-destroying topological change in which the spanning film leaves the bubble behind; foam stability is thereby increased. The system’s behaviour is categorized by a Gibbs–Marangoni parameter, representing the ratio between the rate of motion in tangential and normal directions. Larger values of the Gibbs–Marangoni parameter induce greater variation in surface tension, increase the rate of surfactant redistribution and reduce the likelihood of topological changes. An intermediate regime is, however, identified in which the Gibbs–Marangoni parameter is large enough to create a significant gradient of surface tension but is not great enough to smooth out the flow-induced redistribution of surfactant entirely, resulting in non-monotonic variation in the bubble height, and hence in foam stability.

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A fluid mechanics problem relevant to foam fractionation processes is analysed. Specifically the fluid flow field transporting surfactant from foam Plateau borders (fed with surfactant-rich material) towards comparatively surfactant-lean foam films is considered. The extent to which this surfactant mass transfer is limited by surface viscous effects is studied. Previous work (Vitasari et al., 2015) made assumptions about the likely flow field along the Plateau border surface. These assumptions suggested that ‘high’ surface viscosity (measured by a suitable dimensionless parameter) led to strong suppression of the rate of surfactant mass transfer from Plateau border to film, whereas ‘low’ surface viscosity did not suppress this mass transfer rate in any significant way. More detailed fluid mechanical calculations which are carried out here corroborate the aforementioned assumptions in the ‘high’ surface viscosity regime. However the calculations suggest that in the ‘low’ surface viscosity regime, in contrast to the findings from the previous assumptions, moderate reductions in the rate of surfactant mass transfer are also possible. Counterintuitively these moderate reductions in mass transfer rate potentially have more negative impact on fractionation processes than the aforementioned strong suppression. This is because they tend to arise under conditions for which the efficiency of the fractionation system is particularly sensitive to any reduction whatsoever in the surfactant mass transfer rate