Effect of surfactant redistribution on the flow and stability of foam films

Abstract

<jats:p>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.</jats:p>

Study on high energy absorption of spontaneous closed cell polyacrylate foam

“…With the loose accumulation of surfactant, the elasticity of the surfactant layer becomes smaller due to the reduction of intermolecular hydrogen bonds. [35][36][37] In a word, with the increase of the molecular weight of SI, the elasticity of the cell film becomes smaller and the foam repair effect decreases in the foaming process, that is to say, the stabilizing effect of MMA-g-SI decreases. To prove the functional mechanism of foam stabilizer, the Si element content of pore wall and nonfoaming area were measured by EDS, as shown in Figure 6.…”

The evolution of numerical methods for predicting the distribution of surfactant in the bubble-scale dynamics of foams

“…Critical to predictions of the importance of Marangoni effects is the mobility of the interface: in this case, the dynamics of a soap film with a rigid interface (in, for example, a foam stabilized by proteins) is dominated by the surfactant flow and the drainage of liquid from within the film is largely suppressed. As with simulations of several films using the VFM [11], diffusion of surfactant from the film to the interface is neglected.…”

“…What is lacking from analyses of the five film geometry is any discussion of the effect of bubble pressures. An extension of the VFM attempts to rectify this by considering a single 2D bubble being pushed along channels of various geometries [11]. What this shows is that redistribution of surfactant is critical Figure 4: A 2D system of soap films between four fixed pins at four different times (in units of λ/γ, where λ is the drag coefficient).…”

“…Here we focus on the bubble scale, where the emphasis is on combining existing models, for example of foam rheology and gravity-driven liquid drainage [10] or including Marangoni surfactant redistribution with rheology [11]. This is a response to the recognition that while a model such as Herschel-Bulkley can be fitted to experimental data with high fidelity, the dependence of the fitting parameters (such as the power law exponent) on the material properties (bubble size and polydispersity, for example) is obscure.…”

Surfactant transport between foam films

“…There are hypotheses in the literature (Durand & Stone 2006;Grassia, Oguey & Satomi 2012;Satomi et al 2013) suggesting how a surfactant transport relation might be formulated, but none of them have been subjected to a rigorous fluid mechanical analysis. Indeed, a recent study (Vitasari et al 2020) modelling surfactant transport within a simple foam structure, considered only surfactant transport along individual films, but simply neglected film-to-film surfactant transport for want of a good model. As described below, recent work by Bussonnière & Cantat (2021) has the potential to change that.…”