Modelling relaxation following T1 transformations of foams incorporating surfactant mass transfer by the Marangoni effect

The dynamics following T1 transformation of foams, during which certain foam films shrink and others grow, was modelled. Variation in surface tension due both to change in surfactant concentration and viscous drag was taken into account. Surfactant transfer was also taken into account, which was assumed to take place between connected films and to be caused by the Marangoni effect. Two models were considered in the first instance, one treating the two sides of shrinking films to be identical and another treating them to be different. Numerical results show plausible behaviours in certain parameter regimes, however with several potential issues. In particular, in one model, singularity was observed above a certain value of the surfactant mass transport coefficient, while such an event was avoided in the other model, as large tension differences between adjacent films are then suppressed. Analysing the results and comparing the models, with a view to applying them to a hexagonal honeycomb foam (rather than just to an isolated set of films), led to a possibility of further improvement; namely incorporating an inter-system surfactant transfer and variation in both surface tension and surfactant concentration along individual films, on top of the mechanisms already considered. Inter-system surfactant transfer was readily incorporated into a third model, which again displayed plausible behaviour.

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► New models are given for film growth/surfactant transfer after a T1 transformation.
► The models consider surfactant on films that shrink, as well as on those that grow.
► Shrinking and growing films are therefore treated in a consistent fashion.
► A T1 involving 5 isolated films behaves differently from that in a periodic foam.