Analysis of a model for surfactant transport around a foam meniscus

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Abstract

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.

Original languageEnglish
Article number20220133
Number of pages21
JournalProceedings of the Royal Society A : Mathematical, Physical and Engineering Sciences
Volume478
Issue number2262
Early online date29 Jun 2022
DOIs
Publication statusPublished - 29 Jun 2022

Keywords

  • foam rheology
  • foam films
  • surfactant transport
  • Gibbs elasticity
  • meniscus
  • mathematical modelling

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