Surfactant transport onto a foam film in the presence of surface viscous stress

Vitasari, D. and Grassia, Paul and Martin, Peter (2016) Surfactant transport onto a foam film in the presence of surface viscous stress. Applied Mathematical Modelling, 40. pp. 1941-1958. ISSN 0307-904X (https://doi.org/10.1016/j.apm.2015.09.033)

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Abstract

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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