A single film (typical of a film in a foam) moving in a confined geometry (i.e. confined between closely spaced top and bottom plates) is analysed via the viscous froth model. In the first instance the film is considered to be straight (as viewed from above the top plate) but is not flat. Instead it is curved (with a circular arc cross-section) in the direction across the confining plates. This curvature leads to a maximal possible steady propagation velocity for the film, which is characterised by the curved film meeting the top and bottom plates tangentially. Next the film is considered to propagate in a channel (i.e. between top and bottom plates and sidewalls, with the sidewall separation exceeding that of the top and bottom plates). The film is now curved along as well as across the top and bottom plates. Curvature along the plates arises from viscous drag forces on the channel sidewall boundaries. The maximum steady propagation velocity is unchanged, but can now also be associated with films meeting channel sidewalls tangentially, a situation which should be readily observable if the film is viewed from above the top plate. Observed from above, however, the film need not appear as an arc of a circle. Instead the film may be relatively straight along much of its length, with curvature pushed into boundary layers at the sidewalls.
Grassia, P., Montes-Atenas, G., Lue, L., & Green, T. E. (2008). A foam film propagating in a confined geometry: analysis via the viscous froth model. European Physical Journal E - Soft Matter, 25(1), 39-49. https://doi.org/10.1140/epje/i2007-10262-8