Cox, S. J.; Weaire, D.; Hutzler, S.; Murphy, J.; Phelan, R.; Verbist, G. Applications and generalizations of the foam drainage equation. (English) Zbl 0992.76093 Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 456, No. 2002, 2441-2464 (2000). Summary: We describe some new analytic results concerning the foam drainage equation. The temporal approach to the equilibrium profile of the foam is shown to be exponential, in agreement with numerical calculations. The effect of including the equilibrium distribution of liquid fraction as an initial condition is discussed, with respect to the progress of a solitary wave of liquid through a foam column. Existing analysis is further extended to allow for a variation of bubble sizes within the column, and numerical calculations are compared with experimental results. We then consider the extension of foam drainage equation to two and three dimensions, and, in particular, the effect of confinement in a cylindrical tube. Cited in 9 Documents MSC: 76T10 Liquid-gas two-phase flows, bubbly flows Keywords:coarsening; stability; equilibrium profile of foam; foam drainage equation; solitary wave; foam column; variation of bubble sizes; effect of confinement PDFBibTeX XMLCite \textit{S. J. Cox} et al., Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 456, No. 2002, 2441--2464 (2000; Zbl 0992.76093) Full Text: DOI