ABSTRACT
Before coalescence starts, RFmin is constant and equal to RFmin0 (the value of RFmin in freshly formed foam; an input parameter). The distribution in any volume element in the foam before coalescence starts is therefore the same as that when the foam has just been formed and is given by:
(139)
Once coalescence starts, however, the value of RFmin in an element is not a constant and increases as coalescence proceeds (see Fig. 30). As RFmin increases, the number of
bubbles decreases and the mean bubble volume increases. At the same time, liquids and surfactants from the ruptured films are distributed among the remaining Plateau border channels. It may be noted that we assume RFmax to be a constant. This is not strictly true. It is possible that geometrical rearrangements occurring during coalescence will give rise to films larger than RFmax. It may also be noted that f and RFmin, and hence the mean bubble volume, are functions of only the vertical position (z) and time (t). This is because if wall effects are neglected, the capillary pressure (σ/rp) at a given level (z) is independent of the radial position and any volume element at a given level will have the same distribution of film radii. On the other hand, at any time t and at each z, we need to know the film thickness xF corresponding to each RF so that we can determine when coalescence starts at each level and how quickly coalescence proceeds. Thus, xF is now a function of RF in addition to t and z. Thus, coalescence gives rise to an additional moving boundary
