ABSTRACT
The latter case corresponds to an extremely stable film because dП/dxF is always negative. We will primarily consider isotherms of the type shown in Fig. 3a. For this kind of isotherm, the situation regarding the stability of the film to rupture can be summarized as follows:
(4)
A number of theories that attempt to predict the lifetime of a film using linear and nonlinear stability theories have appeared in the literature [42-47]. The emphasis in these theories is on computing the time elapsed between the onset of instability (the point at which dП/dxF=0 and xF=xFm) and the actual rupture of the film, which is deemed to occur when the waves on the surface become large enough for the two film surfaces to touch (Fig. 4). The mean film thickness at which film rupture occurs (xFc) is actually smaller than the mean thickness (xFm) when the instability begins (i.e., xFc<xFm). Needless to say, these theories are extremely complex and it is practically impossible to incorporate them into a global model for foam collapse. We therefore assume that a film ruptures at the moment its surfaces become unstable. In other words, we assume that xFc≈xFm. This assumption is reasonable because the time scale for the growth of the instability is much shorter than the time for film drainage. For an isotherm of the type shown in Fig. 3a, xFc is therefore the film thickness corresponding to the maximum disjoining pressure (Пmax). The disjoining pressure isotherm and especially the value of the maximum disjoining pressure (Пmax) therefore play a critical role in our model for foam collapse.
