An experimental test of the fractal model for drainage of foam films

Drainage of foam films with different radii (50-150 μm), stabilized by hexathylene glycol dodecyl ether C(12)E(6) and in a presence of 0.024 M NaCl, were analyzed in the light of a recent dynamic fractal classification of [1]. The latter accounts for the effect of film surface corrugations developed during the film drainage. For simplicity, the film surface mobility is neglected since the presence of surfactants reduces dramatically the film surface velocity. The magnitude of surface non-homogeneities, caused by the film drainage, is accounted via a dynamic fractal dimension parameter α being spanned between zero and two. Depending on the α-value the film drains by different kinetic laws. For example, if the thin film is planar α=2 and it drains according to the Reynolds law; if α=1 the film contains an axisymmetric dimple causing faster drainage; if α=1/2 the film exhibits number of asymmetric dimples and the film drains even faster; finally if α=0 the film contains spatially uncorrelated domains causing the fastest possible drainage. The present analysis of experimental data suggests that the parameter α is inversely proportional to the film radius R and it is independent of the type and concentration of surfactants. A semi-empirical model for α is proposed, thus completing the generic dynamic fractal classification.