A fractal classification of the drainage dynamics in thin liquid films

Abstract

It is demonstrated that the dynamic structure is very important for the rate of drainage of a thin liquid film and it can be effectively taken into account by a dynamic fractal dimension. It is shown that the latter is a powerful tool for description of the film drainage and classifies all the known results from the literature. The general expression obtained for the thinning rate is a heuristic one and predicts a variety of drainage models, which are even difficult to simulate in practice. It is a typical example of a scaling law, which explains the origin of the complicated dependence of the thinning rate on the film radius.

Acknowledgement: The authors are grateful to the Alexander von Humboldt Foundation for fellowships.