A fractal classification of the drainage dynamics in thin liquid films

TL;DR

This paper introduces a dynamic fractal dimension to classify and predict the drainage behavior of thin liquid films, unifying various models and explaining complex dependencies.

Contribution

It presents a novel dynamic fractal classification method that effectively describes film drainage and consolidates existing results into a general scaling law.

Findings

The dynamic fractal dimension effectively classifies drainage dynamics.

The general expression predicts diverse drainage models.

It explains the complex dependence of thinning rate on film radius.

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 obtained general expression for the thinning rate is a heuristic one and predicts 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 complicate dependence of the thinning rate on the film radius.