Spreading of a liquid drop over a plane rigid substrate due to intermolecular forces

TL;DR

This paper derives self-similar solutions to model how a liquid drop spreads on a rigid surface driven by intermolecular forces, considering the transition to monomolecular layers at molecular scales.

Contribution

It introduces a method to connect macroscopic spreading dynamics with molecular-scale layer formation using self-similar solutions and boundary condition matching.

Findings

Self-similar solutions describe spreading behavior.

Transition to monomolecular layer modeled at molecular scale.

Method links macroscopic and microscopic spreading regimes.

Abstract

Self-similar solutions of the equation that describes spreading of a liquid layer due to intermolecular forces are found. It is supposed that, when the thickness of the layer reaches some magnitude of the order of the molecular size, it turns into a monomolecular layer, which can be liquid or gaseous. To describe the spreading of a drop, the solutions of the equations that describe evolution of liquid or gaseous monomolecular layers are matched with the self-similar solutions with using relevant boundary conditions.