Some thin film models based on Shikhmurzaev's approach

TL;DR

This paper develops new lubrication approximation models for thin film flows and meniscus formation based on Shikhmurzaev's contact line approach, considering different slip length regimes.

Contribution

It introduces several novel lubrication models derived from Shikhmurzaev's contact line theory, expanding understanding of thin film and meniscus dynamics.

Findings

Models cover different slip length scales.

Provides theoretical framework for contact line problems.

Enhances modeling of meniscus formation.

Abstract

We derive several lubrication approximation models, using Shikhmurzaev's approach to the contact line problem, obtained in \cite{GNV}. The first two lubrication models describe thin film flow of incompressible fluids on solid substrates, based on different orders of magnitude of the slip length parameter. The third lubrication model describes a meniscus formation where a wedge-shaped solid immerses in a thin film of fluid.