Weak solutions to a two-phase thin film model with insoluble surfactant driven by capillary effects

TL;DR

This paper investigates the existence of weak solutions for a complex, coupled system modeling a two-phase thin film with insoluble surfactant influenced by capillary forces, involving degenerate, high-order PDEs.

Contribution

It establishes the existence of non-negative global weak solutions for a novel, strongly coupled two-phase thin film model with insoluble surfactant and capillary effects.

Findings

Proved existence of non-negative weak solutions

Analyzed degenerate, coupled high-order PDEs

Extended mathematical understanding of thin film dynamics

Abstract

Of concern is the study of a system of three equations describing the motion of a viscous complete wetting two-phase thin film endowed with a layer of insoluble surfactant on the surface of the upper fluid under the effects of capillary forces. The governing equations for the film heights of the two-phase flow are degenerate, parabolic and strongly coupled fourth-order equations, which are additionally coupled to a second-order parabolic transport equation for the surfactant concentration. A result on the existence of non-negative global weak solutions is presented.