Symmetry Analysis of Surfactant Driven Thin Liquid Film Equations

TL;DR

This paper uses symmetry analysis to derive semi-analytic solutions for surfactant-driven thin liquid film equations, revealing how surfactant concentration influences fluid spreading and thinning.

Contribution

It applies Lie group symmetry methods to a coupled PDE system for thin film flow, providing new semi-analytic solutions and insights into surfactant effects.

Findings

Surfactant concentration accelerates fluid spreading.

Symmetry analysis yields semi-analytic solutions.

Fluid thins faster with increased surfactant.

Abstract

Spreading of liquid thin film driven by surfactant due to the Marangoni effect is described using a coupled system of second-order partial differential equations. Lie group of transformation are used to obtain the symmetries of the given system of partial differential equations. The symmetries are then used to arrive at a semi-analytic solution of the system. Furthermore, a vector field analysis of the obtained solution is performed to provide additional insights into the problem. The obtained results demonstrate that the surfactant concentration drives the fluid, and thereby the fluid thins faster.