Modeling of thin liquid films with arbitrary many layers

TL;DR

This paper generalizes the thin film equation to multiple layers, deriving pressure models, and employs numerical simulations to analyze stability, dynamics, and equilibrium states of multilayer liquid films.

Contribution

It introduces a generalized multilayer thin film equation, derives pressure models, and validates the approach with numerical simulations and stability analysis.

Findings

The model captures multilayer film dynamics accurately.

Numerical simulations agree with Navier-Stokes results.

Identifies possible equilibrium configurations of multilayer films.

Abstract

We propose the generalization of the thin film equation (TFE) to arbitrarily many immiscible liquid layers. Then, we provide different pathways for deriving the hydrodynamic pressure within the individual layers, showing how to understand the equation as a Cahn-Hilliard-type conservation equation and providing an algorithm to derive the associated Onsager Matrix. Furthermore, we employ a numerical solver based on the multilayer shallow water-lattice Boltzmann method (LBM) for two and three liquid layers in pseudo two and three dimensions to gain insights into the dynamics of the system and to validate the model. We perform a linear stability analysis and assess droplet equilibrium shapes. Furthermore, we compare the dynamics of the proposed thin film equation to full Navier-Stokes simulations and show the possible equilibrium states of the multilayer liquid thin film system.