A lattice Boltzmann method for thin liquid film hydrodynamics

TL;DR

This paper introduces a lattice Boltzmann method tailored for simulating thin liquid film hydrodynamics, accurately capturing phenomena like instabilities, droplet spreading, and dewetting on complex substrates.

Contribution

It presents a novel lattice Boltzmann approach specifically designed for thin film flows, validated against theoretical and experimental benchmarks.

Findings

The method recovers thin film equations in appropriate limits.

It accurately models the Cox-Voinov law and slip effects.

The approach successfully simulates complex dewetting processes.

Abstract

We propose a novel approach to the numerical simulation of thin film flows, based on the lattice Boltzmann method. We outline the basic features of the method, show in which limits the expected thin film equations are recovered and perform validation tests. The numerical scheme is applied to the viscous Rayleigh-Taylor instability of a thin film and to the spreading of a sessile drop towards its equilibrium contact angle configuration. We show that the Cox-Voinov law is satisfied, and that the effect of a tunable slip length on the substrate is correctly captured. We address, then, the problem of a droplet sliding on an inclined plane, finding that the Capillary number scales linearly with the Bond number, in agreement with experimental results. At last, we demonstrate the ability of the method to handle heterogenous and complex systems by showcasing the controlled dewetting of a thin film on a chemically structured substrate.