Droplet motion on chemically heterogeneous substrates with mass transfer. II. Three-dimensional dynamics

TL;DR

This paper develops a mathematical model to describe the three-dimensional motion of droplets on chemically heterogeneous surfaces with mass transfer, using asymptotic analysis and numerical validation to capture complex droplet behaviors.

Contribution

It introduces a novel set of evolution equations for droplet contact lines on heterogeneous substrates, accounting for mass transfer and long-wave dynamics.

Findings

Model accurately predicts droplet motion features.

Excellent agreement between model and numerical experiments.

Captures effects of substrate heterogeneity and mass transfer.

Abstract

We consider a thin droplet that spreads over a flat, horizontal and chemically heterogeneous surface. The droplet is subjected to changes in its volume though a prescribed, arbitrary spatiotemporal function, which varies slowly and vanishes along the contact line. A matched asymptotics analysis is undertaken to derive a set of evolution equations for the Fourier harmonics of nearly circular contact lines, which is applicable in the long-wave limit of the Stokes equations with slip. Numerical experiments highlight the generally excellent agreement between the long-wave model and the derived equations, demonstrating that these are able to capture many of the features which characterize the intricate interplay between substrate heterogeneities and mass transfer on droplet motion.