Droplet motion on chemically heterogeneous substrates with mass transfer. I. Two-dimensional dynamics

TL;DR

This paper develops an analytical model for the two-dimensional motion of viscous droplets on chemically heterogeneous surfaces, incorporating effects of slip, mass transfer, and capillarity, and validates it against simulations.

Contribution

It introduces a reduced integrodifferential system for droplet dynamics under slow mass transfer, extending understanding of complex droplet behaviors on heterogeneous substrates.

Findings

Model predictions match full simulations well.

Droplet dynamics exhibit stick-slip and hysteresis effects.

Mass variation can cause transitions between different droplet states.

Abstract

We consider the dynamics of thin two-dimensional viscous droplets on chemically heterogeneous surfaces moving under the combined effects of slip, mass transfer and capillarity. The resulting long-wave evolution equation for the droplet thickness is treated analytically via the method of matched asymptotic expansions in the limit of slow mass transfer rates, quasi-static dynamics and vanishingly small slip lengths to deduce a lower-dimensional system of integrodifferential equations for the two moving fronts. We demonstrate that the predictions of the deduced system agree excellently with simulations of the full model for a number of representative cases within the domain of applicability of the analysis. Specifically, we focus on situations where the mass of the drop changes periodically to highlight a number of interesting features of the dynamics, which include stick-slip, hysteresis-like effects, as well as the possibility for the droplet to alternate between the constant-radius and constant-angle stages which have been previously reported in related works. These features of the dynamics are further scrutinized by investigating how the bifurcation structure of droplet equilibria evolves as the mass of the droplet varies.