Two-dimensional droplet spreading over random topographical substrates

TL;DR

This paper theoretically investigates how random topographical substrates influence the motion and spreading behavior of two-dimensional droplets, revealing that substrate roughness reduces wetting and causes droplet sliding.

Contribution

It introduces a statistical approach to model droplet dynamics on random substrates and derives variance and distribution properties of droplet displacement over time.

Findings

Droplet shift variance is derived for early and long times.

Droplet footprint follows a normal distribution at all times.

Surface roughness decreases droplet wetting and promotes sliding.

Abstract

We examine theoretically the effects of random topographical substrates on the motion of two-dimensional droplets via appropriate statistical approaches. Different random substrate families are represented as stationary random functions. The variance of the droplet shift at both early times and in the long-time limit is deduced and the droplet footprint is found to be a normal random variable at all times. It is shown that substrate roughness decreases droplet wetting, illustrating also the tendency of the droplet to slide without spreading as equilibrium is approached. Our theoretical predictions are verified by numerical experiments.