Microscopic fluctuations in the spreading fronts of circular wetting liquid droplets

TL;DR

This study numerically investigates the kinetic roughening and fluctuation properties of spreading circular liquid droplets on solid substrates, revealing universal behaviors and anomalous scaling consistent with the KPZ class.

Contribution

It provides the first detailed comparison of kinetic roughening in circular versus band geometries for droplet spreading, highlighting geometry-dependent scaling and fluctuation characteristics.

Findings

Front position scales as t^δ with δ ≲ 1/2, depending on temperature and wettability.

Front fluctuations exhibit KPZ-like statistics close to Tracy-Widom distribution.

Circular droplets show intrinsic anomalous scaling with different roughness exponents at various scales.

Abstract

We study numerically the kinetic roughening properties of the precursor fronts of nonvolatile liquid droplets spreading on solid substrates, for the case of circular droplets, more frequently addressed in experiments. To this end, we perform kinetic Monte Carlo (kMC) simulations of a lattice gas model whose kinetic roughening behavior has been recently assessed in a band geometry [J.\ M.\ Marcos {\em et al.}, Phys.\ Rev.\ E {\bf 105}, 054801 (2022)]. We compare the scaling behaviors of the spreading fronts obtained for the two geometries, in view of the occurrence of, for example, different universality subclasses for different growth geometries for the related important Kardar-Parisi-Zhang (KPZ) universality class. For circular droplets we obtain that the average front position increases (sub-)diffusively as $R\sim t^{\delta}$, where $\delta \lesssim 1/2$ shows a stronger dependence on the conditions considered for temperature and substrate wettability than in band geometry. In spite of this, front fluctuations for circular droplets behave qualitatively similar to those seen for band geometries, with kinetic roughening exponent values which similarly depend on temperature $T$ but become $T$-independent for sufficiently high $T$. Circular droplets also display intrinsic anomalous scaling with different values of the roughness exponent at short and large length scales, and fluctuations statistics which are close to the Tracy-Widom probability distribution function that applies in the corresponding KPZ universality subclass, now the one expected for interfaces with an overall circular symmetry.