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Microscopic fluctuations in the spreading fronts of circular wetting liquid droplets

J. M. Marcos1,2, J. J. Meléndez1,2, R. Cuerno3, and J. J. Ruiz-Lorenzo1,2

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Phys. Rev. E 111, 045504 – Published 10 April, 2025

DOI: https://doi.org/10.1103/PhysRevE.111.045504

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 et al., Phys. Rev. E 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∼tδ, where δ≲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.

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Outline

Information

Phys. Rev. E 111, 045504– Published 10 April, 2025
  • Received 14 November 2024
  • Revised 5 February 2025
  • Accepted 27 March 2025
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