Filling and wetting transitions on sinusoidal substrates: a mean-field study of the Landau-Ginzburg model

TL;DR

This study uses a mean-field Landau-Ginzburg model to analyze how sinusoidal microstructured substrates influence wetting and filling transitions, revealing the effects of roughness on interfacial phenomena and transition characteristics.

Contribution

It provides a detailed mean-field analysis of filling and wetting transitions on sinusoidal substrates, comparing results with macroscopic theories and highlighting the impact of substrate roughness.

Findings

First-order filling transitions occur for large periodicity, ending at a critical point.

Wetting transition temperatures are reduced on rough substrates if the flat transition is first-order.

Roughness does not alter wetting temperature if the flat transition is continuous.

Abstract

We study the interfacial phenomenology of a fluid in contact with a microstructured substrate within the mean-field approximation. The sculpted substrate is a one-dimensional array of infinitely long grooves of sinusoidal section of periodicity length L and amplitude A. The system is modelled using the Landau-Ginzburg functional, with fluid-substrate couplings which correspond to either first-order or critical wetting for a flat substrate. We investigate the effect of the roughness of the substrate in the interfacial phenomenology, paying special attention to filling and wetting phenomena, and compare the results with the predictions of the macroscopic and interfacial Hamiltonian theories. At bulk coexistence, for values of L much larger than the bulk correlation, we observe first-order filling transitions between dry and partially filled interfacial states, which extend off-coexistence, ending at a critical point; and wetting transitions between partially filled and completely wet interfacial states with the same order as for the flat substrate (if first-order, wetting extends off-coexistence in a prewetting line). On the other hand, if the groove height is of order of the correlation length, only wetting transitions between dry and complete wet states are observed. However, their characteristics depend on the order of the wetting transition for the flat substrate. So, if it is first-order, the wetting transition temperature for the rough substrate is reduced with respect to the wetting transition temperature for a flat substrate, and coincides with the Wenzel law prediction for very shallow substrates. On the contrary, if the flat substrate wetting transition is continuous, the roughness does not change the wetting temperature.