Complete Wetting and Drying at Sinusoidal Walls

We investigate complete wetting and drying at sinusoidally corrugated solid walls, focusing on the effects of wall geometry and interaction range. Two distinct interaction models are considered: one incorporating only short-ranged (SR) forces (applied to drying), and another including long-ranged (LR) van der Waals interactions (applied to wetting). The SR model is analyzed within the framework of nonlocal Hamiltonian theory by Parry et al., while the LR model is treated using a sharp-kink approximation. In both cases, we derive scaling relations that describe the dependence of the adsorbed layer’s width and morphology on the wall’s geometric parameters as the system approaches two-phase coexistence. We identify distinct scaling regimes determined by the degree of wall corrugation and highlight the contrasting effects of SR and LR interactions. Theoretical predictions are corroborated by numerical results from classical density functional theory.

💡 Research Summary

This paper presents a comprehensive theoretical and numerical study of complete wetting and drying phenomena at sinusoidally corrugated solid walls. The primary objective is to elucidate how wall geometry (amplitude A and period L/wavenumber k) and the range of intermolecular interactions influence the thickness and morphology of the adsorbed liquid or gas layer as the system approaches two-phase coexistence (δμ → 0).

The research employs two distinct microscopic interaction models tailored for each phenomenon. For analyzing complete drying (adsorption of a gas layer at a wall-liquid interface), a model with purely short-ranged (SR) forces, represented by a simple hard-wall potential, is used. For complete wetting (adsorption of a liquid layer at a wall-gas interface), a model incorporating long-ranged (LR) van der Waals interactions, derived from a uniform distribution of wall atoms, is adopted. The microscopic analysis is conducted using classical density functional theory (DFT), which combines Rosenfeld’s fundamental measure theory for hard-sphere repulsion with a mean-field treatment of truncated Lennard-Jones attractions.

To derive analytical scaling laws, the paper utilizes two complementary mesoscopic approaches. For SR systems, the analysis is based on a nonlocal interfacial Hamiltonian theory developed by Parry et al. This theory describes the effective interaction between the corrugated wall and the liquid-gas interface via a nonlocal kernel (Eq. 30), capturing the exponential decay characteristic of SR forces. For LR systems, the analysis employs a sharp-kink approximation, which models the interface as a mathematically sharp boundary and accounts for the algebraic decay of dispersion forces.

The core theoretical results are scaling relations for the mean height of the adsorbed layer (ℓ) and its corrugation amplitude (ϵ) in terms of δμ, A, and k. The analysis identifies distinct scaling regimes depending on the degree of wall corrugation. For weakly corrugated walls, the interface largely conforms to the wall shape. For strongly corrugated walls, the interface becomes flatter relative to the wall’s peaks and valleys. While the qualitative scaling behavior is similar for SR and LR interactions, the specific exponents differ, reflecting the fundamental contrast between exponential and power-law force decays.

The theoretical predictions are rigorously tested against numerical results obtained from the DFT calculations. The DFT simulations are performed for a wide range of parameters, and the extracted values of ℓ and ϵ show excellent agreement with the scaling laws derived from both the nonlocal Hamiltonian (SR) and the sharp-kink approximation (LR). This agreement validates the mesoscopic models and confirms the predicted dependence on wall geometry and interaction range.

In conclusion, the work provides a detailed picture of how sinusoidal corrugation modulates complete wetting and drying. It successfully bridges microscopic DFT simulations and mesoscopic interfacial models, offering predictive scaling relations that highlight the critical roles of both wall topography and the nature of the underlying molecular forces. The findings advance the understanding of interfacial phenomena on rough or patterned surfaces.