Wetting on a spherical wall: influence of liquid-gas interfacial properties

Abstract

We study the equilibrium of a liquid film on an attractive spherical substrate for an intermolecular interaction model exhibiting both fluid-fluid and fluid-wall long-range forces. We first reexamine the wetting properties of the model in the zero-curvature limit, i.e., for a planar wall, using an effective interfacial Hamiltonian approach in the framework of the well known sharp-kink approximation (SKA). We obtain very good agreement with a mean-field density functional theory (DFT), fully justifying the use of SKA in this limit. We then turn our attention to substrates of finite curvature and appropriately modify the so-called soft-interface approximation (SIA) originally formulated by Napiórkowski and Dietrich [Phys. Rev. B 34, 6469 (1986)] for critical wetting on a planar wall. A detailed asymptotic analysis of SIA confirms the SKA functional form for the film growth. However, it turns out that the agreement between SKA and our DFT is only qualitative. We then show that the quantitative discrepancy between the two is due to the overestimation of the liquid-gas surface tension within SKA. On the other hand, by relaxing the assumption of a sharp interface, with, e.g., a simple smoothing of the density profile there, markedly improves the predictive capability of the theory, making it quantitative and showing that the liquid-gas surface tension plays a crucial role when describing wetting on a curved substrate. In addition, we show that in contrast to SKA, SIA predicts the expected mean-field critical exponent of the liquid-gas surface tension.

References in corpus (3)

• Curvature Dependence of Surface Free Energy of Liquid Drops and Bubbles: A Simulation Study
• Two-dimensional droplet spreading over random topographical substrates
• Evidence for the role of fluctuations in the thermodynamics of nanoscale drops and the implications in computations of the surface tension

Cited by in corpus (14)

• A perspective on the interfacial properties of nanoscopic liquid drops
• Does surface roughness amplify wetting?
• Critical Point Wedge Filling
• The contact line behaviour of solid-liquid-gas diffuse-interface models
• Fluid structure in the immediate vicinity of an equilibrium three-phase contact line and assessment of disjoining pressure models using density functional theory
• The overdamped limit of dynamic density functional theory: Rigorous results
• Equilibrium gas-liquid-solid contact angle from density-functional theory
• Density functional study of complete, first-order and critical wedge filling transitions
• Bridging transitions for spheres and cylinders
• Bridging of liquid drops at chemically structured walls
• Meniscus osculation and adsorption on geometrically structured walls
• Complete wetting near an edge of a rectangular-shaped substrate
• The Influence of Intermolecular Forces at Critical Point Wedge Filling
• Critical effects and scaling at meniscus osculation transitions