A thermodynamically consistent diffuse interface model for the wetting phenomenon of miscible and immiscible ternary fluids

Abstract

The wetting effect has attracted great scientific interest because of its natural significance as well as technical applications. Previous models mostly focus on one-component fluids or binary immiscible liquid mixtures. Modelling of the wetting phenomenon for multicomponent and multiphase fluids is a knotty issue. In this work, we present a thermodynamically consistent diffuse interface model to describe the wetting effect for ternary fluids, as an extension of Cahn's theory for binary fluids. In particular, we consider both immiscible and miscible ternary fluids. For miscible fluids, we validate the equilibrium contact angle and the thermodynamic pressure with Young's law and the Young–Laplace equation, respectively. Distinct flow patterns for dynamic wetting are presented when the surface tension and the viscous force dominate the wetting effect. For immiscible ternary fluids, we manipulate the wettability of two contact droplets deposited on a solid substrate according to three scenarios: (I) both droplets are hydrophilic; (II) a hydrophilic droplet in contact with a hydrophobic one; (III) both droplets are hydrophobic. The contact angles at each triple junction from the simulations are compared with Young's contact angle and Neumann's triangle rule. Simulations for the validation of our work are performed in two and three dimensions. In addition, we model the evaporation process of a ternary droplet and obtain the same power law as that of previous experiments. Our model allows one to relate the interfacial energies with surface composition, enabling the modelling of the coffee-ring phenomenon in further perspective.