A second-order phase field-lattice Boltzmann model for two-phase flows with moving contact line and soluble surfactants

This paper presents a second-order phase field-lattice Boltzmann model for two-phase flows with moving contact lines and soluble surfactants. The phase field and surfactant concentration field are governed by second-order conservative Allen-Cahn equations, while the velocity-based Navier–Stokes equations describe the flow field. The model ensures that surfactant concentration variations do not affect the order parameter distribution, preventing sharpening effects. An approximate explicit equation of state, derived from the Gibbs–Duhem equation, defines the relationship between surfactant concentration and interfacial tension, which is incorporated into Young's equation to determine the equilibrium contact angle. A geometrically defined wetting boundary condition addresses the moving contact line problem. Model validation includes verifying the equation of state using the Laplace law and assessing the equilibrium contact angle based on the geometric properties of droplets spreading on planar surfaces. Simulations explore the effects of wettability, surfactant concentration, and flow parameters on droplet dynamics, including Couette and Poiseuille flows, gravity-driven droplet motion, and droplet behavior on rough surfaces. The study results indicate that increasing surfactant concentration reduces the contact angle on hydrophilic surfaces while increasing it on hydrophobic surfaces, highlighting its impact on surface wettability.