Smoothed profile-lattice Boltzmann method for non-penetration and wetting boundary conditions in two and three dimensions

In this study, the smoothed profile-lattice Boltzmann method (SP-LBM) is proposed to determine the contact line dynamics on a hydrophobic or a hydrophilic curved wall. Two types of smoothed indicator functions are introduced, namely a function that identifies the solid domain for non-slip and non-penetration conditions and a function that denotes the boundary layer for no mass-flux and the wetting boundary conditions. In order to prevent fluid penetration into the solid boundary, the fluid-solid interaction force is computed based on the definition of the fluid velocity as proposed by Guo et al. [1]. In order to implement the Neumann boundary conditions for the order parameter and the chemical potential, the fluxes from the solid surfaces are distributed to relevant physical valuables through a smoothed profile. Several two-dimensional and three-dimensional numerical investigations including those determining the Couette flows, flow around a circular cylinder, transition layer on a wetting boundary, and dynamic behavior of a droplet on a flat or curved plate demonstrate the efficiency of the present method in calculating the contact angle of a droplet on curved surfaces with wall impermeability. The present model provides a simple algorithm to compute the surface normal vector and contact line dynamics on an arbitrarily shaped boundary by using a smoothed-profile.