Improved partially saturated method for the lattice Boltzmann pseudopotential multicomponent flows.

Abstract

This paper extends the partially saturated method (PSM), used for curved or complex walls, to the lattice Boltzmann (LB) pseudopotential multicomponent model and adapts the wetting boundary condition to model the contact angle. The pseudopotential model is widely used for various complex flow simulations due to its simplicity. To simulate the wetting phenomenon within this model, the mesoscopic interaction force between the boundary fluid and solid nodes is used to mimic the microscopic adhesive force between the fluid and the solid wall, and the bounce-back (BB) method is normally adopted to achieve the no-slip boundary condition. In this paper, the pseudopotential interaction forces are computed with eighth-order isotropy since fourth-order isotropy leads to the condensation of the dissolved component on curved walls. Due to the staircase approximation of curved walls in the BB method, the contact angle is sensitive to the shape of corners on curved walls. Furthermore, the staircase approximation makes the movement of the wetting droplet on curved walls not smooth. To solve this problem, the curved boundary method may be used, but due to the interpolation or extrapolation process, most curved boundary conditions suffer from massive mass leakage when applied to the LB pseudopotential model. Through three test cases, it is found that the improved PSM scheme is mass conservative, that nearly identical static contact angles are observed on flat and curved walls under the same wetting condition, and that the movement of a wetting droplet on curved and inclined walls is smoother compared to the usual BB method. The present method is expected to be a promising tool for modeling flows in porous media and in microfluidic channels.