A Level Set Method for the Simulation of Moving Contact Lines in Three Dimensions (Communications in Computational Physics, 2023)
We propose an efficient numerical method for the simulation of the two-phase flows with moving contact lines in three dimensions. The mathematical modelconsists of the incompressible Navier-Stokes equations for the two immiscible fluidswith the standard interface conditions, the Navier slip condition along the solid wall,and a contact angle condition (Ren et al. (2010) [28]). In the numerical method, thegoverning equations for the fluid dynamics are coupled with an advection equation fora level-set function. The latter models the dynamics of the fluid interface. Followingthe standard practice, the interface conditions are taken into account by introducing asingular force on the interface in the momentum equation. This results in a single set ofgoverning equations in the whole fluid domain. Similarly, the contact angle conditionis imposed by introducing a singular force, which acts in the normal direction of thecontact line, into the Navier slip condition. The new boundary condition, which unifiesthe Navier slip condition and the contact angle condition, is imposed along the solidwall. The model is solved using the finite difference method. Numerical results arepresented for the spreading of a droplet on both homogeneous and inhomogeneoussolid walls, as well as the dynamics of a droplet on an inclined plate under gravity.
Keywords: Level set method; two-phase flow; moving contact line; dynamic contact angle; Navier boundary condition.