Volume-of-Fluid based simulation of the withdrawing tape problem using a novel implementation of the generalized Navier boundary condition

The (static or dynamic) contact angle boundary condition is the classical approach to model the wettability of the solid surface in a two-phase flow model of dynamic wetting. It prescribes the orientation of the interface normal at the contact line. In addition, the Navier slip condition is a frequent choice to regularize the moving contact line singularity. The “generalized Navier boundary condition” (GNBC), introduced by Qian et al., combines the modeling of both effects into one single boundary condition for the fluid velocity at the solid boundary. The uncompensated Young stress enters the force balance between friction and viscous stress at the contact line. Hence, the GNBC leads to a dynamic relaxation of the contact angle.

Using the Volume-of-Fluid solver Basilisk, we develop a second-order accurate interface reconstruction method at the boundary. The reconstructed contact angle is used in the sequel to evaluate the uncompensated Young stress in the simulation. We revisit the classical withdrawing-plate problem to study the effect of the GNBC. It is found that (unlike for the standard model) the curvature and the pressure at the contact line are converging to finite values. Hence, the weak singularity in the standard slip model with prescribed contact angle is successfully removed.