Volume of Fluid based study of the three phase dynamic contact line in the wetting of a thin channel.*

To investigate the three-phase dynamic contact line in the wetting of thin channels, we numerically design a setup consisting of a pressure gradient driven two-phase flow inside a thin pore (width ~ 30-50 nm). The two phases are separated by an interfacial layer with surface tension, that meets the moving pore wall, hence, a three-phase dynamic contact line is formed, whose modelling is a significant scientific challenge [1], [2]. This setup is then studied numerically by solving the 2D two-phase Navier-Stokes equation subject to three contact line boundary conditions: The Navier slip boundary condition, the super-slip boundary condition and the generalised Navier boundary condition (GNBC). We use the Basilisk flow solver to do Volume-of-Fluid method based simulations with the surface tension force computed using the Continuous surface force method and curvature calculation using the height function. Steady state solutions are found and a critical capillary number, based on the contact line velocity, is predicted beyond which no steady-state solution exists. We see that the Navier slip model with a constant microscopic contact angle is weakly singular, however, sufficient to predict the critical capillary number for wetting. A parametric study with nanometric slip length is done and scaling laws for the interface bending are discovered in the vicinity of the contact line. Then we study the problem using the super-slip boundary condition and a novel VoF based implementation of the generalised Navier boundary condition GNBC. The results from these methods give direct evidence of more regularised solution in the vicinity of the contact line.

[1] Lācis, U., Pellegrino, M., Sundin, J., Amberg, G., Zaleski, S., Hess, B., & Bagheri, S. (2022). Nanoscale sheared droplet: Volume-of-fluid, phase-field and no-slip molecular dynamics. Journal of Fluid Mechanics, 940, A10.

[2] Liu, C., Vandre, E., Carvalho, M., & Kumar, S. (2016). Dynamic wetting failure and hydrodynamic assist in curtain coating. Journal of Fluid Mechanics, 808, 290-315.