Dynamic wetting failure in curtain coating by the Volume-of-Fluid method and Navier slip model.*

Dynamic wetting failure in a curtain coating setup is studied by solving the 2D two-phase Navier-Stokes equation subjected to a Navier-Slip boundary condition and a constant 90-degree contact angle, using the Volume-of-Fluid method with the surface tension force computed using the Continuous Surface Force method with Height Functions for the curvature (http://basilisk.fr). Sufficient resolution of the slip length is achieved using the quadtree adaptive mesh refinement technique, allowing us to predict the critical parameters of wetting failure. The phenomenon of hydrodynamic assist is seen, wherein, the increasing velocity of the impinging liquid and hence the increasing inertia causes the increase in the value of the critical speed of the solid substrate and hence delaying the wetting failure. The results are validated against previous computations of Liu et al. [C.Y. Liu, E. Vandre, M. Carvalho, S. Kumar, J. Fluid Mech. 808, 290 (2016)]. The logarithmic curvature singularity predicted by theory (and hence a pressure singularity) is discovered at the three-phase contact line, making the slip model weakly singular.