Dynamic wetting in the curtain coating by the Volume-of-Fluid method and Navier-slip model Part 2: the slip length and the inertial effects

The dynamic wetting failure in the curtain coating setup is studied numerically by solving the 2D two-phase Navier-Stokes equation subject to the Navier-Slip boundary condition and a constant contact angle at the grid scale using the Volume of Fluid method. Previously, the results were shown to recover the logarithmic curvature singularity and the hydrodynamic assist property for the reduced model with the slip-length of 10 microns [Kulkarni, Y., Fullana, T., Zaleski, S. (2021). APS Division of Fluid Dynamics Meeting Abstracts (pp. P29-008)]. We now show that the problem involves highly coupled length scales. The inertial effects can not be neglected up to a scale of 10 microns making the apparent contact angle depend on the Reynolds number as well and proving the reduced model slip length to be unphysical large. By decreasing the slip lengths to a few hundreds of nanometers we observe a shift in the stability window. Finally, we compare against the experiments of Blake, Bracke and Shikhmurzaev (1999) and recover the experimentally observed nonlocal hydrodynamic effects on the scale of 20 microns qualitatively. The effect of slip length reduction is seen and the threshold between stable and unstable solution is displaced towards the experimental one.