Contact-line dynamics on a liquid surface

We study the dynamics of a three-fluid contact line on an underlying solid surface, similarly to the motion of a fluid-fluid front on Slippery Liquid-Infused Porous Surfaces (SLIPS). We present full hydrodynamics simulations based on the coupled Navier-Stokes and generalised Cahn-Hilliard equations. We focus on the dependence of the apparent contact angle of the front on the relevant capillary number, and show how, remarkably, the simulation data can be reproduced by the classical result of the Cox-Voinov theory of contact-line dynamics on a solid surface. By analysing the simulation data and deriving a simplified analytical model, we identify and rationalise the relevant length-scale governing the motion of the contact line, thus establishing a clear analogy between the classical problem of contact-line dynamics on a solid, and the emerging topic of dynamic wetting of a liquid surface.