Computing the viscous effect in early-time drop impact dynamics

The impact of a liquid drop on a solid surface involves many intertwined physical effects, being influenced by drop velocity, surface tension, ambient pressure and liquid viscosity, among others. Recent experiments by Kolinski et al. (Phys. Rev. Lett. 112, 134501 (2014)) show that the liquid--air interface begins to deviate away from the solid surface even before contact. This lift-off of the interface starts at a critical time that scales with the square root of the kinematic viscosity of the liquid. To understand this, we study the approach of a liquid drop towards a solid surface in the presence of an intervening gas layer. We solve the Navier--Stokes equations for the liquid, coupled to the compressible lubrication equations for the gas, in two dimensions. With this approach, we recover the experimentally captured early time effect of liquid viscosity on the drop shape at early time, before the drop contacts the surface. By using computation, we are in a position to further probe the flow in the drop, towards understanding the origin of this viscous effect.