Air entrainment in dynamic wetting : Knudsen effects and the influence of ambient air pressure

Here, it is shown that non-equilibrium effects in the gas can account for this behaviour, with ambient pressure reductions increasing the mean free path of the gas and hence the Knudsen number Kn. These effects first manifest themselves through Maxwell slip at the boundaries of the gas, so that for sufficiently small Kn they can be incorporated into a continuum model for dynamic wetting flows.

The resulting mathematical model contains flow structures on the nano-, micro- and millimetre scales and is implemented into a computational platform developed specifically for such multiscale phenomena. The coating flow geometry is used to show that for a fixed gas–liquid–solid system (a) the increased Maxwell slip at reduced pressures can substantially delay air entrainment, i.e. increase the ‘maximum speed of wetting’, (b) unbounded maximum speeds are obtained, as the pressure is reduced only when slip at the gas–liquid interface is allowed for, and (c) the observed behaviour can be rationalised by studying the dynamics of the gas film in front of the moving contact line.