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

Recent experiments on coating flows and liquid drop impact both demonstrate that wetting failures caused by air entrainment can be suppressed by reducing the ambient gas 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 $\mathit{Kn}$ . These effects first manifest themselves through Maxwell slip at the boundaries of the gas, so that for sufficiently small $\mathit{Kn}$ 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. A direct comparison with experimental results obtained from a dip-coating process shows that the model recovers most trends but does not accurately predict some of the high viscosity data at reduced pressures. This discrepancy occurs because the gas flow enters the ‘transition regime’, so that more complex descriptions of its non-equilibrium nature are required. Finally, by collapsing onto a master curve experimental data obtained for drop impact in a reduced pressure gas, it is shown that the same physical mechanisms are also likely to govern splash suppression phenomena.