Liquid-solid impacts with compressible gas cushioning

The role played by gas compressibility in gas-cushioned liquid--solid impacts is investigated within a viscous gas and inviscid liquid regime. A full analysis of the energy conservation in the gas is conducted for the first time, which indicates that both thermal diffusion across the gas film and viscous dissipation play an important role in gas cushioning once gas compression becomes significant. Consequently existing models of gas compressibility based on either an isothermal or an adiabatic equation of state for the gas do not fully reflect the physics associated with this phenomenon. Models incorporating thermal diffusion and viscous dissipation are presented, which are appropriate for length scales consistent with droplet impacts, and for larger scale liquid--solid impacts. The evolution of the free surface is calculated alongside the corresponding pressure, temperature and density profiles. These profiles indicate that a pocket of gas can become trapped during an impact. Differences between the new model and older models based on isothermal and adiabatic equations of state are discussed, along with predictions of the size of the trapped gas pocket.