Droplet deformation by air cushioning prior to impact is considered. A model is presented coupling the free-surface deformation of a droplet with the pressure field in the narrow air layer generated as a droplet approaches an impact. The model is based upon the density and viscosity in the air being small compared with those in the liquid. Additionally, the Reynolds number, defined using the droplet radius ℛ and approach velocity l, is such that lubrication forces dominate in the air layer. In the absence of significant surface tension or compressibility effects, these assumptions lead to coupled nonlinear integro-differential equations describing the evolution of a droplet free surface approaching a solid wall through air, with or without topography.The problem is studied numerically with a boundary-element method in the inviscid droplet coupled with a finite-difference method in the lubricating air. In normal impacts, air cushioning will be shown to deflect the free surface upwards, delaying the moment of touchdown and trapping a bubble. The volume of the bubble is found to be (μg4/3ℛ5/3/ρl4/3l4/3), where μg is the gas viscosity and ρl is the liquid density and the numerically computed pre-factor = 94.48. Bubble volumes predicted by this relationship are shown to be in good agreement with experimental observations. In oblique impact or impact with a moving surface with sufficient horizontal motion a bubble is not trapped beneath the approaching droplet. In this case, the region of touchdown is initially crescent shaped with air effects accelerating the moment of touchdown.

The evolution of the combined solid-fluid motion when a solid body undergoes a skimming impact with (and rebounds from) a shallow liquid layer is investigated. A model is derived coupling the motion of the body to the fluid dynamics of the liquid layer. This predicts that the lift on the body induced by the pressure in the liquid layer is sufficient to entirely retard its incident downward motion before causing the body to rise out of the liquid. Water exit is predicted at a finite scaled time. Analysis for the small-time behaviour immediately after touchdown, and also as water exit is approached, shows close agreement with numerical prediction.

An experimental and theoretical investigation of the air trapping by a blunt, locally spherical body impacting onto the free surface of water is conducted. In the parameter regime previously studied theoretically by Hicks & Purvis (J. Fluid Mech., vol. 649, 2010, pp. 135–163), excellent agreement between experimental data and theoretical modelling is obtained. Earlier predictions of the radius of the trapped air pocket are confirmed. A boundary element method is used to consider air cushioning of an impact of an axisymmetric body into water. Efficient computational methods are obtained by analytically integrating the boundary integral equation over the azimuthal variable. The resulting numerically computed free-surface profiles predict an annular touchdown region in excellent agreement with the experiments.

Air cushioning of a high-speed liquid droplet impact with a finite-depth liquid layer sitting upon a rigid impermeable base is investigated. The evolution of the droplet and liquid-layer free-surfaces is studied alongside the pressure in the gas film dividing the two. The model predicts gas bubbles are trapped between the liquid free-surfaces as the droplet approaches impact. The key balance in the model occurs when the depth of the liquid layer equals the horizontal extent of interactions between the droplet and the gas film. For liquid layer depths significantly less than this a shallow liquid limit is investigated, which ultimately tends towards the air-cushioning behavior seen in droplet impact with a solid surface. Conversely, for liquid layer depths much deeper than this, the rigid base does not affect the air-cushioning of the droplet. The influence of compressibility is discussed and the relevant parameter regime for an incompressible model is identified. The size of the trapped gas bubble as a function of the liquid layer depth is investigated. The deep water model is extended to consider binary droplet collisions. Again, the model predicts gas bubbles will be trapped as the result of air cushioning in high-speed binary droplet impacts

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 phenomena. 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.