Schematic of a liquid droplet with free surface y = f +(x,t), approaching impact with a shallow liquid layer whose free surface is given by y = f −(x,t).
Contour and image system used to solve the potential flow resulting from a droplet impact with a shallow liquid layer.
Regime diagram indicating the different types of compressible behavior for droplet radius and approach speed for an air-water impact at an ambient pressure p 0 = 105 Pa. The solid curve corresponds to K = ɛ and divides the incompressible regime (below the line) from the compressible regime. The dashed line results from the second inequality in Eq. (22), and we must be above this line to have a lubrication equation governing the air flow. The dotted curve corresponds to Θ = ɛ, below which the gas density is independent of temperature.
Air cushioning in two-dimensional droplet impacts with a liquid layer with depth (a) h = 0, (b) h = 0.2, (c) h = 1, (d) h = 5, and (e) h →∞.
Air cushioning in two-dimensional droplet impacts with a shallow liquid layer. (a) shows the upper free-surface, (b) the lower free-surface, and (c) the pressure. The upper free-surface and the pressure evolution are the same as those shown in Figure 4(a) for droplet impact with a solid wall.
Bubble volume as a function of layer depth h, when [f] = 0.185. The horizontal lines indicate the bubble volume at the same point for impact with a solid and impact with deep liquid.
Air cushioning in two-dimensional droplet-droplet impacts. (a) shows the free-surface profiles and (b) the pressure, for (i) α = 1 (the same sized droplets), (ii) α = 2, and (iii) α = 4.
Air cushioning in two-dimensional droplet-droplet impacts. (a) shows the free-surface profiles and (b) the pressure, for a horizontal offset (i) d = 1.5, (ii) d = 3.0, and (iii) d = 4.5.
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