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September 10, 2024
A viscous, lubrication-like response occurs when a thin fluid film is squeezed between a rigid, flat surface and the tip of an incoming projectile. We develop a scaling for this viscous approach stage of fluid-mediated normal impact, particularly for soft impactors. Assuming the mediating fluid is incompressible, the impacting solid exhibits two limit regimes: one dominated by elasticity and the other by inertia. The transition between these regimes is governed by a dimensionless parameter, which represents the ratio between two time scales: the time it takes for surface waves to alert the leading edge of the impactor to the impending impact, and the duration of the final viscous phase of the approach. We also explain why nearly incompressible solids exhibit (a) significant "gliding" before contact during the regime transition, (b) the largest size of the entrapped bubble between the deformed impactor tip and the flat surface, and (c) a sudden decrease in entrapped bubble radius after the regime transition. Finally, we suggest that this dimensionless number can explain the varying dynamics observed experimentally in fluid droplets, depending on their viscosity and surface tension.