High-Speed Impact between a Liquid Drop and a Solid Surface

The dynamics of high-speed impact between a compressible liquid drop and a solid surface are reviewed. Previous estimates for the maximum impact pressure have been based on one-dimensional approximations. This paper presents a two-dimensional approximation, adapted from a closely related analysis of the oblique impact between two solid plates. This is valid only for the ``initial'' phase of the impact during which the expanding shock front generated by the impact still remains attached to the target surface, and no lateral outflow takes place. The derivations assume a linear relationship between shock velocity and particle velocity change across the shock front. Numerical results are presented for water and sodium, and can be generalized as follows: The contact pressure remains substantially equal to the one-dimensional pressure until the contact angle φ at the edge has reached about half of its critical value, at which the assumed model beaks down and lateral outflow must initiate. As this critical condition is further approached, the contact edge pressure increases progressively, and its critical value Pc is taken as the maximum impact pressure. The ratio Pc/ρ0C0V0 always exceeds about 2.75 exhibiting a minimum in the vicinity of V0/C0=0.2, where ρ0 and C0 are the density and acoustic velocity of the liquid, and V0 is the impact velocity. These pressures are considerably higher than have been heretofore supposed, but circumstantial experimental evidence supports the present results.