Impact of drops on solid surfaces: self-similar capillary waves, and splashing as a new type of kinematic discontinuity

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Abstract
The impact of drops impinging one by one on a solid surface is studied experimentally and theoretically. The impact process is observed by means of a charge-coupled-device camera, its pictures processed by computer. Low-velocity impact results in spreading and in propagation of capillary waves, whereas at higher velocities splashing (i.e. the emergence of a cloud of small secondary droplets, absent in the former case) sets in. Capillary waves are studied in some detail in separate experiments. The dynamics of the extension of liquid lamellae produced by an impact in the case of splashing is recorded. The secondary-droplet size distributions and the total volume of these droplets are measured, and the splashing threshold is found as a function of the impact parameters.The pattern of the capillary waves is predicted to be self-similar. The calculated wave profile agrees well with the experimental data. It is shown theoretically that the splashing threshold corresponds to the onset of a velocity discontinuity propagating over the liquid layer on the wall. This discontinuity shows several aspects of a shock. In an incompressible liquid such a discontinuity can only exist in the presence of a sink at its front. The latter results in the emergence of a circular crown-like sheet virtually normal to the wall and propagating with the discontinuity. It is predicted theoretically and recorded in the experiment. The crown is unstable owing to the formation of cusps at the free rim at its top edge, which results in the splashing effect. The onset velocity of splashing and the rate of propagation of the kinematic discontinuity are calculated and the theoretical results agree fairly well with the experimental data. The structure of the discontinuity is shown to match the outer solution.

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