Effect of capillary and viscous forces on spreading of a liquid drop impinging on a solid surface

Abstract

The theoretical models for the deformation of a liquid drop impinging on a solid flat surface at the initial and late stages are proposed. It was found that at the initial stage of the drop impact, the thickness of the emerging film decreases rapidly along its radius r, as r−6, that is similar to the splash jet induced by the blunt-body impact on the liquid surface. The thickness of the film levels off with time due to the viscous force, and the late stage of the drop spreading is controlled by the action of viscous and capillary forces. The influence of the capillary forces is localized in the vicinity of the triple line, and it causes the formation of the thick border (blob) on the edge of the spreading drop. An analytical solution of the model in viscous limit reveals that the minimum film thickness scales as Re−2∕5 and the drop maximum radius in its maximum extension as Re1∕5. The analytical solution for the dynamics of the blob mass growth is also obtained. The kinetic energy of the drop at its maximum extension remains greater than zero in the drop-spreading process even accounting for viscous effect.