The Initial Stage of Liquid Drop Impingement onto a Curved Surface

The simplified analysis of the initial jetless stage of high-speed drop impingement onto a convex solid surface recently proposed by Burson-Thomas et al. (2019) has been extended to a concave surface with the radius of curvature larger than the drop radius. An approximate approach has also been proposed to incorporate the surface curvature into Heymann's analysis (1969) based on the Rankine-Hugoniot equations. It has been shown that the simplified analysis predicts a significantly longer initial stage than Heymann's analysis. As opposed to the convex surface, the duration of the initial jetless stage and the corresponding size of the contact area for the concave surface are larger than for the flat one. For both convex and concave surfaces, the effect of the surface curvature is significant when the radii of curvature of the surface and the drop are nearly equal, and is almost absent if the ratio of the radii is more than 10.