Abstract

A method for studying the dynamics of liquid drops by numerical integration of the Navier-Stokes equations is used to examine the motion of colliding drops, with application to the raindrop problem. Consideration is limited to drops of nearly equal size impacting along their line of centers. The numerical solutions are developed to study the problem of water drop rebound in the presence of air, a situation in which the drops fall to make physical contact, but the results also ]have application to a wider variety of phenomena. The internal motion of the drop, changes in the surface configuration, and the associated energetics of the collision are discussed. The variations with impact speed are presented. Calculations are made for drops of 40 μm to 1 mm diameter. It is demonstrated that except for a small viscous effect the collision characteristics, including the drop shape at the stage of maximum deformation and the time for rebound, suitably normalized, are uniquely determined by the Weber number (We) for the drop. The functional relations are shown for We < 5. It is found that over a large range of Weber number the bouncing time is close to the lowest-order period of oscillation, and hence varies essentially as the square root of the drop mass. Comparison of the present results with available experimental data shows good agreement.

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