The form and motion of draining oil drops

The 3-dimensional form of a draining oil drop is complex and varies with time. Dynamic similarity between the time development of drops of different size may be predicted on the assumption of dependence only on body force, viscosity and surface tension. The edge conditions, which introduce an additional edge height parameter, modify this to an approximate, experimentally verified, similarity with slightly different power laws. The edge velocity versus edge slope variation is found to control the shape and progress of the drop. The form of the head may be predicted by a differential equation based on 2-dimensional flow if allowance is made for transverse curvature. In the tail of the drop the influence of surface tension is mainly an indirect one. The tapering plan form which results from the edge velocity condition modifies the parabolic profile which is obtained in 2-dimensional flow.