COLLISION OF OSCILLATING LIQUID-DROPS

A physical model is presented for the variation in the area of the film during the approach of two equisized liquid drops oscillating between prolate and oblate ellipsoidal forms. The equations derived are applicable to collisions that result in coalescence (for which the area monotonically increases with time) or rebound (for which the area expands until a maxima and then contracts) and are verified with the published experimental results. The oscillating component of the acceleration is initially directed towards the mid-plane and the average acceleration is directed away from the mid-plane for the drops to rebound, while the converse is true for the drops to coalesce. This is consistent with the experimental observation of Scheele and Leng (1971, Chem. Engng Sci. 26, 1867-1879) who noted that the drops oscillated from an initial oblate to a final prolate ellipsoidal form in rebound runs and from a prolate to an oblate form in coalescence runs, the actual shape being dependent on the phase angle at contact. Furthermore, equations are derived for the variation in the film thickness with time due to inertial and viscous drainage. The observed coalescence times can be explained in terms of inertial drainage, allowing for the frictional losses at the surface of the film. These may be extremely high should reverse flow occur in the drops when the oscillatory motion is directed away from the mid-plane as actually occurs in the coalescence runs.