Coalescence of Liquid Drops

When two drops of radius R touch, surface tension drives an initially singular motion which joins them into a bigger drop with smaller surface area. This motion is always viscously dominated at early times. We focus on the early-time behavior of the radius rm of the small bridge between the two drops. The flow is driven by a highly curved meniscus of length 2πrm and width ∆ ≪ rm around the bridge, from which we conclude that the leadingorder problem is asymptotically equivalent to its two-dimensional counterpart. An exact two-dimensional solution for the case of inviscid surroundings [Hopper, J. Fluid Mech. 213, 349 (1990)] shows that ∆ ∝ r3 m and rm ∼ (tγ/πη) ln[tγ/(ηR)]; and thus the same is true in three dimensions. The case of coalescence with an external viscous fluid is also studied in detail both analytically and numerically. A significantly different structure is found in which the outer fluid forms a toroidal bubble of radius ∆ ∝ r 3/2 m at the meniscus and rm ∼ (tγ/4πη) ln[tγ/(ηR)]. This basic difference is due to the presence of the outer fluid viscosity, however small. With lengths scaled by R a full description of the asymptotic flow for rm(t) ≪ 1 involves matching