paper

Coalescence of Liquid Drops

arXiv:physics/9903017 · doi:10.1017/S002211209900662X

Abstract

When two drops of radius 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 $\rmn$ of the small bridge between the two drops. The flow is driven by a highly curved meniscus of length $2π\rmn$ and width $Δ\ll\rmn$ around the bridge, from which we conclude that the leading-order problem is asymptotically equivalent to its two-dimensional counterpart. An exact two-dimensional solution for the case of inviscid surroundings [Hopper, J. Fluid Mech. , 349 (1990)] shows that $Δ\propto \rmn^3$ and $\rmn \sim (tγ/πη)\ln [tγ/(ηR)]$; 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 $Δ\propto \rmn^{3/2}$ at the meniscus and $\rmn \sim (tγ/4πη) \ln [tγ/(ηR)]$. This basic difference is due to the presence of the outer fluid viscosity, however small. With lengths scaled by a full description of the asymptotic flow for $\rmn(t)\ll1$ involves matching of lengthscales of order $\rmn^2, \rmn^{3/2}$, \rmn\rmn^{7/4}$.

36 pages, including 9 figures

References in corpus (1)

Cited by in corpus (72)