Abstract:
Coalescence is one of the canonical examples of singular interfacial dynamics due to a change in topology. When two bubbles touch, a hole is formed in the fluid sheet between them, and surface tension acting on the hole’s tightly curved edge quickly pulls it wider. A similarity solution is derived for the sheet thickness and velocity profile, which shows that the radius of the hole increases as t^0.5 for any Reynolds (Ohnesorge) number. Remarkably, inertia and viscosity have the same scalings with time and remain in fixed proportion.
Similarly, when viscous drops touch, surface tension acts on the tightly curved interface around the fluid bridge between them and widens the bridge radius like t log t. Paulsen (2012) pointed out that Hopper’s (1984) solution for coalescence in Stokes flow is inconsistent with experiment and with even a small amount of inertia. Solution for the full asymptotic structure of the flow at small times resolves this problem by matching between solutions on the four length scales involved.