Bubble coalescence at any Reynolds number (INVITED)

Abstract eng:
When two bubbles touch, a hole is formed in the fluid sheet between them, and surface tension acting on its tightly curved edge drives radial flow which quickly pulls the hole wider. We present similarity solutions for the thickness of the fluid sheet and the velocity profile, which show that the radius of the hole increases as rE ∝ t1/2 for any Reynolds (Ohnesorge) number. Remarkably, the initially quadratic profile of the sheet allows for an exact solution in which inertia and viscosity have the same scalings with time and remain in fixed proportion. Numerical solution of the third-order set of ODEs determines the prefactors and profiles. Asymptotic analysis of the compressional boundary layer structure in the inviscid limit formally justifies and brings new insight to earlier ad hoc ‘blob’ models. There is excellent agreement with full Navier–Stokes simulations and experimental data from Paulsen et al. [1]

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