Spatial and Temporal Scaling of Unequal Microbubble Coalescence

Abstract

We numerically study coalescence of air microbubbles in water, with density ratio 833 and viscosity ratio 50.5, using lattice Boltzmann method. The focus is on the effects of size inequality of parent bubbles on the interfacial dynamics and coalescence time. Twelve cases, varying the size ratio of large to small parent bubble from 5.33 to 1, are systematically investigated. The “coalescence preference,” coalesced bubble closer to the larger parent bubble, is well observed and the captured power-law relation between the preferential relative distance χ and size inequality γ, math formula, is consistent to the recent experimental observations. Meanwhile, the coalescence time also exhibits power-law scaling as math formula, indicating that unequal bubbles coalesce faster than equal bubbles. Such a temporal scaling of coalescence on size inequality is believed to be the first-time observation as the fast coalescence of microbubbles is generally hard to be recorded through laboratory experimentation.