Mechanism of damped oscillation in microbubble coalescence

Abstract

This work is part of our continuous research effort to reveal the underlying physics of bubble coalescence in microfluidics through the GPU-accelerated lattice Boltzmann method. We numerically explore the mechanism of damped oscillation in microbubble coalescence characterized by the Ohnesorge (Oh) number. The focus is to address when and how a damped oscillation occurs during a coalescence process. Sixteen cases with a range of Oh numbers from 0.039 to 1.543, varying in liquid viscosity from 0.002 to 0.08kg/(m · s) correspondingly, are systematically studied. First, a criterion of with or without damped oscillation has been established. It is found that a larger Oh enables faster/slower bubble coalescence with/without damped oscillation when (Oh < 0.477)/(Oh > 0.477) and the fastest coalescence falls at Oh ≈ 0.477. Second, the mechanism behind damped oscillation is explored in terms of the competition between driving and resisting forces. When Oh is small in the range of Oh < 0.477, the energy dissipation due to viscous effect is insignificant, sufficient surface energy initiates a strong inertia and overshoots the neck movement. It results in a successive energy transformation between surface energy and kinetic energy of the coalescing bubble. Through an analogy to the conventional damped harmonic oscillator, the saddle-point trajectory over the entire oscillation can be well predicted analytically.