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Mechanism of damped oscillation in microbubble coalescence. (English) Zbl 1411.76167

Summary: 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 \(0.08\,\text{kg}/(m\cdot s)\) 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 \(Oh \approx 0.477\). 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.

MSC:

76T10 Liquid-gas two-phase flows, bubbly flows
65Y10 Numerical algorithms for specific classes of architectures
76M28 Particle methods and lattice-gas methods
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