We systematically study the effects of liquid viscosity, liquid density, and surface tension on global microbubble coalescence using lattice Boltzmann simulation. The liquid-gas system is characterized by Ohnesorge number Oh ≡ η h / √ ρ h σ r F with η h , ρ h , σ , and r F being viscosity and density of liquid, surface tension, and the radius of the larger parent bubble, respectively. This study focuses on the microbubble coalescence without oscillation in an Oh range between 0.5 and 1.0. The global coalescence time is defined as the time period from initially two parent bubbles touching to finally one child bubble when its half-vertical axis reaches above 99% of the bubble radius. Comprehensive graphics processing unit parallelization, convergence check, and validation are carried out to ensure the physical accuracy and computational efficiency. From 138 simulations of 23 cases, we derive and validate a general power-law temporal scaling T * = A 0 γ −n , that correlates the normalized global coalescence time (T *) with size inequality (γ) of initial parent bubbles. We found that the prefactor A 0 is linear to Oh in the full considered Oh range, whereas the power index n is linear to Oh when Oh < 0.66 and remains constant when Oh > 0.66. The physical insights of the coalescence behavior are explored. Such a general temporal scaling of global microbubble coalescence on size inequality may provide useful guidance for the design, development, and optimization of microfluidic systems for various applications.

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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.