General power-law temporal scaling for unequal-size microbubble coalescence

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}/sqrt[ρ_{h}σr_{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.