GPU Accelerated Lattice Boltzmann Analysis for Dynamics of Global Bubble Coalescence in the Microchannel

Underlying physics in bubble coalescence is critical for understanding bubble transportation. It is one of the major mechanisms of microfluidics. Understanding the mechanism has benefits in the design, development, and optimization of microfluidics for various applications. The underlying physics in bubble coalescence is investigated numerically using the free energy-based lattice Boltzmann method by massive parametrization and classification.

Firstly, comprehensive GPU (Graphics Processing Unit) parallelization, convergence check, and validation are carried out to ensure the computational efficiency and physical accuracy for the numerical simulations.

Then, the liquid-gas system is characterized by an Ohnesorge number (Oh). Two distinct coalescence phenomena with and without oscillation, are separated by a critical Oh (~0.477)number. For the oscillation cases(Oh<0.477), the mechanism of damped oscillation in microbubble coalescence is explored in terms of the competition between driving and resisting forces. Through an analogy to the conventional damped harmonic oscillator, the saddle-point trajectory over the entire oscillation can be well predicted analytically. Without oscillation in the range of 0.50r^-n

After that, the liquid-gas-solid interface is taken into consideration in the liquid-gas system. Six cases based on the experiment set-ups are simulated first for validation of the computational results. Based on these, a hypothesis is established about critical factors to determine if coalescence-induced microbubble detachment (CIMD) will occur. From the eighteen experimental and computational cases, we conclude that when the radius ratio is close to 1 and the father bubble is larger, then it will lead to CIMD.

Lastly, the effects of initial conditions on the coalescence of two equal-sized air microbubbles (R₀) in water are investigated. In both initial scenarios, the neck bridge evolution exhibits a half power-law scaling, r/R₀=A₀(t/t_i)^1/2 after development time. The development time is caused by the significant bias between the capillary forces contributed by the meniscus curvature and the neck bridge curvature. Meanwhile, the physical mechanism behind each behavior has been explored.