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.

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

“…We first develop GPU parallel computing for the LBM code developed in our previous study [14,19]. Based on the previous CUDA-GPU implementation of LBM for several single-phase flows [38][39][40][41], we employ the same CUDA parallel algorithm in the current two-phase flow.…”

“…We also learned that an Ohnesorge number (Oh, defined in Sec. III A) determines whether a damping oscillation would occur in the post-coalescence stage [14]. We have identified a critical Oh value (≈0.477) that separates two distinct post-coalescence behaviors: with or without damping oscillation when Oh is smaller or larger than 0.477, respectively.…”

“…This study focused on the effects of liquid viscosity and surface tension on the decay of the damped oscillation but lacked a quantitative exploration of the underlying physics of the oscillation. It is substantially meaningful to understand the post coalescence because very different behavior could occur in this coalescence stage such as damped oscillation [13,14], shrinking [15], and off-center or head-on separation [16]. However, there remains a challenge to study global coalescence, especially when size inequality of parent bubbles is involved.…”

“…We explore the underlying physics in the global process of microbubble coalescence to support the design and optimization of the prototype. Prior to this work, we have studied the temporal and spatial scalings of air microbubble coalescence in water [19], the effects of the initial conditions on the neck growth [9] in the early coalescence, and the mechanism of damping oscillation in the post coalescence [14] through numerical simulations using the lattice Boltzmann method (LBM) [20,21].…”

Thermodynamic non-equilibrium effects in bubble coalescence: A discrete Boltzmann study

“…There have been many studies on the phenomenon and mechanism of bubble coalescence through experiments [11][12][13][14][15][16][17][18][19], theoretical analyses [12,20,21] and numerical simulations [14,[22][23][24][25][26][27][28][29][30][31]. Stover, et al [14] first investigated the turbulence characteristics of coalescence of bubbles with different sizes, viscosities, and surface tensions.…”