Bubble–bubble interaction effects on dynamics of multiple bubbles in a vortical flow field

Abstract

Bubble-bubble interactions play important roles in the dynamic behaviours of multiple bubbles or bubble clouds in a vortical flow field. Based on the Rayleigh-Plesset equation and the modified Maxey-Riley equation of a single bubble, bubble-bubble interaction terms are derived and introduced for multiple bubbles. Thus, both the Rayleigh-Plesset and modified Maxey-Riley equations are improved by considering bubble-bubble interactions and then applied for the multiple bubbles entrainment into a stationary Gaussian vortex. Runge-Kutta fourth-order scheme is adopted to solve the coupled dynamic and kinematic equations and the convergence study has been conducted. Numerical result has also been compared and validated with the published experimental data. On this basis, the oscillation, trajectory and effects of different parameters of double-bubble and multi-bubble entrainment into Gaussian vortex have been studied and the results have been compared with those of the cases without bubble-bubble interactions. It indicates that bubble-bubble interactions influence the amplitudes and periods of bubble oscillations severely, but have small effects on bubble trajectories.

Interaction between encapsulated microbubbles: A finite element modelling study

“…The definition of the microbubble shell parameters in the finite element model in this paper is based on the modified microbubble model proposed by Sarkar. [19] This model neglects the variation of the film thickness and the changing of the shell parameter with the radius of bubble. In the following work, the modified parameters of Marmottant, Doinkov, and other more complex models can be modified to further improve the accuracy of the FEM simulation results.…”

“…In order to maintain the spherical vibration of the bubble, R j is set to be smaller enough than D(t), and the ratio of D(t) to R j (t) is larger than 10 in the simulation. [18,19] In addition, the common symmetric axis of two bubbles is defined as the z axis in this paper and the initial midpoint of the line segment between two bubbles' centers is set to be as the original point (viz., point O). If the bubbles are considered as air-free bubbles, the gasliquid boundary should satisfy the following boundary conditions:…”

Electrostatic Interaction in Stochastic Electrodynamics

“…The problem of the sign for electro-acoustic charge is unresolved [48] because the acoustic particle (the oscillating bubble) has no spin. A possible solution to the problem of the internal kinetic moment of a charged acoustic particle is a model in which the oscillating bubble is captured by a vortex in the fluid [49][50][51][52][53][54]. Highlighting this property is only possible by modelling the interactions between the two oscillators in the SED formalism, without using the notion of interaction cross-section.…”

Bubble–bubble interaction effects on multiple bubbles dynamics in an ultrasonic cavitation field

“…So single-bubble study is not sufficient to fully understand the cavitation dynamics in practical situations, and bubble–bubble interaction can (sometimes drastically) alter the amplitude and period of bubble oscillation relative to the unmodified equations. 22…”

“…So single-bubble study is not sufficient to fully understand the cavitation dynamics in practical situations, and bubblebubble interaction can (sometimes drastically) alter the amplitude and period of bubble oscillation relative to the unmodified equations. 22 When taking the sound interaction among bubbles in vibratory test into account, 14 the theoretical model used to describe bubble's evolution process is a coupled Keller-Miksis equation, which reads Table 1. Chemical composition of the 6061 alloy (wt.%).…”