Interaction of a bubble and a bubble cluster in an ultrasonic field

Abstract

Using an appropriate approximation, we have formulated the interacting equation of multi-bubble motion for a system of a single bubble and a spherical bubble cluster. The behavior of the bubbles is observed in coupled and uncoupled states. The oscillation of bubbles inside the cluster is in a coupled state. The numerical simulation demonstrates that the secondary Bjerknes force can be influenced by the number density, initial radius, distance, driving frequency, and amplitude of ultrasound. However, if a bubble approaches a bubble cluster of the same initial radii, coupled oscillation would be induced and a repulsive force is evoked, which may be the reason why the bubble cluster can exist steadily. With the increment of the number density of the bubble cluster, a secondary Bjerknes force acting on the bubbles inside the cluster decreases due to the strong suppression of the coupled bubbles. It is shown that there may be an optimal number density for a bubble cluster which can generate an optimal cavitation effect in liquid for a stable driving ultrasound.

The role of the bubble–bubble interaction on radial pulsations of bubbles

“…Yasui obtained a similar result through numerical simulations of radial pulsations in multi-bubble environment by assuming that the ambient radius of each bubble is the same for all the bubbles and by introducing a new variable named the coupling strengths ( , where is the distance from the bubble numbered i ) [14] , [15] , [16] , [17] . Wang formulated an interacting equation of multi-bubble motion for a system of a single bubble and a spherical bubble cluster, and found that the maximum radius of a bubble is suppressed and the suppression is enhanced as the bubble density increases [18] , which confirmed the result achieved by Yasui. The numerical simulation obtained by An suggested that the interaction between bubbles suppresses bubble expansion and the violent extent of the bubble collapse by analyzing the characteristics of cavitation in acoustic standing waves [19] .…”

A review of recent theoretical and computational studies on pinned surface nanobubbles

“…For instance, the lattice Boltzmann method [80] , which is an approach in between continuum dynamics simulations and MD simulations, may have great potential to study the collective effect [81] in the dissolving and formation process of surface nanobubbles [33] . This kind of studies would certainly deepen our understanding on cavitation and bubble nucleation and collapse [82][83][84][85][86][87] .…”

Interactions of bubbles in acoustic Lichtenberg figure

“…When the bubble chain is far enough away from the cluster, the secondary radiation pressure on the nearest bubble can be approximated as where is the bubble separation distance. Therefore, the dynamic equation of the bubble in the chain can be approximated as where is the liquid pressure on the bubble wall, is the van der Waals hard-core radius [38] , is the polytropic exponent, P 0 is the hydrostatic pressure, and , , and c are the liquid surface tension, viscosity, and sound speed, respectively. P a and f are the pressure amplitude and frequency of the external acoustic field, respectively.…”

“…Fig. 8 presents the secondary Bjerknes force ( F B2 ) using a grayscale color range in the R 10 – R 20 plane [34] by setting f = 20 kHz, D = 2 mm, N 1 = 10 3 [38] , and P a = 1.2 and 1.4 atm. The lighter and darker regions represent positive or negative values of F B 2 , respectively.…”