Experimental and Theoretical Studies on the Movements of Two Bubbles in an Acoustic Standing Wave Field

Abstract

When subjected to an ultrasonic standing-wave field, cavitation bubbles smaller than the resonance size migrate to the pressure antinodes. As bubbles approach the antinode, they also move toward each other and either form a cluster or coalesce. In this study, the translational trajectory of two bubbles moving toward each other in an ultrasonic standing wave at 22.4 kHz was observed using an imaging system with a high-speed video camera. This allowed the speed of the approaching bubbles to be measured for much closer distances than those reported in the prior literature. The trajectory of two approaching bubbles was modeled using coupled equations of radial and translational motions, showing similar trends with the experimental results. We also indirectly measured the secondary Bjerknes force by monitoring the acceleration when bubbles are close to each other under different acoustic pressure amplitudes. Bubbles begin to accelerate toward each other as the distance between them gets shorter, and this acceleration increases with increasing acoustic pressure. The current study provides experimental data that validates the theory on the movement of bubbles and forces acting between them in an acoustic field that will be useful in understanding bubble coalescence in an acoustic field.

Experimental and theoretical analysis of secondary Bjerknes forces between two bubbles in a standing wave

“…The translational movement of bubbles in an acoustic field is controlled by the acoustic and hydrodynamic forces. Note that the secondary Bjerknes force is significantly higher than the primary Bjerknes force when bubbles are close to each other (at distances 60.2 mm) [19]. Hence, the focus of this study was the translational motion of bubbles when the distance between two bubbles is less or equal to 0.2 mm.…”

“…1(a)), similar to that described by Jiao et al [19], was used to collect experimental data. A cylindrical Pyrex cell containing two parallel flat surfaces for viewing and back lighting purposes was used.…”

“…There are in fact small variations in the magnitude of the secondary Bjerknes force within the regions of attraction and repulsion that are rarely discussed. Experimental evidence of the secondary Bjerknes force is limited due to the practical difficulties in measuring these forces in an acoustic field [8], especially at short separation distances where the secondary Bjerknes force is the main dominant force [19]. Therefore, existing experimental studies are either qualitative [20,21] or restricted to long bubble-bubble separations (>2 mm) and large bubble sizes in the order of millimeters [4,16].…”

A parametric review of sonochemistry: Control and augmentation of sonochemical activity in aqueous solutions

“…At higher pressures, the primary and secondary Bjerknes' forces increases and bubbles experience an increased driving force towards one another [133]. Bubble coalescence can also increase with pressure amplitude because of a rise in approach velocity [134]. This is only true up to the point where the rate of film drainage between bubbles in contact starts to decrease, upon which there is rise in critical thickness for rupture to take place and rebound is more likely to occur [35].…”

“…This is only true up to the point where the rate of film drainage between bubbles in contact starts to decrease, upon which there is rise in critical thickness for rupture to take place and rebound is more likely to occur [35]. A further consideration is that an increase in pressure amplitude causes increased propagation of bubble-bubble oscillation and consequently the bubbles influence each other at increased distances [134].…”