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

Abstract

Bubbles in an acoustic field are affected by forces such as primary and secondary Bjerknes forces, which have been shown to be influenced by acoustic pressure, frequency, bubble size and separation distance between bubbles. However, such studies are predominantly theoretical, and are mostly focused on the sign reversal of the secondary Bjerknes force. This study provides experimental data on the effect of a range of bubble sizes (8-30 μm), distances (⩽0.2 mm), acoustic pressures (20-40 kPa) and frequencies (40-100 kHz) on the relative acceleration of two approaching bubbles. Under these conditions, only variations in the magnitude of the attractive force were observed. Using coupled equations of radial and translational motions, the acceleration and secondary Bjerknes force were calculated and compared to the experimental data. The variations in the magnitude of the secondary Bjerknes forces were explained by simulating bubble radius and coupled volume oscillation as a function of time.

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

“…At low approach velocities the rate of increase in contact area is slow enough to allow drainage and rupture [36]. In general, in the presence of ultrasound, an increase in frequency (at high frequencies) and the acoustic pressure increases the secondary Bjerknes force and the approach velocity [37]. Therefore at some point rebound will be more favourable as opposed to coalescence.…”

“…At higher frequencies there will be a reduction in the distance between antinode regions which can contribute to an increase in coalescence [159]. Additionally, at higher frequencies, the small bubbles in solution are closer to the resonance size, which induces a greater secondary Bjerknes force between them which can lead to coalescence [37]. But this force is proportional to the volume change and since bubble size decreases with increasing frequency, there will be a smaller volume change and the force will decrease, decreasing coalescence [160].…”

“…But this force is proportional to the volume change and since bubble size decreases with increasing frequency, there will be a smaller volume change and the force will decrease, decreasing coalescence [160]. It has been shown for a two bubble system, that frequencies of 80 kHz and 100 kHz have similar approach velocities but for bubbles in lower frequencies it decreases [37]. Also, smaller bubbles have a shorter film drainage time which increases the likelihood of coalescence compared to larger bubbles [161].…”

The secondary Bjerknes force between two oscillating bubbles in Kelvin-Voigt-type viscoelastic fluids driven by harmonic ultrasonic pressure

“…The dependence on the inter-bubble distance is explained qualitatively by linear or weakly nonlinear theories [45,9]. Subsequent research has looked into the effects of multiple scattering, nonlinearity, compressibility, shape oscillations, the coupling with the translation of the bubbles, and dual-frequency driving [36,37,11,31,3,16,35,44,21,46]. Suggestions have been made to use the force to manipulate bubbles as carriers of micro-devices [18,24,1].…”

Sound-mediated stable configurations for polystyrene particles

“…In some sense, the ARF can be viewed as acoustically-induced mutual force (AIMF) between the particles, since the uniform external field by itself does not exert ARF on the particles. Recently, several efforts have been devoted to detect the magnitude of the AIMF [25][26][27][28][29][30], in which the inter-particle attraction and aggregation have been demonstrated experimentally.…”