Primary Bjerknes force

Bubbles not only interact with their environment but also with the sound field and the neighboring bubbles. In this section, the problem of the sound field propagation in a bubbly liquid is not addressed because the conditions considered in experimental and theoretical studies are rather far from those encoimtered in sonochemistry. We will focus on the forces between bubbles and the acoustic field (primary Bjerknes force) and between bubbles (mutual or secondary Bjerknes force).H9 Though the primary Bjerknes force is present in progressive 

118 Brunton, J.H. Proc. 2nd Int. Conf Rain Eros (Fyall, A.A. King, R.B. Eds.), Royal Aircraft Establishment, Famborough, UK, 1967, p. 291. 

It may be noted that bubbles with R Rres are attracted towards the pressure antinodes while bubbles with R Rres are attracted towards the nodes. Since bubbles at the antinodes experience greater acoustic pressures, their dynamics is more energetic and the chemical and sonoluminescent effects are preferentially detected at pressure antinodes. i 

The problem with which we are dealing in sonochemistry is the relation between a bubble in a bubble cloud interacting with the radiation force. Here, the problem of the interaction between two bubbles in an incident sound field is described 

The case of two spherical bubbles, smaller than resonance size, for example (i.e., pulsating in phase), is considered. Of course, the situation can be transposed to bubbles larger than resonance size both vibrating out-of-phase with respect to the acoustic pressure, i.e., in phase with one another. In Fig. 26, the left-hand L and 

---

The coalescence of bubbles is driven by the two mechanisms. One is the attractive radiation force between bubbles called secondary Bjerknes force. The other is the other radiation force called the primary Bjerknes force which drives active bubbles to the pressure antinode of a standing wave field, ft should be noted, however, too strong acoustic wave repels bubbles from the pressure antinode as described in the next section [29, 30]. 

When the driving ultrasound is a standing wave, p(x t) is expressed as follows for the primary Bjerknes force. 

Radiation Forces on a Bubble (Primary and Secondary Bjerknes Forces)... 

Both the primary and secondary Bjerknes forces are originated from the pressure gradient across a bubble [35]. 

FIGURE 44.1 Fluorescently labeled polystyrene particles gathered in the pressure nodal plane (in plane with the image focus) of an acoustic standing wave by the primary acoustic radiation force in a 70 xm deep microchannel. The microbeads are also clustered in a dense hexagonal pattern by Bjerknes forces. 

Primary and secondary Bjerknes forces lead to structures known as cavitation streamers. A large bubble above the resonance size oscillating with surface insta-... 

Like the Bjerknes forces, solid particles whose acoustic properties differ from those of the liquid are subject to primary and secondary forces. Primary forces drive particles into pressure nodes, where secondary forces between particles are responsible for further aggregation. 

Secondary Radiation Forces In addition to the axial and lateral radiation forces attributable to the primary acoustic field, secondary acoustic forces are produced between particles themselves. These particle-particle interactions, known as Bjerknes forces, aid the formaticai of aggregates within a standing wave, but are negligible until the particles are in close proximity. 

---