Bubble interactions

In a multibubble field, every pulsating bubble radiates secondary acoustic wave called acoustic cavitation noise. The pulsation of a bubble is driven by both the primary ultrasound and the acoustic cavitation noise. The influence of the latter on the bubble pulsation is called bubble-bubble interaction [89, 90]. Generally speaking, the bubble-bubble interaction suppresses the bubble expansion as shown in Fig. 1.16 [38, 89-91]. Further studies are required on this topic. 

Yasui K, Lee J, Tuziuti T, Towata A, Kozuka T, Iida Y (2009) Influence of the bubble-bubble interaction on destruction of encapsulated microbubbles under ultrasound. J Acoust Soc Am 126 973-982... 

Ida M, Naoe T, Futakawa M (2007) Suppression of cavitation inception by gas bubble injection A numerical study focusing on bubble-bubble interaction. Phys Rev E 76 046309... 

For the discrete bubble model described in Section V.C, future work will be focused on implementation of closure equations in the force balance, like empirical relations for bubble-rise velocities and the interaction between bubbles. Clearly, a more refined model for the bubble-bubble interaction, including coalescence and breakup, is required along with a more realistic description of the rheology of fluidized suspensions. Finally, the adapted model should be augmented with a thermal energy balance, and associated closures for the thermophysical properties, to study heat transport in large-scale fluidized beds, such as FCC-regenerators and PE and PP gas-phase polymerization reactors. 

Since the estimated MLE is negative, Am < 0, we can say that this case displays as essential regular dynamical behavior. The Poincare map displays an orbit set contained in a short line. The above results can be imputed to the following fact The bubbles rise in an almost-linearly pathway and the liquid phase falls downward between bubbles streams (see scheme in the Figure 10a). This means that the bubbles interactions are feeble. In this way, the modes induced by one bubble stream can not affect another one. 

M. Preuss and H.-J. Butt Direct Measurement of Particle-Bubble Interactions in Aqueous Electrolyte Dependence on Surfactant. Langmuir 14, 3164 (1998). 

Bavarian F, Fan LS, Chalmers JJ. Microscopic visualization of insect cell-bubble interactions. I rising bubbles, air-medium interface, and the foam layer. Biotechnol Bioeng 1991 7 140-150. 

Michaels JD, Mallik AK, Papoutsakis ET (1996), Sparging and agitation-induced injury of cultured animal cells - do cell-to-bubble interactions in the bulk liquid injure cells , Biotechnol. Bioeng. 51 399-409. 

Fig. 4. Schematic of cavitation bubbles interacting with a slurry of precipitated gel particles. The configuration shows typical two orifice processing as afforded in the CaviPro 300 processor. Cavitating bubbles initially form, expand in the recovery zone, and collapse with the formation of a microjet and shock wave.

Ma, N., J.J. Chalmers, J.G. Aunins, W. Zhou, and L. Xie. 2004. Quantitative studies of cell-bubble interactions and cell damage at different Pluronic F-68 and cell concentrations. Biotechnol Prog 20 1183-1191. 

If the probability for a motion caused only by bubbles-liquid interactions is Pa = uAt, then the following 1 — p = 1 — uAt, gives the probability for a displacement due to the bubble-bubble interactions. When we have the last type of motion in the interval of time At, one bubble changes its velocity v to velocity v ... 

The assembly resulting from a bubble-bubble interaction, which takes the velocity of the bubble having the higher velocity ... 

These tvko last relations respect the follovking interaction rule (1) the assembly resulting from a bubble-bubble interaction takes the higher velocity higher of any of the individual velocities of the bubbles. 

The net rate of bubble generation, H, describes redistribution of mass in bubble-bubble interactions. Thus, H is a nonlinear functional of F(x,m,t) and Equations (2) and (3) are a pair of coupled, nonlinear, integro-differential equations in the bubble number density, similar to Boltzmann s equation in the kinetic theory of gases (26,27) or to Payatakes et al (22) equations of oil ganglia dynamics. 

The second term in Equations (1) and (2) accounts for diffu-sional transfer across the bubble boundary. (A factor e /(1+e p is sometimes (e.g. 49) included in the bracket of Eq. 2 o account for the dense phase diffusional resistance.) There is some question (30) of the extent to which there is interference between the bulk flow and diffusion terms. Nevertheless, most experimental evidence suggests that the two terms are additive and that the diffusional term is described by the penetration theory. With these changes, and including a small enhancement factor for bubble interaction. Sit and Grace (35) have recommended the following equations as being in best accord with existing experimental data ... 

Sit, S.P. Grace, J.R. Effect of bubble interaction on interphase mass transfer in gas fluidized beds, Chem. Eng. Sci. 1981, 327. 

Proc. Symp. Blood Bubble Interaction in Decompression Sickness, K. N. Ackles, Ed., Defense Civil Inst. Environmental Med. (DCIEM 73-CP-960) (1973) 49-70. 

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