Maximum bubble size

The maximum bubble size for Group A powders is of great significance for design. The single most important parameter controlling bubble size is... 

Figure 5. Internal circulation and maximum bubble size.

The maximum bubble size, where the total gas leakage through the bubble boundary equals the total jet flow, can be obtained from either Eq. (32) or Eq. (33) ... 

Cboo coefficient in relation for local maximum bubble size dba,... 

For a homogeneous and isotropic turbulent field, Hinze (H6) has shown that k in Eq. (159) equals [(l/2)(AVe )]3/5> where NWecr is the critical Weber number of maximum bubble size capable of survival. 

NFr Froude number Npr Substitution given in the text NFr Modified Froude group NRe Reynolds number Nrc Substitution given in the text Nr, Modified Reynolds number NwlCr Critical Weber number of maximum bubble size capable of survival... 

Group B 100-800 Bubbling occurs at velocity >umf. Most bubbles have velocities greater than interstitial gas velocity. No evidence of maximum bubble size. Sand. 

In general an increase in intensity (I) will provide for an increase in the sonochemical effects. Cavitation bubbles, initially difficult to create at the higher frequencies (due to the shorter time periods involved in the rarefaction cycles) will now be possible, and since both the collapse time (Eq. 2.27), the temperature (Eq. 2.35) and the pressure (Eq. 2.36) on collapse are dependent on P i(=Ph + PA)> bubble collapse will be more violent. However it must be realised that intensity cannot be increased indefinitely, since (the maximum bubble size) is also dependent upon the pressure amplitude (Eq. 2.38). With increase in the pressure amplitude (P ) the bubble may grow so large on rarefaction (R g, ) that the time available for collapse is insufficient. 

Bubble breakup and coalescence are both complex processes. In a turbulent-flow held, bubbles are broken up mainly due to the turbulent shear force, and the eventual bubble size is a balance between this force and the surface tension force. For a given gas-liquid system and how held, a maximum bubble size exists. Any bubbles larger than this size will be broken up. According to theory (14), this maximum bubble size relates to gas-liquid physical properties and flow characteristics ... 

Group B powders are characterised by having nmb = umf. Bubbles rise faster than the interstitial gas velocity, coalescence is the dominant phenomenon and there is no evidence of a maximum bubble size, as defined for Group A materials. Bubble size increases with increasing fluidising gas velocity, see Figure 14. The interparticle forces are considered to be negligible for these powders. 

The fluid particle breakage controls the maximum bubble size and can be greatly influenced by the continuous phase hydrodynamics and interfacial interactions. Therefore, a generalized breakage mechanism can be expressed as a balance between external stresses (dominating component), o, that attempts to disrupt the bubble and the surface stress, ai/d, that resists the particle deformation. Thus, at the point of breakage, these forces must balance, o This balance leads to the prediction of a critical Weber number, above which the fluid particle is no longer stable. It is defined by [36] ... 

It is known that the variation of bubble size with pressure is the key for understanding pressure effects on hydrodynamics. The upper limit of the bubble size is set by the maximum stable bubble size, Z)jnax. above which the bubble is subjected to breakup and hence is unstable. Several mechanisms have been proposed for the bubble breakup phenomenon, and based on these mechanisms theories have been established to predict the maximum bubble size in gas-liquid systems. In this section, the mechanisms of bubble breakup and the theories to predict the maximum bubble size are covered. 

Hinze (1955) proposed that bubble breakup is caused by the dynamic pressure and the shear stresses on the bubble surface induced by different liquid flow patterns, e.g., shear flow and turbulence. When the maximum hydrodynamic force in the liquid is larger than the surfaee tension foree, the bubble disintegrates into smaller bubbles. This mechanism can be quantified by the liquid Weber number. When the Weber number is larger than a eritical value, the bubble is not stable and disintegrates. This theory was adopted to prediet the breakup of bubbles in gas liquid systems (Walter and Blaneh, 1986). Calculations by Lin et al. (1998) showed that the theory underprediets the maximum bubble size and cannot predict the effeet of pressure on the maximum bubble size. 

Disturbances in the liquid with a wavelength larger than the critical wavelength can break up a bubble. Equation (16) indicates that the critical wavelength decreases with an increase in pressure and therefore bubbles are easier to break apart by disturbances at higher pressures. However, the critical wavelength is not equivalent to the maximum stable bubble size, and Eq. (16) alone cannot account for the effect of pressure on the maximum bubble size. 

Equation (17) severely underpredicts the maximum bubble size in the air-water system, although it shows a significant effect of pressure on the maximum bubble size. 

The comparison of experimental maximum bubble sizes and the predictions by various instability theories is shown in Fig. 11. The internal circulation model can reasonably predict the observed pressure effect on the maximum bubble size, indicating that the internal circulation model captures the intrinsic physics of bubble breakup at high pressures. The comparison of the predictions by different models further indicates that bubble breakup is governed by the internal circulation mechanism at high pressures over 1.0 MPa, whereas the Rayleigh-Taylor instability or the Kelvin-Helmholtz instability is the dominant mechanism at low pressure. 

There is little published data to confirm the existence of a maximum bubble size because the columns used in academic research are too small bubble growth is then stopped by the column walls before the bubbles can grow to their maximum size. However, data from industrial columns seem to confirm the existence of a maximum bubble size [41]. Although there is some controversy about the mechanism which stops bubble growth, all interpretations postulate that solid particles penetrating into the bubbles are responsible for bubble breakup. 

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