Bubble sizes, maximum stable

Bubbles can grow to on the order of a meter in diameter in Group B powders in large beds. The maximum stable bubble size is limited by the size of the vessel or the stabiUty of the bubble itself. In large fluidized beds, the limit to bubble growth occurs when the roof of the bubble becomes unstable and the bubble spHts. EmpidcaHy, it has been found that the maximum stable bubble size may be calculated for Group A particles from... 

This equation predicts that the height of a theoretical diffusion stage increases, ie, mass-transfer resistance increases, both with bed height and bed diameter. The diffusion resistance for Group B particles where the maximum stable bubble size and the bed height are critical parameters may also be calculated (21). 

Bubble growth will be hmited by the containing vessel and the bubble hydrodynamic stability. Bubbles in group-B systems can grow to several meters in diameter. Bubbles in group-A materials with high fines may reach a maximum stable bubble size of only several cm. 

For Group B particles, there is no particulate fluidization regime. In this case, Umf equals Umb. The bubble size increases with the bed height and bed expansion is moderate. For Group B particle fluidization, there exists no maximum stable bubble size. 

The bubble size may also be estimated on the basis of the correlation of Darton et al. (1977) under conditions of free bubbling beds without slugging and maximum stable bubble size as... 

In the Davidson and Harrison s (1963) maximum stable bubble size model, the bubble disintegration takes place when the relative velocity between the bubble and the particles exceeds the particle terminal velocity. Considering that, for a vertical gas-solid flow system, choking occurs when the maximum stable bubble size is equal to the column size, Yang (1976) obtained the following choking criterion for fine particles fluidization ... 

Geldart4 distinguished these powders as those for which umb/uml- > 1. At gas velocities above wmb bubbles begin to appear, which constantly split and coalesce, and a maximum stable bubble size is achieved. The flow of bubbles produces high solids and gas back-mixing, which makes the powders circulate easily, giving good bed-to-surface heat transfer. 

Matsen (MIO), in studies of bubble diameters in a 61-cm-i.d. fluid bed, recognized that small difference in particle size distribution could produce significant changes in the character of fluidization. With Coke-5 particles (dp at 50 cumulative wt.% = 70 ixm, pp = 2.1 g/cm ), his probe measurements showed initial formation of 25-cm-diameter bubbles, which broke into smaller stable bubbles of —6-13 cm. The maximum stable bubble size in a 13.8-cm-i.d. fluid bed with 26-p,m particles was estimated as 2.5 cm. Massimilla (M3) also reported that smooth fluidization was obtained with fine particles. 

Clift ct al. (C6), in their study of bubbles in fluidized beds, indicate that instead of having a discrete maximum stable bubble size we can expect bubble splitting to occur over a relatively broad and continuous range of bubble sizes. Whether or not a particular bubble splits will depend not only on size but also on angular position, wavelength, and amplitude of disturbances of the bubble interface. It seems likely that measured maximum stable bubble diameters correspond to mean diameters for systems in which dynamic equilibrium has been achieved between coalescence and splitting. 

Luo X, Lee DJ, Lau R, Yang G, Fan L-S. (1999) Maximum stable bubble size and gas hold up in high pressure slurry bubble columns. AICHEJ, 45 665-680. 

In Group A powders limb > limf, bubbles are constantly splitting and coalescing, and a maximum stable bubble size is achieved. This makes for good quality. 

It was suggested by Harrison et al. (1961) that aggregative fluidization may be expected if the ratio of maximum stable bubble size to particle diameter, ( B)max/ is larger than 10, and particulate fluidization, if the ratio is less than or equal to unity. A transition region exists with the ratio between 1 and 10. They proposed to calculate the ratio as follows ... 

Eqs. (26) and (27) are only applicable when the maximum stable bubble size is much smaller than the bed diameter, i.e., without wall effect. Experimental... 

Matsen JM. Evidence of maximum stable bubble size in a fluidized bed. AIChE Symp Ser 69(128) 3(H33, 1973. 

The bubbles are considered to grow continuously while passing through the bed until they reach the maximum stable size or reach the diameter of the bed column. The maximum stable bubble size, can be calculated by (Harrison et al., 1961)... 

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. 

The Kelvin-Helmholtz instability is similar to the Rayleigh-Taylor instability, except that the former allows a relative velocity between the fluids, u. Using the same concept of Grace et al. (1978), Kitscha and Kocamustafaogullari (1989) applied the Kelvin-Helmholtz instability theory to model the breakup of large bubbles in liquids. Wilkinson and van Dierendonck (1990) applied the critical wavelength to explain the maximum stable bubble size in high-pressure bubble columns ... 

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. 

When the centrifugal force is larger than the surface tension force, the bubble would be stretched in the x-direction. During the stretching, the aspect ratio, a, becomes smaller while d, and M), can be assumed to remain constant. As a result, the centrifugal force increases, the surface tension force decreases, and the bubble stretching becomes an irreversible process. Using the Davies-Taylor equation (Davies and Taylor, 1950) for the bubble rise velocity, the maximum stable bubble size is expressed by... 

Figure 11 Comparison of maximum stable bubble size obtained experimentally and the predictions by various models. (From Fan et al., 1999.)... 

---