Bubble Sizes

A very important quantity is the bubble size. It not only is important for the hydrodynamics but also directly influences the predictions of, for example, oxygen transfer. In the CFD simulations, it is present in the drag force and thus influences the flow of both the gas and the liquid phase. Small bubbles have a much smaller terminal velocity than larger ones and therefore a longer residence. This directly influences the gas fraction in the fermenter, which has direct consequences on the entire flow behavior. 

Experimental data on the gas fraction for this case are available from Vrabel et ed. [18]. For an impeller speed of 115 rpm and a gas flow rate of 26.3 ls , a gas fraction of 4.7% was deduced from the Vrabel data. The choice of the bubble size has a significant influence on the predicted gas fraction (see the table below). 

In this equation, nj(3r, t) is the number density at position x and time t of the bubbles with size between r/, and di + 5d. These bubbles have a velocity , which depends on the hydrodynamics and needs to be calculated during the simulation. The four terms on the right-hand side are 

Q the production of bubbles of size class i due to coalescence of smaller 

Although the formalism is clear, it has two major draw backs (i) it increases the required computation time even further, and (ii) it requires closure of the production and death rates. Especially, point (ii) is a serious problem the description of breakup and coalescence is rather empirical, making the simulations less reliable. Nevertheless, since the bubble size has such a profound influence on the CFD results, some form of computing the bubble size is needed. 

The gas-liquid interfacial area per unit volume of gas-liquid mixture a (L 1. or L ), calculated by Equation 7.26 from the measured values of the fractional gas holdup and the volume-surface mean bubble diameter d, were correlated 

Values of obtained by dividing k a by a, vfeie correlated by the following dimensionless equation  

For with non-Newtonian (excluding viscoelastic) fluids. Equation 7.45 [23], which is based on data with water and aqueous solutions of sucrose and car-boxymethylcellulose (CMC) in a 15 cm column, may be useful. Note that k a in 

For in bubble columns for non-Newtonian (including viscoelastic) fluids, see Section 12.4.1. 

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The specific surface, a, is also relatively insensitive to the duid dynamics, especially in low viscosity broths. On the other hand, it is quite sensitive to the composition of the duid, especially to the presence of substances which inhibit coalescence. In the presence of coalescence inhibitors, the Sauter mean bubble size, is significantly smaller (24), and, especially in stirred bioreactors, bubbles very easily circulate with the broth. This leads to a large hold-up, ie, increased volume fraction of gas phase, 8. Sp, and a are all related... 

Increases in broth viscosity significantly reduce k a and cause bubble size distributions to become bimodal (30). Overall, k a decreases approximately as the square root of the apparent broth viscosity (31). k a can also be related to temperature by the relationship (32)... 

Two main operational variables that differentiate the flotation of finely dispersed coUoids and precipitates in water treatment from the flotation of minerals is the need for quiescent pulp conditions (low turbulence) and the need for very fine bubble sizes in the former. This is accompHshed by the use of electroflotation and dissolved air flotation instead of mechanically generated bubbles which is common in mineral flotation practice. Electroflotation is a technique where fine gas bubbles (hydrogen and oxygen) are generated in the pulp by the appHcation of electricity to electrodes. These very fine bubbles are more suited to the flotation of very fine particles encountered in water treatment. Its industrial usage is not widespread. Dissolved air flotation is similar to vacuum flotation. Air-saturated slurries are subjected to vacuum for the generation of bubbles. The process finds limited appHcation in water treatment and in paper pulp effluent purification. The need to mn it batchwise renders it less versatile. 

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

Fig. 5. Effect of fines particle size on (a) bubble size for FCC catalyst, of Pp = 1250 kg/m, decreases with increa sing fines content, U = 0.1 m/s and...

Classical bubbles do not exist in the vigorously bubbling, or turbulent fluidization regimes. Rather, bubbles coalesce constantly, and the bed can be treated as a pseudohomogenous reactor. Small bubble size improves heat transfer and conversion, as shown in Figure 5b. Increasing fines levels beyond 30—40% tends to lower heat transfer and conversion as the powder moves into Group C. 

Bubble size control is achieved by controlling particle size distribution or by increasing gas velocity. The data as to whether internal baffles also lower bubble size are contradictory. (Internals are commonly used in fluidized beds for heat exchange, control of soflds hackmixing, and other purposes.)... 

In some cases it seems that internals can increase bubble size. 

As bubbles rise through the bed, they coalesce into larger bubbles. The actual bubble size at any height above the distributor, in the bed is a function of the initial bubble size as it emerges from the gas distributor and the gas flow rate (16) ... 

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). 

Interfacial Forces. Neighboring bubbles in a foam interact through a variety of forces which depend on the composition and thickness of Hquid between them, and on the physical chemistry of their Hquid—vapor interfaces. For a foam to be relatively stable, the net interaction must be sufficiently repulsive at short distances to maintain a significant layer of Hquid in between neighboring bubbles. Otherwise two bubbles could approach so closely as to expel all the Hquid and fuse into one larger bubble. Repulsive interactions typically become important only for bubble separations smaller than a few hundredths of a micrometer, a length small in comparison with typical bubble sizes. Thus attention can be restricted to the vapor—Hquid—vapor film stmcture formed between neighboring bubbles, and this stmcture can be considered essentially flat. 

I, have a fairly broad distribution of bubble sizes and can therefore maintain spherical bubbles with significantly less Hquid. Empirically, foams with greater than about 5% Hquid tend to have bubbles that are stiH approximately spherical, and are referred to as wet foams. Such is the case for the bubbles toward the bottom of the foam shown in Figure 1. Nevertheless, it is important to note that even in the case of these wet foams, some of the bubbles are deformed, if only by a small amount. 

Because the reaction takes place in the Hquid, the amount of Hquid held in the contacting vessel is important, as are the Hquid physical properties such as viscosity, density, and surface tension. These properties affect gas bubble size and therefore phase boundary area and diffusion properties for rate considerations. Chemically, the oxidation rate is also dependent on the concentration of the anthrahydroquinone, the actual oxygen concentration in the Hquid, and the system temperature (64). The oxidation reaction is also exothermic, releasing the remaining 45% of the heat of formation from the elements. Temperature can be controUed by the various options described under hydrogenation. Added heat release can result from decomposition of hydrogen peroxide or direct reaction of H2O2 and hydroquinone (HQ) at a catalytic site (eq. 19). 

In the presence of excess fatty acid, different soap crystalline phase compounds can form, commonly referred to as acid—soaps. Acid—soap crystals are composed of stoichiometric amounts of soap and fatty acid and associate in similar bilayer stmctures as pure soap crystals. There are a number of different documented acid—soap crystals. The existence of crystals of the composition 2 acid—1 soap, 1 acid—1 soap, and 1 acid—2 soap has been reported (13). The presence of the acid—soaps can also have a dramatic impact on the physical and performance properties of the finished soap. The presence of acid—soaps increases the plasticity of the soap during processing and decreases product firmness, potentially to the point of stickiness during processing. Furthermore, the presence of the acid—soap changes the character of the lather, decreasing the bubble size and subsequently increasing lather stabiUty and... 

Ozone is only slightly soluble in water. Thus, factors that affect the mass transfer between the gas and Hquid phases are important and include temperature, pressure, contact time, contact surface area (bubble size), and pH. 

Z. 5-25-Y, large huhhles = AA = 0.42 (NG..) Wi dy > 0.25 cm Dr luterfacial area 6 fig volume dy [E] Use with arithmetic concentration difference, ffg = fractional gas holdup, volume gas/total volume. For large huhhles, k is independent of bubble size aud independent of agitation or liquid velocity. Resistance is entirely in liquid phase for most gas-liquid mass transfer. [79][91] p. 452 [109] p. 119 [114] p. 249... 

Droplets from the jet caused by liquid rushing to fill the cavity left by the bubble (see Fig. 14-89). These droplets range up to 1000 Im, their size depending on bubble size. This is important only at modest loadings. Once foam forms over the surface, drop ejection by this mode decreases sharply. 

Forveiy thin hquids, Eqs. (14-206) and (14-207) are expected to be vahd up to a gas-flow Reynolds number of 200 (Valentin, op. cit., p. 8). For liquid viscosities up to 100 cP, Datta, Napier, and Newitt [Trans. In.st. Chem. Eng., 28, 14 (1950)] and Siems and Kauffman [Chem. Eng. Sci, 5, 127 (1956)] have shown that liquid viscosity has veiy little effec t on the bubble volume, but Davidson and Schuler [Trans. Instn. Chem. Eng., 38, 144 (I960)] and Krishnamiirthi et al. [Ind. Eng. Chem. Fundam., 7, 549 (1968)] have shown that bubble size increases considerably over that predic ted by Eq. (14-206) for hquid viscosities above 1000 cP. In fac t, Davidson et al. (op. cit.) found that their data agreed veiy well with a theoretical equation obtained by equating the buoyant force to drag based on Stokes law and the velocity of the bubble equator at break-off ... 

Wilkinson et al. (op. cit.) make the following observation about the effect of gas density on bubble size The fad that the bubble size decreases shghtly for higher gas densities can be explained on the basis of a force balance. ... 

David W. Taylor Model Basin, Washington, September 1953 Jackson, loc. cit. Valentin, op. cit.. Chap. 2 Soo, op. cit.. Chap. 3 Calderbank, loc. cit., p. CE220 and Levich, op. cit.. Chap. 8). A comprehensive and apparently accurate predictive method has been publisned [Jami-alahamadi et al., Trans ICE, 72, part A, 119-122 (1994)]. Small bubbles (below 0.2 mm in diameter) are essentially rigid spheres and rise at terminal velocities that place them clearly in the laminar-flow region hence their rising velocity may be calculated from Stokes law. As bubble size increases to about 2 mm, the spherical shape is retained, and the Reynolds number is still sufficiently small (<10) that Stokes law should be nearly obeyed. 

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