Bubble size predictions

It is seldom possible to specify an initial mixer design requirement for an absolute bubble size prediction, particularly if coalescence and dispersion are involved. However, if data are available on the actual system, then many of these correlations could be used to predict relative changes in drop size conditions with changes in fluid properties or impeller variables. 

Geary NW, Rice RG (1991) Bubble Size Prediction for Rigid and Flexible Spargers. AIChE J 37(2) 161-168. 

Varley, J. (1995), Submerged gas-liquid jets Bubble size prediction, Chemical Engineering Science, 50(5) 901-905. 

Bubble size predictions. There are many equations available for predicting bubble sizes in fluidized beds. Those which have mechanistic underpinnings (4,32) are preferred to those which are solely empirical. However, the bubble size should not be allowed to exceed the "maximum stable size predicted from Equation (7). For bundles of horizontal tubes, will also not exceed 1 to 1.5 times the tube-to-tube spacing. 

Garnier C, Lance M, Marie JL (2002) Measurement of local flow characteristics in buoyancy-driven bubbly flow at high void fraction. Exp Therm Fluid Sci 26 811—815 Geary NW, Rice RG (1991) Bubble size prediction for rigid and flexible spaigers. AIChE J 37(2) 161-168... 

Essadki H., Nikov L, Deknas H., (1997), Electrochemical Probe for Bubble Size Prediction in a Bubble Column, Experimental Thermal and Fluid Science, 243-250. 

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). 

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. 

Practical separation techniques for gases dispersed in liquids are discussed. Processes and methods for dispersing gas in hquid have been discussed earlier in this section, together with information for predicting the bubble size produced. Gas-in-hquid dispersions are also produced in chemical reactions and elec trochemic cells in which a gas is liberated. Such dispersions are likely to be much finer than those produced by the dispersion of a gas. Dispersions may also be uninten-tionaUy created in the vaporization of a hquid. 

The prediction of drop sizes in liquid-liquid systems is difficult. Most of the studies have used very pure fluids as two of the immiscible liquids, and in industrial practice there almost always are other chemicals that are surface-active to some degree and make the pre-dic tion of absolute drop sizes veiy difficult. In addition, techniques to measure drop sizes in experimental studies have all types of experimental and interpretation variations and difficulties so that many of the equations and correlations in the literature give contradictoiy results under similar conditions. Experimental difficulties include dispersion and coalescence effects, difficulty of measuring ac tual drop size, the effect of visual or photographic studies on where in the tank you can make these obseiwations, and the difficulty of using probes that measure bubble size or bubble area by hght or other sample transmission techniques which are veiy sensitive to the concentration of the dispersed phase and often are used in veiy dilute solutions. 

Bubble sizes at formation generally increase with surface tension and orifice diameter. Prediction of sizes in swarms from multiple orifices is difficult. In aqueous solutions of low surface tension, Bubble diameters of the order of 1 mm are common. Bubbles produced by the more complicated techniques of pressure flotation or vacuum flotation are usually smaller, with diameters of the order of 0.1 mm or less. 

Steam-liquid flow. Two-phase flow maps and heat transfer prediction methods which exist for vaporization in macro-channels and are inapplicable in micro-channels. Due to the predominance of surface tension over the gravity forces, the orientation of micro-channel has a negligible influence on the flow pattern. The models of convection boiling should correlate the frequencies, length and velocities of the bubbles and the coalescence processes, which control the flow pattern transitions, with the heat flux and the mass flux. The vapor bubble size distribution must be taken into account. 

Bubble size in the circulating beds increases with Ug, but decreases with Ul or solid circulation rate (Gs) bubble rising velocity increases with Ug or Ul but decreases with Gs the ffequeney of bubbles increases with Ug, Ul or Gs. The axial or radial dispersion coefficient of liquid phase (Dz or Dr) has been determined by using steady or unsteady state dispersion model. The values of Dz and D, increase with increasing Ug or Gs, but decrease (slightly) with increasing Ul- The values of Dz and Dr can be predicted by Eqs.(9) and (10) with a correlation coefficient of 0.93 and 0.95, respectively[10]. 

In bubbling, the control of the bubble diameter is a little easier. In these methods bubbles are made at an orifice or a multitude of orifices. If there is only one orifice, of radius r, and if bubble formation is slow and undisturbed, the greatest possible bubble volume is 27rry/gp] y is the surface tension of the liquid, p the difference between the densities of liquid and gas (practically equal to the density of the liquid), and g is acceleration due to gravity. Every type of agitation lowers the real bubble size. On the other hand, if there are many orifices near enough to each other, the actual bubble may be much larger than predicted by the above expression. 

Figure 9 compares Equation 20 with the recent pressure drop flow rate data of Friedmann, Chen, and Gauglitz (5) for a 1 wt% commercial sodium alkyl sulfonate dimer (Chaser SD-1000) stabilized foam in a Berea sandstone. These data are particularly useful because they have been corrected for foam blockage and therefore correctly reflect the flowing bubble regime. The solid line in Figure 9 is best fit according to Equation 20. Unfortunately, neither of the parameters c or 6 is available. Two sets of estimates are shown in Figure 9. When e - 0 (i.e., no surfactant effect) the bubble size is about 30% of a grain diameter. When — 0.1 mm (i.e., a value characteristic of those in Figure 8) the bubble size is about 10 grain diameters. We assert that Equation 20 not only predicts the correct velocity behavior of foam but it does so with reasonable parameter values (23).

Optical probes were used to measure the bubble size, frequency and velocity within the dense bed. The bubble velocity for an actively bubbling bed was found to closely agree with the drift flux form proposed by Davidson and Harrison (1963). In contrast, the volumetric flow rate of the bubbles was found to be far less than that predicted by the two-phase hypothesis (Fig. 40). 

Bubble Dynamics. To adequately describe the jet, the bubble size generated by the jet needs to be studied. A substantial amount of gas leaks from the bubble, to the emulsion phase during bubble formation stage, particularly when the bed is less than minimally fluidized. A model developed on the basis of this mechanism predicted the experimental bubble diameter well when the experimental bubble frequency was used as an input. The experimentally observed bubble frequency is smaller by a factor of 3 to 5 than that calculated from the Davidson and Harrison model (1963), which assumed no net gas interchange between the bubble and the emulsion phase. This discrepancy is due primarily to the extensive bubble coalescence above the jet nozzle and the assumption that no gas leaks from the bubble phase. 

Maier (M2) has given quantitative data showing that the continuous-phase velocity results in a reduction in bubble size. During a study of bubble formation from vertical nozzles, Krishnamurthy et al. (K13) observed a decrease in the bubble volume resulting from an increase in buoyancy caused by the continuous-phase velocity. These authors developed equations based on drag considerations which can predict the bubble volume when the continuous phase has a velocity. But, in their study, the continuous-phase velocity is so directed as to decrease the bubble volume, and hence the results cannot be generalized. 

Calderbank and Rennie (C4) and Rennie and Evans (R5) have found Sauter mean bubble diameters both photographically and from foam densities by y-ray absorption technique. Their bubble size could be predicted by the equation of Leibson et al. (L2) with a frothing system, for orifice Reynolds numbers between 2000 and 10,000. Thus,... 

R. Lemlich Prediction of Changes in Bubble Size Distribution Due to Interbubble Gas Diffusion in Foam. Ind. Eng. Chem. Fund. 17, 89 (1978). 

Figure 20.10 Performance of a fluidized bed as a function of bubble size, as determined by Eq. 21. Compare with the plug flow and mixed flow predictions.

The power of this class of model should be apparent. For example, even the simplest of these models, the one considered here, gives unexpected predictions (e.g., that most of the gas in the bed may be flowing downward) which are subsequently verified. More important still, this type of model can be tested, it can be shown to be wrong, and it can be rejected, because its one parameter, the bubble size, can be compared with observation. 

Two-phase systems are often exposed to turbulent flow conditions in order to maximize the interfacial area of the fluids being contacted. In addition, turbulence is often present in wind tunnels and other laboratory equipment, as well as in nature where it can influence breakup processes (F5). Prediction of drop or bubble sizes in turbulent contacting equipment for any geometry and operating conditions is a formidable problem, primarily because of the inherent theoretical and experimental diflBculties in treating turbulent flows. To these difficulties, which exist in single phase systems, must be added the complexity of interaction of dispersed particles with turbulent flow fields. 

Although bubble sizes for large particles with the a-methyl styrene system have not been measured directly and any prediction must be regarded as highly speculative, Fig. 4.21 shows an estimate of the variation of mean bubble diameter with size of catalyst particles06 . This estimate is based on measurements with glass beads in water, with subsequent adjustments to allow for the different densities of the particles and differences in the viscosity and surface tension of the liquids. 

For very thin liquids, Eqs. (14-206) and (14-207) are expected to be valid 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. Inst. Chem. Eng., 28, 14 (1950)] and Siems and Kauffman [Chem. Eng. Sci., 5, 127 (1956)] have shown that liquid viscosity has very little effect on the bubble volume, but Davidson and Schuler [Trans. Instn. Chem. Eng., 38, 144 (I960)] and Krishnamurthi et al. [Ind. Eng. Chem. Funaam., 7, 549 (1968)] have shown that bubble size increases considerably over that predicted by Eq. (14-206) for liquid viscosities above 1000 cP. In fact, Davidson et al. (op. cit.) found that their data agreed very 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 ... 

Interpretation of available data is frustrated by lack of knowledge of certain fundamental quantities such as Interfacial area, mass transfer coefficients, solubility data, diffusion coefficients, bubble sizes, etc.. Existing equations for almost all of these variables have been developed on the basis of experiments conducted at atmospheric pressure and around room temperature. Use of such predictive equations at the reacting conditions involves large extrapolation, and the combined errors would make the analysis of kinetic data very suspect. In spite of this, most work reported in the literature does use such correlations. 

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