Bubble size data

Bakker and van den Akker [41] estimated Cb to be 0.4 from bubble size data reported by Greaves and Barigou [42]. 

Figure 4.7 (A) Average relative deviation (in %) between two independent time-averaged vector images over a certain number of data fiies as a function of that number and (B) average relative deviation (in %) between two independent time-averaged bubble size data files as a function of the number of bubbies encountered in that series on a doubie iogarithmic scaie. Reprinted from De Jong et al. (2011) with permission from Elsevier.

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.)... 

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 ... 

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. 

Gal-Or (G4) has recently reported bubble-size distribution data in air-water dispersions. The equipment used to evaluate the bubble-size distribution is a new type of multistage gas-liquid contactor without pressure drop in each stage, in which the gas is drawn in from the bottom of the vessel. Typical bubble-size—cumulative-volume data are given in Fig. 2.f The data show that for 99% of the bubbles, 0.1 < 1.4 mm. The surface mean radius a32... 

Fig. 2. Typical data for the bubble-size distribution in a gas-liquid dispersion produced in a new type of contactor without a pressure drop per stage (G4). Dispersed phase air. Continuous phase water. The solid lines were calculated from Eq. (17) and Eq. (258) or (260). [after Gal-Or and Hoelscher (G5)].

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).

Such spatial variations in, e.g., mixing rate, bubble size, drop size, or crystal size usually are the direct or indirect result of spatial variations in the turbulence parameters across the flow domain. Stirred vessels are notorious indeed, due to the wide spread in turbulence intensity as a result of the action of the revolving impeller. Scale-up is still an important issue in the field of mixing, for at least two good reasons first, usually it is not just a single nondimensional number that should be kept constant, and, secondly, average values for specific parameters such as the specific power input do not reflect the wide spread in turbulent conditions within the vessel and the nonlinear interactions between flow and process. Colenbrander (2000) reported experimental data on the steady drop size distributions of liquid-liquid dispersions in stirred vessels of different sizes and on the response of the drop size distribution to a sudden change in stirred speed. 

In spite of all the simplifications Bakker and Van den Akker applied and given the black box approach for the impeller swept domain, their simulations resulted in values for the bubble size just below the liquid surface, overall holdup, and average kfl values which are in good agreement with their experimental data (see Table II). The major step forward they made was the acquisition of the different spatial distributions of average bubble size (see Fig. 13), bubble holdup and kfl as effected by three common impeller types. As a matter of fact, their approach may be restricted to low values of the gas hold-up. 

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. 

Quigley, Johnson, and Harris (Ql) find that the surface tension has no effect on the bubble size. A comparison of their data with the present general model is not possible because they conducted their experiments under constant pressure, not constant flow, conditions. However, the flow rates employed by them are high in such cases, even for constant flow conditions, the influence of surface tension is small. 

Experimental data for much higher flow rates and for various orifice orientations have been collected by the above investigators, under both constant flow and constant pressure conditions. The data of the above workers, for liquids of different physical properties under constant flow conditions, show that for any definite set of conditions, the bubble size does not decrease continuously with increasing angle of orientation. The data for a viscous liquid are presented in Fig. 20. The orifice oriented at 15° yields higher bubble volumes than the one oriented horizontally. Similarly, the vertically oriented orifice yields higher bubble volumes than that oriented at 60°, under otherwise... 

Figure 20.11 Different bubble size gives different reactor performance. Data from Example 20.1 and Problems 20.3 and 20.4.

Fermentation broths are suspensions of microbial cells in a culture media. Although we need not consider the enhancement factor E for respiration reactions (as noted above), the physical presence per se of microbial cells in the broth will affect the k a values in bubbling-type fermentors. The rates of oxygen absorption into aqueous suspensions of sterilized yeast cells were measured in (i) an unaerated stirred tank with a known free gas-liquid interfacial area (ii) a bubble column and (iii) an aerated stirred tank [6]. Data acquired with scheme (i) showed that the A l values were only minimally affected by the presence of cells, whereas for schemes (ii) and (iii), the gas holdup and k a values were decreased somewhat with increasing cell concentrations, because of smaller a due to increased bubble sizes. 

High-pressure conditions favour a smaller bubble size and narrower bubble-size distribution, and therefore lead to higher gas hold-up in BSCR, except in systems operated with porous plate distributors and at low gas velocities. For design purposes in BSCR at high pressure, where the liquids operate in the batch mode, Luo et al. [31] proposed the following formula for the calculation of the gas hold-up, based on their proper experimental data and those of many other authors [1,26,31-34] for various systems of gas, liquid and solids ... 

A foam is a colloidal dispersion in which a gas is dispersed in a continuous liquid phase. The dispersed phase is sometimes referred to as the internal (disperse) phase, and the continuous phase as the external phase. Despite the fact that the bubbles in persistent foams are polyhedral and not spherical, it is nevertheless conventional to refer to the diameters of gas bubbles in foams as if they were spherical. In practical occurrences of foams, the bubble sizes usually exceed the classical size limit given above, as may the thin liquid film thicknesses. In fact, foam bubbles usually have diameters greater than 10 pm and may be larger than 1000 pm. Foam stability is not necessarily a function of drop size, although there may be an optimum size for an individual foam type. It is common but almost always inappropriate to characterize a foam in terms of a given bubble size since there is inevitably a size distribution. This is usually represented by a histogram of sizes, or, if there are sufficient data, a distribution function. 

Figure 5.4 Data of bubble size probability density distribution in an aerated stirred vessel and fitted PSD curve based on new PSD function.

Data of bubble size probability density distribution in an aerated stirred... 

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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