Distribution, bubble-size

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)... 

Bubble size distribution Growth stimulants Specific substrate uptake rate... 

C. Average Bubble Diameter and Bubble-Size Distribution. 307... 

J. Effect of Bubble-Size Distribution and Holdup on Mass- or Heat-Transfer... 

This brief discussion of some of the many effects and interrelations involved in changing only one of the operating variables points up quite clearly the reasons why no exact analysis of the dispersion of gases in a liquid phase has been possible. However, some of the interrelationships can be estimated by using mathematical models for example, the effects of bubble-size distribution, gas holdup, and contact times on the instantaneous and average mass-transfer fluxes have recently been reported elsewhere (G5, G9). 

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)].

Most studies on heat- and mass-transfer to or from bubbles in continuous media have primarily been limited to the transfer mechanism for a single moving bubble. Transfer to or from swarms of bubbles moving in an arbitrary fluid field is complex and has only been analyzed theoretically for certain simple cases. To achieve a useful analysis, the assumption is commonly made that the bubbles are of uniform size. This permits calculation of the total interfacial area of the dispersion, the contact time of the bubble, and the transfer coefficient based on the average size. However, it is well known that the bubble-size distribution is not uniform, and the assumption of uniformity may lead to error. Of particular importance is the effect of the coalescence and breakup of bubbles and the effect of these phenomena on the bubble-size distribution. In addition, the interaction between adjacent bubbles in the dispersion should be taken into account in the estimation of the transfer rates... 

Gal-Or and Hoelscher (G5) have recently proposed a mathematical model that takes into account interaction between bubbles (or drops) in a swarm as well as the effect of bubble-size distribution. The analysis is presented for unsteady-state mass transfer with and without chemical reaction, and for steady-state diffusion to a family of moving bubbles. 

This model is proposed for the case of transfer from a swarm of bubbles (with bubble-size distribution) suspended in an agitated liquid with interaction between adjacent bubbles in the presence of surfactants. 

L. Coupled Heat Transfer and Multicomponent Mass Transfer, with Residence-Time and Bubble-Size Distributions... 

In this section, a general formulation will be given for the effect of bubble residence-time and bubble-size distributions on simultaneous and thermodynamically coupled heat- and mass-transfer in a multicomponent gas-liquid dispersion consisting of a large number of spherical bubbles. Here one can... 

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. 

For fluid particles that continuously coalesce and breakup and where the bubble size distributions have local variations, there is still no generally accepted model available and the existing models are contradictory [20]. A population density model is required to describe the changing bubble and drop size. Usually, it is sufficient to simulate a handful of sizes or use some quadrature model, for example, direct quadrature method of moments (DQMOM) to decrease the number of variables. 

The bubble size distribution is closely related to the hydrodynamics and mass transfer behavior. Therefore, the gas distributor should be properly designed to give a good performance of distributing gas bubbles. Lin et al. [21] studied the influence of different gas distributor, i.e., porous sinter-plate (case 1) and perforated plate (case 2) in an external-loop ALR. Figure 3 compares the bubble sizes in the two cases. The bubble sizes are much smaller in case 1 than in case 2, indicating a better distribution performance of the porous sinter-plate. Their results also show the radial profile of the gas holdup in case 1 is much flatter than that in case 2 at the superficial gas velocities in their work. 

The retention time in the flotation chamber is usually about 3 to 5 min, depending on the characteristics of the process water and the performance of the flotation unit. The process effectiveness depends upon the attachment of air bubbles to the particles to be removed from the process water.57 The attraction between the air bubbles and particles is primarily a result of the particle surface charges and bubble size distribution. The more uniform the distribution of water and microbubbles, the shallower the flotation unit can be. 

Iida Y, Ashokkumar M, Tuziuti T, Kozuka T, Yasui K, Towata A, Lee J (2010) Bubble population phenomena in sonochemical reactor II Estimation of bubble size distribution and its number density by simple coalescence model calculation. Ultrason Sonochem 17 480-486... 

Brotchie A, Grieser F, Ashokkumar M (2009) Effect of power and frequency on bubble-size distributions in acoustic cavitation. Phys Rev Lett 102 084302 (4 pages)... 

The interpretation of trends in MBSL and sonochemical yield with electrolyte concentration needs to be revised in light of the aforementioned finding as changes in bubble size distribution and number population not only determine the number of cavitation events occurring but will have a marked effect on sound wave transmission and the local environment surrounding bubbles, influencing collapse symmetry. 

Gas-Liquid Mass Transfer. Gas-liquid mass transfer within the three-phase fluidized bed bioreactor is dependent on the interfacial area available for mass transfer, a the gas-liquid mass transfer coefficient, kx, and the driving force that results from the concentration difference between the bulk liquid and the bulk gas. The latter can be easily controlled by varying the inlet gas concentration. Because estimations of the interfacial area available for mass transfer depends on somewhat challenging measurements of bubble size and bubble size distribution, much of the research on increasing mass transfer rates has concentrated on increasing the overall mass transfer coefficient, kxa, though several studies look at the influence of various process conditions on the individual parameters. Typical values of kxa reported in the literature are listed in Table 19. 

Bubbles, in fluidized beds, 11 805-806 Bubble size control, 11 805 in fluidized beds, 11 819, 821 Bubble size distribution, 12 14 in foams, 12 11 Bubble tear-offs, 20 229 Bubble tray absorbers, 1 27, 29 design, 1 83-86 Bubble-tube reactor, 25 194 Bubble tube viscometer, 21 739 Bubble two-phase theory of fluidization, 11 805-806... 

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

The foam drainage, surface viscosity, and bubble size distributions have been reported for different systems consisting of detergents and proteins. Foam drainage was investigated by using an incident light interference microscope technique. 

Although the above derivation is for crystals, the theory is also applicable to bubble size distribution. In addition to the above four assumptions, the other conditions for its application include (v) no Ostwald ripening, which would modify CSD, and (vi) no coalescence of bubbles. 

Toramam A. (1989) Vesiculation process and bubble size distributions in ascending magmas with constant velocities. /. Geophys. Res. 94, 17523-17542. 

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