Bubble Size and Frequency

Temperature and pressure also interact with particle size to affect bubble size and frequency in fluidized beds. Information on the effect of temperature on bubble size in the literature is somewhat inconsistent. However, the information that does exist suggests that bubble size decreases slightly with temperature for Group A materials (Geldart and 

Kapoor, 1976 Kai and Furusaki, 1985 Yoshida et al., 1976). Although less information exists for larger particle sizes, bubble size appears to not change with temperature for Group B materials (Sishtla et al., 1986 Wittman et al., 1981), and to increase with temperature for Group D materials (Sittiphong et al. 1981). 

Workers generally report that bubble frequency increases with temperature (Mii et al., 1973 Otake et al., 1975 Yoshida et al., 1974). There is an initial rapid increase in frequency with temperature near ambient, which then tapers off at higher temperatures. 

Experimental observations show that the dense-phase viscosity for small Group A particles decreases significantly with pressure (King and Harrison et al., 1980 May and Russell, 1953) as shown in Fig. 11. However, the dense-phase viscosity of Group B and Group D particles 

Pressure also appears to cause bubble frequency to increase. This has been reported by both Rowe et al., (1984) and Chan et al., (1987). Rowe et al., (1984) also reported that bubbles were flatter at elevated pressures. 

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Zhang K, Cui Z, Field RW. Effect of bubble size and frequency on mass transfer in flat sheet MBR. J. Membr. Sci. 2009 332 30-37. 

Choi et al. (1998) proposed a generalized bubble-growth model on mean bubble size and frequency for Geldart s Group A, B, and D particles. The model made use of empirical correlations for volumetric bubble flux and bubble splitting frequency. The proposed model correlated well with the extensive data reported in the literature on mean bubble size and frequency. They also found that the equilibrium bubble diameter increased linearly with the ratio of volumetric bubble flux to the splitting frequency of a bubble. 

The jets in fluidized beds have the following properties the jet penetration depth, the jet expansion angle (or the jet half angle), gas and solids entrainment, initial bubble size, and frequency issuing from the jets. They will be discussed now. 

Choi JH, Son JE, Kim SD. Generalized model for bubble size and frequency in gas-fluidized beds. Ind Eng Chem Res 37 2559-2564, 1998. 

As shown in Section 2.2.5.1, a value of C d of 1.5 X 10-4 is recommended for sodium and a value of 4.65 X 10-4 for potassium (because of their respective modified Jakob numbers). Suffice it to say that the relationship between bubble size and detachment frequency in nucleate boiling of liquid metals is not yet well established, even though it is fundamental to a good understanding of such boiling process. 

Geldart, D., The Size and Frequency of Bubbles in Two-and Three-Dimensional Gas-Fluidised Beds, Powder Technol., 4 41 (1970)... 

From the bubble size and the average flow rate, a first approximation of frequency (thereby total cycle time), as well as the limits between which the chamber pressure oscillates, is determined. The weeping time is calculated from the wave-form equations of chamber pressure, which are ... 

Intensified turbulence can destroy the stability of large bubbles, which leads to smaller bubbles, and increase the frequency of bubble coalescence and breakup, which improves the surface renewal frequency of bubbles [17,18]. Intensified turbulence can be achieved by changing the gas sparger to decrease the initial bubble size and improve its radial distribution, but the effective region of the gas sparger is only limited to a certain height above the distributor [19]. 

The contribution of bubbles to sound speed and attenuation depends on the bubble size and sound fi equency. For instance, a lOO-pm bubble has a resonance frequency of about 60 kHz. This frequency is reciprocally proportional to the bubble diameter. A bubble of 10 om diameter will have a resonance frequency of about 0.6 MHz. 

The effects of gas distributor design and its extent depend on the superficial gas velocity and fiow regime in which the BC operates. In the case of heterogeneous flow, the sparger has a negligible influence on the bubble size and gas-liquid mass transfer because the bubble dynamics are determined by the rate of coalescence and breakup, which are controlled by the liquid properties and the nature and frequency of bubble collisions (Chaumat et al., 2005). Hence, the sparger effect is more pronounced at lower superficial gas velocities (Uq < 0.15m/s) while it is much less important at Uq > 0.20 m/s and nonexistent at Uq > 0.30m/s (Han and Al-Dahhan, 2007). Viscous liquids are also not affected by the gas distributor design if the column is sufficiently tall (Zahradnik et al., 1997). 

Geldart D. The size and frequency of bubbles in two- and three-dimensional gas-fluidised beds. Powder Technol 4 41, 1970. 

N2 2000 Bubble size and velocity decrease bubble frequency increases with pressure more gas flows in bubble wakes and less in bubble voids. 

During a small scale trial the level of contaminants remaining in PCR can be readily observed. In particular, the size and frequency of gels and dirt particles may not only affect the performance of the finished product but also lead to excessive scrap levels during manufacturing. Similar to the sensory assessment, the level of contaminants can be evaluated visually. These observations should also include an assessment of build up on dies or screen packs, and in film production, tear-off or bubble loss. 

There would appear to be no thorough systematic study of the defoaming effect of ultrasound (at frequencies > 20 Hz) as a function of acoustic pressure and frequency in the case of foams prepared from dilute aqueous surfactant solutions. This could be made with foam of different bubble sizes and low polydispersity to establish, for example, whether there exists a relation between frequency, bubble size, and defoaming. It should include consideration of the effect of foam age and therefore drainage. The application of the relevant method to additionally study the effects of the continuous phase viscosity could also be made. The mechanism of defoaming could be probed further if such studies could be combined with study of the effects of changes in the surface dynamic and rheological behavior of the surfactant solutions. 

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. 

Variation of bubble size, bubble frequency, and the standard deviation of -APbed with variation of Ug in the conical fluidized beds with a uniform gas distributor (Fopen = 3.87 %) is shown in Fig. 7. As can be seen, the standard deviation of - APbed and the bubble size increase with increasing Ug in the fully fluidized region. However, bubble frequency remains unchanged with variation of Ug that may imply the bubble size will increase as much as the volumetric gas flow increases. As shown, the bubble size dramatically increases with increasing Ug. Also, it is confirmed that the increase of standard deviation of -APbed is closely related to bubble size. 

Fig. 7. Variation of bubble size, bubble frequency and the standard deviation of -...

The following phenomena pertaining to bubble departure from a heated surface are discussed in this section bubble size at departure, departure frequency, boiling sound, and heat transfer effects by departing bubbles. 

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