Transfer of Bubbles

Similarly the bubbling bed model may be visualized as a kind of direct contact model when is much greater than k r in Eq. (7-12), since the equation is now reduced to Eq. (7-9) with an apparent equality of/ eb = v under this extreme. Actually, however, the transfer of bubble gas to the cloud-wake region is limited by so that the amount of catalyst y Cb should be greater than v to account for the above data such a large/ Cb again seems unreasonable. 

Coalescenceis especially typical in concentrated emulsions. In such systems coalescence mainly determines the lifetime of emulsions prior to phase separation. In finely dispersed emulsions, both dilute and concentrated, the average size of drops may noticeably increase due to Ostwald ripening. At the same level of dispersion Ostwald ripening of emulsion droplets is a slower process than mass transfer of bubbles in foams [60]. This is due to a rather low interfacial energy, and consequently, low difference in chemical potentials of substance in droplets of different size, as well as due to a lower mutual solubility of liquids as compared to the solubility of gases in liquids. 

The second term in the left-hand side is the convective transfer of bubbles, which is equal to the velocity of a bubble of volume V. We assume that bubbles are small enough, so that u = and a = lApg/i/ti for bubbles with... 

S.P. Levitsky, and Z.P. Shubnan, Dynamics and heat and mass transfer of bubbles in polymeric liquids,... 

Figure 7.2.1. Dependence of the vapor content of air-vapor bubble in toluene from radius at different temperatures. [Adapted, by permission from S.P. Levitsky, and Z.P. Shulman, Dynamics and heat and mass transfer of bubbles In polymeric liquids, Nauka i Tekhnika, Minsk, 1990.]...

Rate of Mass Transfer in Bubble Plates. The Murphree vapor efficiency, much like the height of a transfer unit in packed absorbers, characterizes the rate of mass transfer in the equipment. The value of the efficiency depends on a large number of parameters not normally known, and its prediction is therefore difficult and involved. Correlations have led to widely used empirical relationships, which can be used for rough estimates (109,110). The most fundamental approach for tray efficiency estimation, however, summarizing intensive research on this topic, may be found in reference 111. 

Pressure. Within limits, pressure may have Htfle effect in air-sparged LPO reactors. Consider the case where the pressure is high enough to supply oxygen to the Hquid at a reasonable rate and to maintain the gas holdup relatively low. If pressure is doubled, the concentration of oxygen in the bubbles is approximately doubled and the rate of oxygen deHvery from each bubble is also approximately doubled in the mass-transfer rate-limited zone. The total number of bubbles, however, is approximately halved. The overall effect, therefore, can be small. The optimum pressure is likely to be determined by the permissible maximum gas holdup and/or the desirable maximum vapor load in the vent gas. 

Gas Handling. The reactants are often gaseous under ambient conditions. To maximize the rate of the catalytic reaction, it is often necessary to minimize the resistance to gas—Uquid mass transfer, and the gases are therefore introduced as swarms of bubbles into a weU-stirred Hquid or into devices such as packed columns that faciHtate gas—Hquid mixing and gas absorption. 

The modeling of fluidized beds remains a difficult problem since the usual assumptions made for the heat and mass transfer processes in coal combustion in stagnant air are no longer vaUd. Furthermore, the prediction of bubble behavior, generation, growth, coalescence, stabiUty, and interaction with heat exchange tubes, as well as attrition and elutriation of particles, are not well understood and much more research needs to be done. Good reviews on various aspects of fluidized-bed combustion appear in References 121 and 122 (Table 2). 

Three principal vapor—Hquid contacting devices are used in current crossflow plate design the sieve plate, the valve plate, and the bubble cap plate. These devices provide the needed intimate contacting of vapor and Hquid, requisite to maximizing transfer of mass across the interfacial boundary. 

Heat transfer by nucleate boiling is an important mechanism in the vaporization of liqmds. It occurs in the vaporization of liquids in kettle-type and natural-circulation reboilers commonly usea in the process industries. High rates of heat transfer per unit of area (heat flux) are obtained as a result of bubble formation at the liquid-solid interface rather than from mechanical devices external to the heat exchanger. There are available several expressions from which reasonable values of the film coefficients may be obtained. 

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... 

The choice of a bubble column or an agitated vessel depends primarily on the solubihty of the gas in the liquid, the corrosiveness of the liquid (often a gas compressor can be made of inexpensive material, whereas a mechanical agitator may have to be made of exotic, expensive materials), and the rate of chemical reac tion as compared with the mass-transfer rate. Bubble columns and agitated vessels are seldom used for gas absorption except in chemical reac tors. As a general rule. 

Mechanical agitation is needed to break up the gas bubbles but must avoid rupturing the cells. The disk turbine with radial action is most suitable. It can tolerate a superficial gas velocity up to 120 m/h. (394 ft/h) without flooding, whereas the propeller is limited to about 20 i7i/h (66 ft/h). When flooding occurs, the impeller is working in a gas phase and cannot assist the transfer of gas to the liquid phase. Power input by agitation and air sparger is 1 to 4 W/L (97 to 387 Btu/[fF-h]) of liquid. 

The actual shape of the curve illustrated in Fig. 12.4 can vary according to factors such as metal properties and cavitation intensity. (Cavitation intensity relates to the number of bubbles created in a unit volume of fluid and the amount of energy transferred during the col-... 

The effectiveness of a fluidized bed as a ehemical reactor depends to a large extent on the amount of convective and diffusive transfer between bubble gas and emulsion phase, since reaction usually occurs only when gas and solids are in contact. Often gas in the bubble cloud complex passes through the reactor in plug flow with little back mixing, while the solids are assumed to be well mixed. Actual reactor models depend greatly on kinetics and fluidization characteristics and become too complex to treat here. 

Where heat transfer is taking place at the saturation temperature of a fluid, evaporation or condensation (mass transfer) will occur at the interface, depending on the direction of heat flow. In such cases, the convective heat transfer of the fluid is accompanied by conduction at the surface to or from a thin layer in the liquid state. Since the latent heat and density of fluids are much greater than the sensible heat and density of the vapour, the rates of heat transfer are considerably higher. The process can be improved by shaping the heat exchanger face (where this is a solid) to improve the drainage of condensate or the escape of bubbles of vapour. The total heat transfer will be the sum of the two components. 

For slightly soluble gases, H is defined as a large value (4.2 X 104 bar mol-1 that is the mole fraction of oxygen in H20). The liquid phase controls, kL = Kv For the oxygen transfer rate, the interface area is important. For oxygen bubbles, the surface area of bubbles is defined as ... 

Bubble-column slurry operations are usually characterized by zero net liquid flow, and the particles are held suspended by momentum transferred from the gas phase to the solid phase via the liquid medium. The relationships between solids holdup and gas flow rate is of importance for design of bubble-column slurries, and some studies of this aspect will be reviewed prior to the discussion of transport phenomena. 

Only one publication on gas-liquid mass transfer in bubble-column slurry reactors has come to the author s attention. However, a relatively large volume of information regarding mass transfer between single bubbles or bubble swarms and pure liquid containing no suspended solids is available, and this information is probably of some relevance to the analysis of systems... 

Coppock and Meiklejohn (C9) determined liquid mass-transfer coefficients for the absorption of oxygen in water. The value of k, was observed to vary markedly with variations of bubble velocity, from 0.028 to 0.055 cm/sec for a velocity range from 22 to 28 cm/sec. These results appear to be in general agreement with the results obtained by Datta et al. (D2) and by Guyer and Pfister (G9) for the absorption of carbon dioxide by water. 

Recent publications on mass transfer from single bubbles include a theoretical study by Ruckenstein (R4) and theoretical and experimental studies by Lochiel and Calderbank (C4, L7). Bowman and Johnson (B8, J3) and Li et al. (L5) have studied mass transfer from streams of bubbles rising in water. 

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