Solid-liquid mass transfer enhancement factors

Ultrasound can thus be used to enhance kinetics, flow, and mass and heat transfer. The overall results are that organic synthetic reactions show increased rate (sometimes even from hours to minutes, up to 25 times faster), and/or increased yield (tens of percentages, sometimes even starting from 0% yield in nonsonicated conditions). In multiphase systems, gas-liquid and solid-liquid mass transfer has been observed to increase by 5- and 20-fold, respectively [35]. Membrane fluxes have been enhanced by up to a factor of 8 [56]. Despite these results, use of acoustics, and ultrasound in particular, in chemical industry is mainly limited to the fields of cleaning and decontamination [55]. One of the main barriers to industrial application of sonochemical processes is control and scale-up of ultrasound concepts into operable processes. Therefore, a better understanding is required of the relation between a cavitation coUapse and chemical reactivity, as weU as a better understanding and reproducibility of the influence of various design and operational parameters on the cavitation process. Also, rehable mathematical models and scale-up procedures need to be developed [35, 54, 55]. 

As in any solid-liquid reaction, when the solid is sparingly soluble, reaction occurs within the solid by diffusion of the liquid-phase reactant into it across the liquid film surrounding the solid. Thus two diffusion parameters are operative, the solid-liquid mass transfer coefficient sl and the effective diffusivity D. of the reactant in the solid. A reaction in the solid can occur by any of several mechanisms. The simpler and more common of these were briefly explained in Chapter 15. For reactions following the sharp interface model, ultrasound can enhance either or both these constants. Indeed, in a typical solid-liquid reaction such as the synthesis of dibenzyl sulfide from benzyl chloride and sodium sulfide ultrasound enhances SL by a factor of 2 and by a factor of 3.3 (Hagenson and Doraiswamy, 1998). Similar enhancement in was found for a Michael addition reaction (Ratoarinoro et al., 1995) and for another mass transfer-limited reaction (Worsley and Mills, 1996). 

E will be different from 1 only if R4 is small relative to / 2, resulting in a bulk concentration of c — 0 and in a real parallel mechanism of the enhancement. The advantage of the concept of the enhancement factor as defined by eq 33 is the separation of the influence of hydrodynamic effects on gas-liquid mass transfer (incorporated in Al) and of the effects induced by the presence of a solid surface (incorporated in E ), indeed in a similar way as is common in mass transfer with homogeneous reactions. The above analysis shows that an adequate description of mass transfer with chemical reaction in slurry reactors needs reliable data on ... 

Gas-to-liquid mass transfer is a transport phenomenon that involves the transfer of a component (or multiple components) between gas and liquid phases. Gas-liquid contactors, such as gas-liquid absorption/ stripping columns, gas-liquid-solid fluidized beds, airlift reactors, gas bubble reactors, and trickle-bed reactors (TBRs) are frequently encountered in chemical industry. Gas-to-liquid mass transfer is also applied in environmental control systems, e.g., aeration in wastewater treatment where oxygen is transferred from air to water, trickle-bed filters, and scrubbers for the removal of volatile organic compounds. In addition, gas-to-liquid mass transfer is an important factor in gas-liquid emulsion polymerization, and the rate of polymerization could, thus, be enhanced significantly by mechanical agitation. 

For a semi-batch operation, the liquid-solid mass-transfer coefficient can also be obtained by monitoring a reaction between the dissolving solid B and a liquid reactant C. If this reaction is instantaneous, the enhancement factor for the reaction is... 

Reactants migrate between phases in order to react from gas phase to liquid, from fluid to solid, and between liquids when the reaction occurs in both phases. One of the liquids usually is aqueous. Resistance to mass transfer may have a strong effect on the overall rate of reaction. A principal factor is the interfacial area. Its magnitude is enhanced by agitation, spraying, sparging, use of trays or packing, and by size reduction or increase of the porosity of solids. These are the same operations that are used to effect physical mass transfer between... 

Historically, the analysis of gas/liquid systems arose from the problem of gas absorption accompanied by chemical reaction. Since the chemical reaction in this instance tends to increase the rate of absorption (mass transfer), much of the analysis is based on exploring the effects of chemical reaction on a diffusional process. This is just the opposite of the viewpoint in the theory for gas/solid systems, where we have explored the effects of appending a diffusional process to a chemical reaction. The net result of this difference in viewpoints is that most theories of gas/liquid reactions are concerned with determining enhancement factors for the mass-transfer coefficient rather than penalty functions, such as the effectiveness factor for the reaction kinetic constant. This difference in viewpoints can be rather refreshing in pointing out the various contrasts between the two approaches. 

The performance of these reactors is greatly influenced by (1) axial, radial, and global distribution of liquid and solids in the bed and (2) changes in bubble size, velocity, breakup, and coalescence. The second set of factors leads to an enhancement in the rates of heat and mass transfer. This happens because each particle (assumed to be spherical) is surrounded by a gas-liquid mixture of low pseudohomogheneous density. Consequently, the particle terminal velocity increases, which in turn has a positive effect on the mass transfer coefficient. A number of papers have been published (e.g., Arters and Fan, 1986, 1990 Fan, 1989 Nikov and Delmas, 1992 Boskovic et al., 1994 Kikuchi et al., 1995) on mass transfer in these reactors. 

The connection between chemical reaction engineering and transport phenomena also stems from multiphase reactions. For solid catalyzed gas or liquid reactions, mass transfer in the bulk or on the surface may become a problem. For gas-liquid reactions, the transport of the species to the reaction zone has to be considered. Similar problems arise for liquid-liquid reactions. Thns, we intend to give a brief introduction to these problems and, in the process, introdnce dimensionless qnantities such as the Thiele modulus, Damkohler number, Hatta modulus, effectiveness factor, and enhancement factor, and nse them in designing reactors. 

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