Mass transfer-controlled

This is the important rule of additivity of resistances. In practice, and are often of the same order of magnitude, but the distribution coefficient m can vary considerably. For solutes which preferentially distribute toward solvent B, m is large and the controlling resistance Hes in phased. Conversely, if the distribution favors solvent A the controlling mass-transfer resistance Hes in phase B. 

The enhanced rate expressions for regimes 3 and 4 have been presented (48) and can be appHed (49,50) when one phase consists of a pure reactant, for example in the saponification of an ester. However, it should be noted that in the more general case where component C in equation 19 is transferred from one inert solvent (A) to another (B), an enhancement of the mass-transfer coefficient in the B-rich phase has the effect of moving the controlling mass-transfer resistance to the A-rich phase, in accordance with equation 17. Resistance in both Hquid phases is taken into account in a detailed model (51) which is apphcable to the reversible reactions involved in metal extraction. This model, which can accommodate the case of interfacial reaction, has been successfully compared with rate data from the Hterature (51). 

Diffusion-controlled mass transfer is assumed when the vapor or liquid flow conforms to Tick s second law of diffusion. This is stated in the unsteady-state-diffusion equation using mass-transfer notation as... 

Design of inorganic absorbers quite often involves a system whose major parameters are well defined such as system film control, mass transfer coefficient equations, etc. Ludwig gives design data for certain well-known systems sueh as NH3-Air-H20, CI2-H2O, COi in alkaline solutions, etc. Likewise, data for commercially available packings is well documented such as packing factors, HETP, HTU, etc. 

Equation (14), although derived from the approximate random walk theory, is rigorously correct and applies to heterogeneous surfaces containing wide variations in properties and to perfectly uniform surfaces. It can also be used as the starting point for the random walk treatment of diffusion controlled mass transfer similar to that which takes place in the stationary phase in GC and LC columns. 

Even at 1,500 F, equilibrium eonstants for the first two reactions are high enough (about 10) to expect reaction to go essentially to completion except for kinetic-rate limitations. The reaction zone might be expected to be sized by volume of rabbled carbon bed, considering that the carbon gasification reactions that occur in it are governed by kinetics and are reaction-rate limited. Actually, it is sized by hearth area. The area exposed to the gases controls mass transfer of reactants from the gas phase to the carbon and heat transfer to support the endothermic reactions. 

The homogeneously catalyzed oxidation of butyraldehyde to butyric acid was used to analyse reactor performance for different flow patterns (or for different Weber numbers) [9,10]. Hence it relates to the possibility of setting various flow patterns in gas/Hquid micro devices and hence controlling mass transfer. 

In this chapter the simulation examples are described. As seen from the Table of Contents, the examples are organised according to twelve application areas Batch Reactors, Continuous Tank Reactors, Tubular Reactors, Semi-Continuous Reactors, Mixing Models, Tank Flow Examples, Process Control, Mass Transfer Processes, Distillation Processes, Heat Transfer, and Dynamic Numerical Examples. There are aspects of some examples which relate them to more than one application area, which is usually apparent from the titles of the examples. Within each section, the examples are listed in order of their degree of difficulty. 

Jin F, Balasubramaniam R, Stebe KJ (2004) Surfactant adsorption to spherical particles the intrinsic length-scale governing the shift from diffusion to kinetic-controlled mass transfer. J Adhes 80 773-796... 

Due to the ionic nature of cephalosporin molecules, the interfacial chemical reaction may in general be assumed to be much faster than the mass transfer rate in the carrier facilitated transport process. Furthermore, the rate controlling mass transfer steps can be assumed to be the transfer of cephalosporin anion or its complex, but not that of the carrier. The distribution of the solute anion at the F/M and M/R interfaces can provide the equilibrium relationship [36, 69]. The equilibrium may be presumably expressed by the distribution coefficients, mf and m at the F/M and M/R interfaces, respectively and these are defined as... 

The main mass transport resistance in liquid fluidized beds of relatively small particles lies in the liquid film. Thus, for ion exchange and adsorption on small particles, the mass transfer limitation provides a simple liquid-film diffusion-controlled mass transfer process (Hausmann el al., 2000 Menoud et al., 1998). The same holds for catalysis. 

The absorption of ammonia into water is a typical case where gas-phase resistance controls mass transfer rates. 

With ex situ treatment of contaminated soils, a controlled environment for soil treatment can be maintained- With mixing, nutrient addition, aeration, and other environmental controls, mass transfer rates that typically limit in situ bioremediation can be greatly increased. Of course, the disadvantages of ex situ bioremediation are the costs of soil excavation and reactor operation. Thus, ex situ bioremediation is favored by localized, shallow soil contamination. 

For diffusing gases of similar molecular weight, the properties that control heat transfer follow the same rules as those that control mass transfer. As a result, the NH3 scrubbing and gas cooling processes achieve similar approaches to equilibrium. 

Interfacial Area This consideration in agitated vessels has been reviewed and summarized by Tatterson (op. cit.). Predictive methods for interfacial area are not presented here because correlations are given for the overall volumetric mass transfer coefficient liquid phase controlling mass transfer. 

Guo F, Zhao Y, Cui J, Guo K, Chen J, Zheng C. Effect of inner packing support on liquid controlled mass transfer process in rotating packed beds. In Gough M, ed. 4th International Conference on Process Intensification in Practice. London BHR Group, 2001 107-113. 

Also chain growth to oligomerization is not uncommon, coating and blocking reactors by precipitation. Furthermore, the insolubility of fluorine in most solvents challenges reactant dosing because the gas-liquid interface, typically not well defined, is now the means to determine and control mass transfer and reaction rate and selectivity. 

Diffusion in porous solids is usually the most important factor controlling mass transfer in adsorption, ion exchange, drying, heterogeneous catalysis, leaching, and many other applications. Some of the applications of interest are outlined in Table 5-16. Applications of these equations are found in Secs. 16, 22, and 23. 

Migration Diffusion- and/or partitioning-controlled mass transfer from a packaging material or article into food or a food simulant. Classically, migration is experimentally determined by standardised tests using food simulants. Due to the scientific progress in this field, migration can also be mathematically modelled and conservatively predicted. 

Details of the numerical procedure will be published elsewhere [10]. The sample geometry (e.g. spherical or cylindrical symmetry) is taken into account. The parameters adjusted in fitting the experimental data are (a) the transport difiSisivity, D, and (b) the rate controlling mass transfer from the surrounding gas phase into the zeolite, m. The crystal size has been determined from SEM micrographs and is thus fixed. 

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