Mass Transfer Phenomena

Each stage of particle formation is controlled variously by the type of reactor, i.e. gas-liquid contacting apparatus. Gas-liquid mass transfer phenomena determine the level of solute supersaturation and its spatial distribution in the liquid phase the counterpart role in liquid-liquid reaction systems may be played by micromixing phenomena. The agglomeration and subsequent ageing processes are likely to be affected by the flow dynamics such as motion of the suspension of solids and the fluid shear stress distribution. Thus, the choice of reactor is of substantial importance for the tailoring of product quality as well as for production efficiency. 

Although the absorption of a gas in a gas-liquid disperser is governed by basic mass-transfer phenomena, our knowledge of bubble dynamics and of the fluid dynamic conditions in the vessel are insufficient to permit the calculation of mass-transfer rates from first principles. One approach that is sometimes fruitful under conditions where our knowledge is insufficient to completely define the system is that of dimensional analysis. 

The heat and mass transfer phenomena associated with packed-bed reactors are described in... 

Adsorption/desorption [24-25], as well as mass transfer phenomena [26] were also proved to be important for photocatalysis. 

Step 4 Estimate the effectiveness factor i) for the removal and the cleanup time required to obtain a residual toluene concentration of 150 mg/L. The phase distribution calculations carried out in Step 2 indicate that the equilibrium concentration of toluene in the gas phase is Ca equil = 109 mg/L (see Table 14.4). The concentration measured in the extracted air during the field tests is lower, at Q,flew = 78 mg/L, indicating that the removal effectiveness is limited either as a result of mass transfer phenomena or the existence of uncontaminated zones in the airflow pattern. The corresponding effectiveness factor is T = 78/109 = 0.716. 

The understanding of heat and mass transfer phenomena occurring during... 

Mass transfer phenomena exist everywhere in nature and are important in the pharmaceutical sciences. We may think of drug synthesis preformulation studies dosage form design and manufacture and drug absorption, distribution, metabolism, and excretion. Mass transfer plays a significant role in each. Mass transfer is referred to as the movement of molecules caused not only by diffusion but also by convection [1],... 

GL Flynn, SH Yalkowsky, TJ Roseman. Mass transfer phenomena and models Theoretical concepts. J Pharm Sci 63 479-510 (1974). 

Further details on air-water mass transfer phenomena may be found in Thibodeaux (1996) and Stumm and Morgan (1981). 

Mass transfer phenomena usually are very effective on distance scales much larger than the dimensions of the cell wall and the double layer dimensions. Thicknesses of steady-state diffusion layers1 in mildly stirred systems are of the order of 10 5 m. Thus, one may generally adopt a picture where the local interphasial properties define boundary conditions while the actual mass transfer processes take place on a much larger spatial scale. 

As can be seen, there are quite a few degrees of freedom for the heat and mass transfer phenomena within a fuel bed or a packed bed. Consequently, the phenomenology is extremely complex. [15]... 

A perspective based on kinetics leads to a better understanding of the adsorption mechanism of both ionic and nonionic compounds. Boyd et al. (1947) stated that the ion exchange process is diffusion controlled and the reaction rate is limited by mass transfer phenomena that are either film diffusion (FD) or particle diffusion (PD) controlled. Sparks (1988) and Pignatello (1989) provide a comprehensive overview on this topic. 

Several parameters have been seen to influence the crystallization of ice crystals in subcooled aqueous solutions. The primary factor is the extent of subcooling of the solution. Other factors include the agitation rate, the types and levels of solutes in solution. Huige (6) has summarized past work on conditions under which dusk-shaped and spherical crystals can be found in suspension crystallizers. The effects of heat and mass transfer phenomena on the morphology of an ice crystal growing in a suspension have not been fully understood. 

Di Matteo, P, Donsi, G. and Ferrari, G., The role of heat and mass transfer phenomena in atmospheric freeze-drying of foods in a fluidised bed, /. Food. Eng., 59 (2003) 267-275. 

Various models have been proposed to describe the facilitated mass transfer phenomena, although five basic categories of models have mostly been reported in the literature [29]. The same models can essentially be applicable for Type II facilitated transport. 

By definition, the turnover frequency is expressed per number of active sites. So, catalytic samples that differ only in the amount active sites must exhibit the same values of turnover frequency. If not, heat and mass transfer phenomena are present. Specifically, the correct measurement of intrinsic kinetic data in heterogeneous catalysis is difficult due to the effect of heat and mass transfer, especially inside the pores of high specific-area materials. The turnover frequency reveals these phenomena. In other words, in the case of supported... 

The size (diameter) and the shape of the solid particles affect the mass transfer phenomena within the particle, and thus the effectiveness in the case of a catalyst. The following shapes and sizes are frequently used in applications ... 

A high Damkohler number means that the global rate is controlled by mass transfer phenomena. So, the process rate can be rewritten in terms of the Damkohler number and the external effectiveness factor for each reaction order can be deduced, as shown in Table 5.5. In Figure 5.3, the external effectiveness factor versus the Damkohler number is depicted for various reaction orders. It is clear that the higher the reaction order, the more obvious the external mass transfer limitation. For Damkohler numbers higher than 0.10, external mass transfer phenomena control the global rate. In the case of n = 1, the external effec-... 

External mass transfer-limited reactions In the expression (5.191), km has to be known, but it is not necessaiy if the external mass transfer phenomena are very intense. Actually, if strong mass resistance exists, the knowledge of the rate law is not essential, because the rate can be written as... 

To sum up, special attention should be given to the effect of temperature on the process during the design and control of commercial catalytic reactors. Moreover, the same size of catalyst particles should be used at any scale so that the catalyst effectiveness factor also remains the same. The available catalytic surface per reactor volume and the space velocity (when the rate is not controlled by mass transfer phenomena) should also be left unchanged at any scale. 

The idea of convection was introduced, which is not in contradiction with Thiele principle it is possible to take into account not only the diffusion itself, but also the mass transfer phenomena (electric field, convection, etc.). 

Consider that the mass transfer phenomena are negligible and that y= 0.997 for a current density of 100 pA cm-2. (Zinola)... 

The catalyst and particulate filter models were developed individually with different university partners. They are described in the following sections. A key issue for all models is robustness and scalability as the applications range from passenger cars to heavy-duty commercial vehicles. The models are physical and chemically based, consisting of a transport model for heat and mass transfer phenomena in the monolith in gas and solid phases, cf. Fig. 6. The monolith reactor modeling is discussed in more detail in Section III. 

In this section the models employed for simulation of catalytic monolith reactor are discussed, focusing on effective description of heat and mass transfer phenomena in monolith channel. The number of different mathematical models developed for converters of automobile exhaust gases over the last decades is huge—cf., e.g. Heck et al. (1976), Young and Finlayson (1976), Oh and Cavendish (1982), Zygourakis and Aris (1983), Chen et al. (1988),... 

B. Benadda, K. Kafoufi, P. Monkam and M. Otterbein, Hydrodynamics and mass transfer phenomena in countercurrent packed column at elevated pressures, Chem. Engng. Science, in press. 

The current chapter shows the application of mainly thermodynamic calculations, which have their basis in Chapters 4 and 5. However, as indicated in Chapter 3, a fundamental kinetic model, separated from heat and mass transfer phenomena, has yet to be established, particularly at high concentrations to extend the measurements pioneered in the laboratory of Bishnoi during the last three decades. The generation of such a time-dependent growth model and its application is one of the major remaining hydrate challenges. 

The packed bed breakthrough method for investigation of mass transfer phenomena in sorbent systems can in many instances offer certain advantages not found in other experimental methods. The method is especially useful when the adsorption isotherms for the principal sorbate exhibit favorable curvature (convex toward loading axis). In such a case, there is the potential for a portion of the sorption front to approach a stable wave form (shape of the front invariant with time). Given the existence of a stable or "steady-state" mass transfer zone (MTZ) and a detailed knowledge of the equilibrium loading characteristics within that zone, one can extract local values of the effective mass transfer resistance at any concentration in the zone. 

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