Diffusional aspects

H. Mehrer and G. Rummel. Amorphous metallic alloys—diffusional aspects. In H. Jain and D. Gupta, editors, Diffusion in Amorphous Materials, pages 163-176, Warrendale, PA, 1994. The Minerals, Metals and Materials Society. 

We wish to quantify some of the diffusional aspects of the particle. 

This chapter deals with the diffusional transfer of mass to and across a phase boundary. In particular, gas-liquid, gas-solid, and liquid-liquid phase combinations have been considered. Process applications include absorption, stripping, distillation, extraction, adsorption, and the diffusional aspects of chemical reactions on a solid surface. For steady-state transfer operations, the rates of mass transfer can be correlated by variations of Pick s first law, which states that the rate is directly proportional to the concentration driving force and the extent of interfacial area, and inversely proportional to the distance of movement of the mass to the interface. 

The strategy is exactly that used before. The time domains associated with variations in dc and are assumed to differ greatly, so that the diffusional aspects of the two parts of the experiment can be uncoupled. This assumption will hold as long as the scan rate, V, is not too large compared to the ac frequency (28). More precisely, dE Jdt = v should be much smaller than the amplitude of dEldt, which is LEo). Then, we can take the mean surface concentrations enforced by E as effective bulk values for the ac perturbation, just as we did earlier. The current amplitude and phase angle then follow easily from the impedance properties. 

The phenomenological aspects of diffusional mass transfer in adsorption systems can be described in terms of Fick s law ... 

Theoretical aspects of diffusional resistances are discussed in Part I of this volume. Following these discussions, parallel transcellular and paracellular ... 

M. Bisrat, E. K. Anderberg, M. I. Barnett, C. Nystrom. Physicochemical aspects of drug release. XV. Investigation of diffusional transport in dissolution of suspended, sparingly soluble drugs. Int. J. Pharm. 1992, 80, 191-201. 

This section will begin by looking at how thermodynamic and kinetic modelling has been combined to understand time-temperature-transformation diagrams in steels. The woric, for the most part, is semi-empirical in nature, which is forced upon the topic area by difficulties associated with the diffusional transformations, particularly where nucleation aspects have to be considered. The approaches have considered how best to predict the time/temperature conditions for austenite to... 

There are many factors that influence the outcome of enzymatic reactions in carbon dioxide. These include enzyme activity, enzyme stability, temperature, pH, pressure, diffusional limitations of a two-phase heterogeneous mixture, solubility of enzyme and/or substrates, water content of the reaction system, and flow rate of carbon dioxide (continuous and semibatch reactions). It is important to understand the aspects that control and limit biocatalysis in carbon dioxide if one wants to improve upon the process. This chapter serves as a brief introduction to enzyme chemistry in carbon dioxide. The advantages and disadvantages of running reactions in this medium, as well as the factors that influence reactions, are all presented. Many of the reactions studied in this area are summarized in a manner that is easy to read and referenced in Table 6.1. 

It should be emphasised that the term diffusional growth only reflects one aspect of the layer-growth mechanism, namely, atomic diffusion. The differences in terminology are not so unimportant as it may seem at first sight. 

In conventional reforming the reactor s high aspect ratio (L/D) requires that large catalyst particles be used in order to avoid excessive pressure drop. Due to intra-particle diffusional limitations in large particles, 95% of the catalyst is not utilized (Adris et al., 1996). In UMR, the use of low aspect ratio reactors allows the use of small catalyst particles and as a result the effectiveness factors of the catalyst are higher. 

The non-diffusional methods of bringing D and A together may also result in payment of an ultimate price of diminished overall efficiency since BET within contact ion pairs is usually more rapid than in solvent separated ion pairs (see below). Indeed, the most important aspect of the forward electron transfer is that it presets the conditions for the competition between BET and the fragmentation reaction. The reactive intermediates (ion pairs) are generated in specific solvation and spin states. That state can be controlled or at least influenced by a selection of the excited state component, the ground state component and solvent [20], as well as by magnetic and electric fields [36]. 

Notes ko (%/min), zero-order constant ka (%/min1 2), Higuchi s slope k (%/min"), kinetic constant of Korsmeyer model n, diffusional exponent kA (%/minm), diffusional constant of Peppas and Sahlin model kr (%/min2 ), relaxational constant of Peppas and Sahlin model m, diffusional exponent that depends on geometric shape of releasing device through its aspect ratio (see Table 25). 

Madon and Boudart propose a simple experimental criterion for the absence of artifacts in the measurement of rates of heterogeneous catalytic reactions [R. J. Madon and M. Boudart, Ind. Eng. Chem. Fundam., 21 (1982) 438]. The experiment involves making rate measurements on catalysts in which the concentration of active material has been purposely changed. In the absence of artifacts from transport limitations, the reaction rate is directly proportional to the concentration of active material. In other words, the intrinsic turnover frequency should be independent of the concentration of active material in a catalyst. One way of varying the concentration of active material in a catalyst pellet is to mix inert particles together with active catalyst particles and then pelletize the mixture. Of course, the diffusional characteristics of the inert particles must be the same as the catalyst particles, and the initial particles in the mixture must be much smaller than the final pellet size. If the diluted catalyst pellets contain 50 percent inert powder, then the observed reaction rate should be 50 percent of the rate observed over the undiluted pellets. An intriguing aspect of this experiment is that measurement of the number of active catalytic sites is not involved with this test. However, care should be exercised when the dilution method is used with catalysts having a bimodal pore size distribution. Internal diffusion in the micropores may be important for both the diluted and undiluted catalysts. 

In this review the intrinsic kinetic aspects are dealt with in the first place The progressive coverage of active sites of the catalyst, which affects its activity and the process selectivity, is cast in a mechanistic form. These kinetic aspects are then studied in combination with the influence of the catalyst morphology, first at the pore level, then at the particle level, seen as a network of pores. Next, growth of coke, leading eventually to pore blcx kage and diffusional limitations are introduced The practical application of the models in kinetic studies is given particular attention. Finally, the effect of catalyst deactivation on the behavior of the reactor is discussed. 

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