Process film diffusion

Furthermore, at steady-state, (— rA) is also the rate of mass transfer of A across the exterior film, such mass transfer being in series with the combined intraparticle processes of diffusion and reaction hence, from the definition of kAg,... 

There are four main processes (i.e., bulk transport chemical reaction film and particle diffusion) which can affect the rate of solid phase chemical reactions and can broadly be classified as transport and chemical reaction processes [10, 31,103 -107]. The slowest of these will limit the rate of a particular reaction. Bulk transport process of a certain pollutant(s), which occurs in the aqueous phase, is very rapid and is normally not rate-limiting. In the laboratory, it can be eliminated by rapid mixing. The actual chemical reaction at the surface of a solid phase (e.g., adsorption) is also rapid and usually not rate limiting. The two remaining transport or mass transfer processes (i.e.,film and particle diffusion processes), either singly or in combination, are normally rate-limiting. Film diffusion invol-... 

It is important to differentiate between two terms that are widely used in the literature, namely chemical kinetics and kinetics . Chemical kinetics is defined as the investigation of chemical reaction rates and the molecular processes by which reactions occur where transport (e.g., in the solution phase, film diffusion, and particle diffusion) is not limiting. On the other hand, kinetics is the study of time-dependent processes. Because of the different particle sizes and porosities of soils and sediments, as well as the problem to reduce transport processes in these solid phase components, it is difficult to examine the chemical kinetics processes. Thus, when dealing with solid phase components, usually the kinetics of these reactions are studied. 

Consider two simple cases of extraction processes in which kinetics are controlled by interfacial film diffusion (the solutions are always considered stirred). The two cases are treated with the simplifying assumptions introduced in section 2 (i.e., steady-state and linear concentration gradients throughout the diffusional films). 

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. 

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. 

According to their analysis, if is zero (practically much lower than 1), then the liquid-film diffusion controls the process rate, while if tfis infinite (practically much higher than 1), then the solid diffusion controls the process rate. Essentially, the so-called mechanical parameter represents the ratio of the diffusion resistances (solid and liquid film). The authors did not refer to any assumption concerning the type of isotherm for the derivation of the above-mentioned criterion it is sufficient to be favorable (not only rectangular). They noted that for >1.6, the particle diffusion is more significant, whereas if < 0.14, the external mass transfer controls the adsorption rate. 

Finally, the agitation rate does not affect the uptake rate if the particle diffusion controls the process. However, the latter criterion may be not safe the agitation in solution may have attained its limiting hydrodynamic efficiency, so that a change in the agitation rate has no effect on the uptake rate even in film diffusion-controlled systems. 

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