Physical transfer processes

In the design and operation of various bioreactors, a practical knowledge of physical transfer processes - that is, mass and heat transfer, as described in the relevant previous chapters - are often also required in addition to knowledge of the kinetics of biochemical reactions and of cell kinetics. Some basic concepts on the effects of diffusion inside the particles of catalysts, or of immobilized enzymes or cells, is provided in the following section. 

More advanced models of the drying process are discussed by Kirk [88]. More recent reviews include those written by Nederveen et al. [94] and Wilhelmsson et al. [95]. The latter authors identify 20 models that have been proposed to simulate multicylinder paper dryers. In some of these models, the physical transfer processes are simulated in detail, while others adopt a less detailed viewpoint and rely on more empirical coefficients to fit the data. 

Except for elements with one or more radiogenic isotopes, the isotopic composition of an element in Nature can be considered constant for most applications of stable isotope techniques. However, they are not invariable (see also Chapter 1). Stable isotopes of an element differ slightly in mass, which may cause changes in the element s isotopic composition if a chemical or physical transfer process is sensitive to the isotopes masses and if the transfer is incomplete. For reasons of mass balance, the isotopic abundances cannot be changed if all matter is transferred from a source to a target compartment. 

Physical transfer processes include evaporation and precipitation, and also membrane diffusion as a basic mechanism of element transfer in the human body. A difference in diffusion rates between isotopes inevitably results in their fractionation over the course of element transport (kinetic isotope fractionation effect). When an element undergoes a chemical reaction, this can also be described as an element transfer process from one element species into another. Again, if reaction rates between isotopologs differ, this gives rise to a difference in isotopic... 

This mass transfer step has been extensively studied, primarily through the examination of simple physical transfer processes, such as vaporization or drying. Thus, the mass transfer component of the overall reaction sequence is perhaps the best understood. While it is possible to calculate the rate of mass transfer between a moving gas stream and a solid surface by the simultaneous solution of the appropriate fluid flow and diffusion equations [1, Chapter 17], here we shall adopt a more empirical approach through the use of mass transfer coefficients, although some comments will be made about the way these two approaches may be regarded as complementary. 

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