Mechanical Versus Molecular Transport

While the formalism of irreversible thermodynamics provides an elegant framework for describing molecular displacements, it provides too little substance and too much conceptual difficulty to justify its development here. For instance, it provides no values, not even estimates, for various transport coefficients such as the diffusion coefficient. Cussler has noted the disappointment of scientists in several disciplines with the subject [7]. It is the author s opinion that a clearer understanding of the transport processes and interrelationships that underlie separations can be obtained from a mechanical-statistical approach. This is developed in the subsequent sections. 

Mechanical motion—the motion of macroscopic bodies—is described by simple Newtonian physics. The study of mechanical motion is a logical precursor to the study of molecular displacements. It is useful to highlight the principal similarities and differences here. 

We note first that the final goals of the descriptions of mechanical and molecular motions are distinctly different. In the theory of mechanical motion, we wish to follow the path of individual objects (like a space probe or baseball), while for molecular motion we are rarely interested in individual particles (molecules or colloids) but rather in the changes in the spatial distribution of large numbers of such particles. 

Despite the difference in goals, single molecules respond to forces much like macroscopic bodies. The mathematics, too, is analogous, as shown by the two equations 

Quantities 9 and /i differ only in the greater comprehensiveness of the latter. Chemical potential fi includes 9 in an implicit manner in the term for external forces /iext. However, encompasses even more than 9 for it also includes the effects of phase distribution forces in /x° and the entropy influence of the term 9 7Inc as shown in Eq. 2.17. The entropy term is dwarfed by 9 and is thus negligible for macroscopic bodies, but it has a major influence in governing the transport of molecules and colloids. It is responsible for the diffusion of these microscopic particles and makes it necessary to describe molecular transport in terms of distributions (i.e., concentration distributions) as just noted. 

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The measurement of diffusion rates as functions of various activities, in particular oxygen fugacity, is extremely important to clarifying the diffusion mechanisms and aid in extrapolation. The work of Ryerson et al. (1989) is the only geochemical example of such type of work. Questions of concern include under what conditions does the /02-dependence occur, and what does it tell us about the main mechanism of O2 transport (e.g. permeation versus diffusion, network versus molecular oxygen diffusion etc.). 

The Brunauer type I is the characteristic shape that arises from uniform micro-porous sorbents such as zeolite molecular sieves. It must be admitted though that there are indeed some deviations from pure Brunauer type I behavior in zeoHtes. From this we derive the concept of the favorable versus an unfavorable isotherm for adsorption. The computation of mass transfer coefficients can be accompHshed through the construction of a multiple mass transfer resistance model. Resistance modehng utilizes the analogy between electrical current flow and transport of molecular species. In electrical current flow voltage difference represents the driving force and current flow represents the transport In mass transport the driving force is typically concentration difference and the flux of the species into the sorbent is resisted by various mechanisms. 

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