Concentration gradients, interpretation

A combination of continuum transport theory and the Poisson distribution of solution charges has been popular in interpreting transport of ions or conductivity of electrolytes. Assuming zero gradient in pressure and concentration of other species, the flux of an ion depends on the concentration gradient, the electrical potential gradient, and a convection... 

Water and hydrocarbons occurring together, in shallow aquifer systems, may be considered immiscible for flow calculation purposes however, each is somewhat soluble in the other. Since groundwater cleanup is the purpose behind restorations, it receives greater attention. Definition of water quality based on samples retrieved from monitoring wells relies heavily upon the concentration of individual chemical components found dissolved in those samples. An understanding of the processes that cause concentration gradients is important for the proper interpretation of analytical results. 

Fig. 7.82. Transport processes are interpretable in terms of the concept of energies of activation (which are, however, relatively veiy low) and concentration gradients.

Unless carried out very carefully, data from flow reactors may be influenced by experimental uncertainties. Potential problems with the flow reactor technique include imperfect mixing of reactants, radial gradients of concentration and temperature, and catalytic effects on reactor walls. Uncertainties in induction times, introduced by finite rate mixing of reactants, presence of impurities, or catalytic effects, may require interpretation of the data in terms of concentration gradients, rather than just exhaust composition [442]. 

Hore importantly, the response curves are noticeably affected where one or both of the components is adsorbable, even at low tracer concentrations. The interpretation of data is then much more complex and requires analysis using the non-isobaric model. Figs 7 and 8 show how adsorption of influences the fluxes observed for He (the tracer), despite the fact that it is the non-adsorbable component. The role played by the induced pressure gradient, in association with the concentration profiles, can be clearly seen. It is notable that the greatest sensitivity is exhibited for small values of the adsorption coefficient, which is often the case with many common porous solids used as catalyst supports. This suggests that routine determination of effective diffusion coefficients will require considerable checks for consistency and emphasizes the need for using the Wicke-Kallenbach cell in conjunction with permeability measurements. 

The effect of concentration gradients in electrode reactions is really not a problem of mechanism but rather a troublesome source of possible systematic ambiguity in the interpretation of the product distributions observed, one of the tasks that lies close to the heart of the organic chemist. To see how this comes about, it is instructive to make the mental experiment that we generate acetoxy radicals by the Kolbe reaction of acetate ion in acetic acid [eqn (52)] at an electrode of 1 cm2 surface area, passing a current of 1 A during... 

Figure 1 shows the schematic of a tubular reactor, of radius a and length L, where a — a/Lis the aspect ratio. Clearly, ifa>S> 1, or a <3C 1, a physical length scale separation exists in the reactor. This length scale separation could also be interpreted in terms of time scales. For example, a 1 implies that the time scale for radial diffusion is much smaller than that of either convection and axial diffusion, and concentration gradients in the transverse direction are small compared to that in the axial direction. 

If step (b), surface diffusion to the growth center, is a rate limiting step, component concentration gradients are formed at the surface of the deposit (D). The observed overpotential could then be interpreted as a form of concentration overpotential, and is independent of the working electrode potential of the PEVD system. 

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