The Onsager Phenomenological Equations

The development of an electroneutrality field introduces an interaction between flows and makes the flux of one species dependent on the fluxes of all the other species. To treat situations in which there is a coupling between the drift of one species and that of another, a general formalism will be developed. It is only when there is zero coupling or zero interaction that one can accurately write the Nemst-Planck flux equation 

Once the interaction (due to the electroneutrality field) develops, a correction term is required, i.e.. 

It is in the treatment of such interacting transport processes, or coupled flows, that the methods of near-equilibrium thermodynamics yield a clear understanding of such phenomena, but only from a macroscopic or phenomenological point of view. These methods, as relevant to the present discussion, can be summarized with the following series of statements  

As long as the system remains close to equilibrium and the fluxes are independent, the fluxes are treated as proportional to the driving forces. Experience (Table 4.17) commends this view for diffusion [Pick s law, Eq. (4.16)], conduction [Ohm s law, Eq. (4.130)], and heat flow (Fourier s law). Thus, the independent flux of an ionic species 1 given by the Nernst-Planck equation (4.231) is written 

When there is eoupling, the flux of one species (e.g Vjl is not simply proportional to its own (or as itis called, conjugate) driving force (i.e., F,), but receives contributions from the driving forces on all the other particles. In symbols, 

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The expression for the diffusion potential can be obtained in a straightforward though hardly brief manner by using the Onsager phenomenological equations to describe the interaction flows. Consido an electrolytic solution consisting of the ionic species and A " and the solvent. When a transport process involves the ions in the system, there are two ionic fluxes,/ and J. Since, however, the ions are solvated, the solvent also participates in the motion of ions and hence there is also a solvent flux Jq. 

The significance of conformational fluctuations for catalysis has been particularly emphasized by Careri et al. (1975,1979). They used an approach based on the Onsager phenomenological equations. They assumed that weakly bound water molecules play an important role in inducing fluctuations of the backbone by which the protein can exchange free energy with its environment. These fluctuations propagate to the active site and help... 

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