Generalized phenomenological transport

A Generalized Phenomenological Transport Model and Simple Consequences... 

Thus, this interspace model has been cast in the form of the general phenomenological model of Section 2b (Eqns. 33 and 35), and the relevant parameters of coupled water transport may be calculated as outlined there. 

Define mobility and write the general phenomenological equation for transport. Give examples of how this generalized equation can be applied to electri-cal/thermal conduction, diffusion, and convection, respectively. 

In this chapter, we shall first make a brief review of the phenomenological aspect of Brownian motion and we shall then show how the general transport equation derived in Section II allows an exact microscopic theory to be developed. 

As summarized above, there are many transport models and flow mechanisms describing reverse osmosis. Each requires some specific assumptions regarding membrane structure. In general, membranes could be continuous or discontinuous and porous or non-porous and homogeneous or non-homogeneous. One must be reasonably sure about the membrane structure before he analyzes a particular set of experimental data based on one of the above theories. Since this is difficult, in many cases, it would be desirable to develop a model-independent phenomenological theory which can interpret the experimental data. 

Irreversible processes are driven by generalized forces, X, and are characterized by transport (or Onsager) phenomenological coefficients, L [21,22], where these transport coefficients, Lip are defined by linear relations between the generalized flux densities,./, which are the rates of change with time of state variables, and the corresponding generalized forces X . 

There are general relationships of transport phenomena based on phenomenological theory, i.e., on the correlations between macroscopically measurable quantities. The molecular theories explain the mechanism of transport processes taking into account the molecular structure of the given medium, applying the kinetic-statistical theory of matter. The hydrodynamic theories are also applied especially to describe - convection. 

The phenomenological equations (6.9.1) have thus been reexpressed in (6.9.9) solely in terms of the measurable transport coefficients a, k, and o. The Seebeck coefficient may be interpreted as the entropy carried per electronic charge. Equation (6.9.9a) represents a further generalization of Ohm s Law, showing how the current density behaves in the presence of a temperature gradient see also Exercise 6.9.3. Equation (6.9.9b) specifies the entropy flux under the joint action of a gradient in electrochemical potential and in temperature this represents a generalization of Fourier s Law. 

Here we have assumed that the fluxes and generalized forces are collinear and are oriented along one dimension only, which allows us to drop the vector notation. We also adopted the definition = /t,- -f Zicq) for the electrochemical potential. Note the signs of the second set of phenomenological coefficients that depend on the sign of the charge that is being transported. 

In summary, I have discussed a semi-phenomenological elastic theory for ion clustering in ionomers. The theory is consistent with observed trends in perfluorinated ionomers. I have also demonstrated the percolatlve nature of ion transport in these ionomers and computed quantitatively their tensile modulus. Finally, I have discussed the Influence of morphology on ion selectivity in perfluorinated ionomer blends. In particular, I have pointed out that an universally preferred morphology beneficial to all blends does not exist the ideal morphology must be individually determined based on component properties. Most of the theories and conclusions here are very general and applicable to other composite polymer systems. 

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