Mass and Charge Transport in the Presence of Concentration Gradients

3 Mass and Charge Transport in the Presence of Concentration Gradients 

This equation has been introduced from two points of view. In the macroscopic 

On the other hand, in the atomistic approach, the time-dependent configurations of the system are determined from the probabilities of the elementary atonuc process. The random walk approach calculates the probability of finding the system in a certain state after a certain time given an initial distribution of particles. It is then possible to show that the distributions are solutions of the diffusion equation. 

It was shown in Section 2.1.2.4 that the general flux equations (e.g. the Nemst-Planck equation) contain, in addition to the diffusion terms, a contribution from migration, that is the movement of charged particles under the influence of an electric field. Under certain circumstances it is quite possible to carry out experiments in which the field is negligibly small compared to the concentration or activity driving force. 

The purposes of this section is to discuss the electrical analogs of diffusion processes in the absence of migration and to present suitable electrical equivalent circuits for analysis of data obtained under these circumstances. 

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In this section we are concerned with the electrical response of solids with a uniform composition. Mass and charge transport in the presence of concentration gradients are discussed in Section 2.1.3. 

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