The diffusion system in the presence of an electric current

Abstract

First we consider a system which has no electrodes but contains an electrolyte solution in which an electric current can exist. This in effect means that the electrodes are a very great distance away from the cell which we are observing. Alternatively we could have a closed loop of electrolyte solution, parts of which we can move through a static magnetic field. As we shall see below, the characterization of the system as a closed loop is a more fundamental picture than a cell construction where the electrodes are at very large distances from the section being observed. Assume now that we have switched on an electric current J _q by some device. The electric current can be identified by a magnetic field around the cell. When the electric current is switched on let it be constant in time. Since electric work is performed on the system, in order to keep the temperature constant, heat has to be continuously delivered to the surroundings. Of course, the electric current is constant along the total system. For simplicity we assume that the cross-section A of the tube containing the electrolyte solution is constant. J _q is the electric current density and we have

$$div{j_2} = 0$$

((71))

Let the electrolyte solution be the same as previously in that it contains the four constitutents, Na, K, Cl, and I, and as before, the composition is not constant everywhere along the coordinate x which gives the location in the cell. The positive x direction is the same as the positive direction of the vector J _q . For the description of the composition we apply the total solute-constituents coordinate system.