Diffusion of Ionic Species in an Electrolyte Solution

As shown in Sects. E.6.2 and E.6.3, the diffusion property of an electrically neutral species can be denoted by the gradient of the chemical potential. Similarly, the transport and diffusion of ionic species in an electrolyte solution are designated by the gradient of the electrochemical potential (E.88). 

Recall that the coefficient / of (E.77) represents the viscous drag. The inverse M = 1// may give the mobility of the ionic species in the solution. Then the particle velocity of species a is defined by 

The first and second terms of the r.h.s. of (E.l 15) represent diffusivity and electric migration, respectively. 

Let 1 mole of electrolyte A be ionized into v+ mole of cations with a charge of z+ and v mole of anions with a charge of z, and both ions flow at the same velocity v. Then we have 

On the other hand, let tie the flux of the diffusing concentration and Da be the diffusivity. Then Pick s law can be written as 

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