Electrohydrodynamic Transport Theory

In this section, we attempt to develop appropriate equations of change governing the motion and behavior of species acted upon by an electric field. Let us assume the solution to be dilute. The criterion of diluteness is based on interparticle distance which is large enough such that motion of any particle is unaffected by the neighboring particles. For dilute solutions, the flux contributions from diffusion, electromigration, and convection can be linearly superposed. The molar flux (j ) of the tth species is the superposition of all individual contributions  

The first, second, and third term of the above equation, respectively, represents electromigration, diffusion, and convection. Here, the molar average velocity u (= has been 

The above two equations are called Nemst-Planck equations. The current density can be written using equation (6.17) as 

The above equation can also be written using electrical conductivity similar to Ohm s law as 

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