Steady State with Drift and Diffusion

In general, the flux of the ions is controlled by both the diffusion and convection, as given by Elquation 8.4. If the diffusive part dominates over the convective (drift) part, the situation is referred to as the diffusion-dominated regime. In general, the behavior of ion fluxes is in the crossover region between the drift-dominated and diffusion-dominated regimes. 

Considering the one-dimensional case of ion transport along the pore (jc-axis), the charge flux due to the /-type ions follows from Equations 8.4, 8.6, and 8.7 as 

This equation can be rearranged into two equivalent forms. By multiplying and dividing the first term on the right-hand side by Ci(x), we get 

The other convenient form is obtained by performing the same rearrangement as in Section 6.5.2 as 

In the steady state, the charge flux Ii x) is a constant independent of the variable X. In this limit, the above two equations can be readily integrated between X = 0 andx=L to obtain the following useful formulas. 

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