# Limiting current vs Steady-state limiting current

I have been reading on the concept of limiting current. In books, the mass-transfer limiting current is given by,

$$i_L = \frac{nFADC^*}{\delta}$$

Often the Cottrell equation is introduced.

However, later on there is the introduction of a 'steady-state' limiting current at long time scales, given by:

$$i_{ss} = \gamma nFDC^*r_0$$

What is the difference (if any) between these two 'limiting' currents, can they be considered the same under certain conditions?

An example of a book where this is discussed is "Handbook of Electrochemistry" by C. Zoski, also seen it in "Electrochemical Methods" by Bard and Faulkner.

• The steady-state limiting current is especially important for microelectrodes, because the diffusion mode is not semi-linear, but radial. Commented Jul 17 at 9:32

The general equation for the limiting current is usually written this way : $$i_{l} = nFAmC^*$$, with m the mass tranfer coefficient. This is the maximum current measurable at the electrode because of mass transfer.
The steady state current is the (limiting) current you can actually measure at an electrode after a potential step under mass transfer limitations. This is usually measured for small electrodes, it takes too long to establish for macro electrodes and you would have convection mixing in. The exact form depends on the geometry (the $$\gamma$$ term in your equation).