Steady-State Concentration Profile in Spherical Space

1 Steady-State Concentration Profile in Spherical Space Problem 

Prove or verify that for a spherical or hemispherical microelectrode of radius fe under steady-state conditions, the concentration (c) profile of an electroactive species undergoing transport limited electrolysis is 

The steady-state diffusion equation for a spherical or hemispherical microelectrode is 

Substitution into Eq. 5.1 verifies that the suggested concentration profile is indeed a solution to the equation. It also obeys the required boundary conditions. 

This result shows that the steady-state flux increases with decrease of the electrode radius in accordance with our expectations of convergent diffusion. It follows that 

---