A2
 
Dimensionless variables
for the rotating disc electrode
 

If the radial diffusion is assumed to be negligible, the mass transport equation is a function of a single spatial dimension:

(A2.1)

The convection term is a function of a dimensionless normal co-ordinate (z):

where and w = 2pf(A2.2)

This function has been evaluated numerically by Cochran1, and later by Benton2. Close to the electrode surface it may be approximated as a series expansion in z.

(A2.3)

where ai are constants and according to Benton2 a0 = 0.510233 and b0 = -0.61592.

This may be rewritten as a series expansion in real space:

(A2.4)

where

; ; (A2.5)

If the dimensionless variables are introduced:

; (A2.6)

the mass transport equation becomes:

(A2.7)

where

for i=1,2...(A2.8)

Subsituting for ci

(A2.9)

it is apparent that ki and thus the steady-state transport-limited current are a sole function of the Schmidt number, since a = a(t, Z, Sc).

A second co-ordinate transformation may now be applied to the normal co-ordinate. The Hale co-ordinate transform3 is given by:

where (A2.10)

Differentiating:

(A2.11)

Thus

(A2.12)

and

(A2.13)

The dimensionless mass transport equation in Hale space is therefore:

(A2.14)

where

(A2.15)

References

1 W.G. Cochran, Proc. Cambr. Phil. Soc., 30, (1934), 365.
2 E.R. Benton, J. Fluid Mech., 24, (1966), 781.
3 J.M. Hale, J. Electroanal. Chem., 6, (1963), 187.