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 Cochran^{1}, and later by Benton^{2}. Close to the electrode surface it may be approximated as a series expansion in z.

(A2.3) |

where a_{i} are constants and according to Benton^{2} a_{0 }= 0.510233 and b_{0 }= -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 c_{i}

(A2.9) |

it is apparent that k_{i} 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 transform^{3} 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) |

^{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.