Peclet number for the wall-jet electrode

The mass transport equation is:

(A4.1) |

where (under a 1^{st} order convection approximation):

and | (A4.2) |

and

, and | (A4.3) |

Defining the dimensionless lengths:

R = r/r_{e} and Z = z/r_{e} | (A4.4) |

and substituting for R and Z, gives the dimensionless form of the mass transport equation:

(A4.5) |

Similarly the velocity expressions become:

(A4.6) |

(A4.7) |

Substituting for v_{r} and v_{z} gives:

(A4.8) |

where P_{s} is the (shear rate) Peclet number:

= | (A4.9) |

Hence:

a = a(R,Z,P_{s}) | (A4.10) |

However the dimensionless current:

(A4.11) |

is calculated from the flux at the electrode surface, where Z = 0. Furthermore R is integrated out, thus the dimensionless current is a sole function of the Peclet number. Note that this result is only valid for a 1^{st} order convection approximation.