Page 82 - Geochemical Remote Sensing of The Sub-Surface

Geoelectrochemistry and stream dispersion 59

where, z = charge of the ion-carriers of current, F = Faraday constant, a = rate of current
density change with time (current density rate).
Applying the integral Laplace transformation relative to time x, Putikov (1993)
obtains a solution of equation (2.31) under conditions (2.32) to (2.34),

x
a 2 ~e~Cf~d~,_ x 1
C-C~ + zF~ --~ ~ (2.35)

where, Erf(y) = 1-erf(y), and erf(y) is the probability integral,

2
erf (y) = -~K ~e-~dzl

At the mineral surface for x = 0 we have, from (2.35),

a
4
CIx=o -Co +~ zF 4~ r 3/2 (2.36)

At the limiting time for a given electrochemical reaction x = 171im, the ion-carriers of
current near the mineral surface reach a maximum value, Cmax, which depends upon the
dissolution production of the corresponding compound. Taking these points into account
we can obtain from (2.36) for x = Xlim,

4 a ~ (2.37)
C max = Co + -~ zF 4nO r)jm

V 3 )zF ~-~l~a -~ (2.38)
- L (c m.x -Co

With respect to (2.33) it is possible to write,

E 3 l a '~ (2.39)
'~- (Cma x - C 0 ) zF~
Jlim -- a g-,i m ~

Taking logarithms of equation (2.39) we obtain,