Page 63 - Geochemical Remote Sensing of The Sub-Surface

40 O.F. Putikov and B. Wen

l

.,$

+ * H+ \ S=I \3
12o

Fig. 2-18. Scheme of concentration distribution of ions in and out of an element collector: C,
concentration of metal in element collector; Co, concentration of metal outside element collector;
I- solution of acid in element collector; 2- elementary pillar of solution in element collector with
unit bottom surface S = I and height h; 3- semi-permeable membrane (reproduced with permission
from Putikov, 1993).

According to Ohm's law, E = 9J, where E is electrical field strength, P the resistivity
of the membrane and j is the current density. Taking this into consideration, we can
rewrite equation (2.18),

dC k (c C ) + UpJ c + U E,j/(T. )C (2 19)
dx --h - o h o ~ o

Equation (2.19) lays down the theoretical basis of the element-collector function for
the CHIM methods (and for the MDE method, described below).
For the high values of current and current density in the CHIM method we can
suppose,

lu ,JCol >> I- (C-Co>l

lupjCol >> luE.,(= >Col

Then equation (2.19) takes the form,

dC upj
~C o (2.20)
d~ h

Solution of equation (2.20) for the initial condition,

C 1~=o - 0 (2.21)