Page 81 - Geochemical Remote Sensing of The Sub-Surface

58 O.F. Putikov and B. Wen

ore body. This answers certain questions related to the quality of the ore body.
Quantitative problems are addressed by using the limiting current values of the
electrochemical reactions (wave height) to determine the total surface area, size,
concentration and mass of minerals (metals) of an ore body. First consider the limiting
current density, because the limiting current is the product of the limiting current density
and the surface area. In the general case the current density is,

J=jo+jM+jc (2.29)

where, jD = diffusion current density, jM = migration current density, jc = convection
current density. When the electric field intensity is low and the liquid phase is
immovable we can neglect jM and jc such that,

j =jD (2.30)

As is evident from Fig.2-37, only the first anodic and cathodic reactions (equations
(2.25) and (2.27) for sulphides) have finite limiting currents. According to equations
(2.25) and (2.27) some ion-carriers of current (sulphide ions or metal ions ) transfer from
the solid phase into the liquid phase. For a planar ore body the concentration C of the
ion-carriers of current in the ion-conducting host rocks satisfies the one-dimensional
differential diffusion equation,

02C 1 c~
~2 D Or -0 (2.31)

where, x = distance from the mineral surface of the ore body, D = diffusion coefficient
of the ion carriers of current in the host rocks, x = time.
The initial condition can be written as,

C I,-=o - C o (2.32)

where Co is the initial concentration of ion-carriers of current in the host rocks. For the
galvanodynamic polarisation mode, in which current density is a linear function of time,
from (2.30) we can write,
Jo Ix=o = -zFD- l

Jl,=o- -ar (2.33)
x=O

C lx ~oo -> C o (2.34)