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C i
t 1
t 2
t 3
v i
Direction of flow
Figure 5.8
Principle of chromatographic fractionation. Different ions propagate along the column at different
speeds. Each curve represents the concentration profile of the same element at different times
( t 1 <t 2 <t 3 ). If the speed of propagation of an element i in the porous medium depends on its
concentration C i
in the liquid and partition coefficient D i , concentration fronts rise and collapse.
particles take the place of the liquid occupying porosity
of the general theory, while
seawater plays the role of the rock matrix. What conditions reactivity is the seawater-
particle partition coefficient D i of elements between seawater and particulate matter
(note the direction of exchange, which gives reactivity a counter-intuitive character).
Elements that are not reactive with particles ( D i
ϕ
), such as sodium and chlorine,
remain motionless and are not affected by particle flow. Elements subjected to intense
entrainment by solids ( D i
≈∞
0), such as lead, cadmium, and rare-earths, move down
the water column almost as quickly as the particles and are soon evacuated from the
system.
5.4 Reaction rates
Let us consider the reaction by which marine sulfates are reduced at the water-sediment
interface by accumulated organic matter, which we will represent by the very simple chem-
ical formula CH 2 O (the precise formula is immaterial to the explanation). This reaction
produces hydrogen sulfide, which will precipitate as pyrite FeS 2 with the ambient iron,
and a bicarbonate ion from the reaction:
SO 2 4
2HCO 3
2CH 2 O
+
H 2 S
+
(5.21)
By indicating the molar concentrations of the species with square brackets, the conser-
vation of matter during the reaction imposes the following conditions of evolution (see
Appendix C ) :
d SO 2 4
d HCO 3
2
d [CH 2 O]
2
d [H 2 S]
1
=−
=+
=+
=
d
ξ
(5.22)
1
where
d t is the reaction
rate. This depends on the probability that the reactants will collide and, therefore, on their
concentration; and, as with a diffusion coefficient, on the frequency
ξ
is the degree of advancement of the reaction. The quantity d
ξ/
ν
of vibrations and on
 
 
 
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