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The reaction kinetics for one flush
We are concerned here with
the chemistry of the initial wet
phase of a single flush.
The time epoch for the post-flush
reaction is the duration of
the wet phase, T.
Disregarding diffusion and flow
of COC laden salt water across
the marsh after a flush, we may
focus on the chemistry ongoing
within a single cell of rhizosphere.
Considering a single COC, we
propose a hierarchy of models
for its geobiochemical interaction
with the bacteria of the rhizosphere,
beginning with the most naive.
First approximation: exponential decay
In this model we assume
that the flush of COC does not
significantly decriment the
rhizobacterial population,
and is independent of the carbon
cycle of the salt marsh ecosystem.
We take the availability of bacteria
in the rhizosphere as a constant, B, throughout
the diffusion-reaction following each
flush.
In that case, the kinetics are first-order,
and linear, and the conversion of COC is by
exponential decay.
COC -> Resultant
X' = -KXBBX
X = concentration of one COC in one cell
KXB = reaction rate, a constant
B = rhizobacterial population, a constant
throughout the root layer of the salt marsh
in this model
Second approximation: second order kinetics
In this model we assume that rhizobacterial
population is consumed in the COC conversion.
Then the kinetics for the two
concentrations, X and B, may be taken as follows.
COC + bacteria -> Resultant.
X' = -KXBBX
B' = -KBXBX
X = concentration of one COC in one cell
B = rhizobacterial population in cell
KXB = reaction rate, a constant
KBX = reaction rate, a constant
Third approximation: Monod kinetics
In this model we assume that rhizobacterial
population is consumed in the COC conversion,
as above, and also that it is regenerated
by the rhizospheric substrate.
The Monod rule is one way of accounting
for the regeneration of B in the rhizosphere
ecosystem. Then
the kinetics for the two
concentrations, X and B, may be taken as follows.
COC + bacteria -> Resultant.
X' = -KXBBX
B' = -KBXBX + MS/(Km - S)
X = concentration of one COC in one cell
B = rhizobacterial population in cell
KXB = reaction rate, a constant
KBX = reaction rate, a constant
M = Monod constant, maximum growth rate for B
Km = Michaelis/Menton constant
S = measure of rhizospheric substrate,
assumed proportional to the biomass
of cordgrass, a control parameter in
this model (it varies seasonally)
Cf. (Koch, 1998, p. 65) for explication of this.
Fourth approximation: geobiochemistry
Next we consider more realistic and complex chemistry.
For example, if the COC is ammonium, then
assimilation as R-NH2 might be the primary reaction.
We might thus take a nitrogen cycle model to account
for the full complexity of the COC reaction.
But as aerobic oxygen respiration and sulfate reduction
are of primary importance in the salt marsh ecology
(cf. Howarth) we would probably combine three cycles
in this approximation.
Revised by Ralph Abraham 26 August 1998
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