Environmental Engineering Reference
In-Depth Information
V
=
0
k
D
V
=
0
mem
mem
(
m
v
)
P
=
=
P
·
10
.
.
(9.4)
d
mem
Lieb.and.Stein.[3].showed.that.log.
P
V=0
.correlates.with.log.
k
ow
.with.a.slope.of.
0.0546..This.allows.for.the.description.of.the.overall.permeability.in.terms.of.vol-
ume.and.partition.as.follows:
V
=
0
(
m V
)
P
=
P
⋅
10
ν
V
=
0
P
P
=
.
.
(9.5)
(
m V
)
10
ν
0 0546
.
log
k
ow
10
=
1
0
(
m
ν
)
Thus,.the.initial.inlux.rate.(
J
mem
).can.be.determined.as.follows:
dC
dx
J
= −
D
mem
mem
=
·
D
P dx
mem
.
dn
dt
dC
dx
.
(9.6)
= −
D
A
mem
mem
dn
= −
PA
·
dC
mem
dt
where.
n
.is.the.number.of.particles,.
A
mem
.is.the.membrane.surface.area.available.for.
absorption,.and.
dC/dx
.is.the.concentration.gradient.
The.diffusion.model,.as.parameterized,.predicts.the.trans-membrane.lux.from.
extracellular.to.intracellular.spaces.within.the.digestive.epithelium..This,.however,.
is.expected.to.be.initially.faster.than.diffusion.from.the.intercellular.to.the.central.
compartment.because:.(1).while.the.permeability.
P
.is.not.likely.to.differ.signiicantly.
across.the.epithelial.cells,.the.microvilli.on.the.exterior.of.the.digestive.epithelium.
dramatically.increase.the.cellular.surface.area.(
A
mem
);.and.(2).the.initial.concentra-
tion.gradient.from.the.digestive.tract.to.the.intracellular.compartment.is.greater.than.
the.gradient.from.the.epithelium.to.the.central.compartment.
To.predict.transport.kinetics.from.the.digestive.tract.to.the.central.compartment,.
the. membrane. diffusion. model. must. be. coupled. into. a. three-compartment. model.
(Figure.9.2).to.isolate.the.rate-limiting.step.as.follows:
dn
dt
(
)
1
= −
PA
[
C
]
−
[
C
]
GI
IC
GI
.
.
(9.7)
dn
dt
(
)
2
= −
PA
· [
C
]
−
[
C
]
CC
CC
CI
