Biomedical Engineering Reference
In-Depth Information
Extracellular
medium
Cell
J
v
c
si
> c
so
P
i
> P
o
J
vs
J
vs
FIGURE 8.4
A model of an aquatic plant cell (
c
si
,c
so
is the concentrations;
P
i
,P
o
is the
pressures,
J
v
,J
vs
,J
vs
is the volume fluxes).
To maintain a steady concentration gradient there must be an active influx
of the same solute, described as
J
vs
in the figure. In such a stationary state
there is a constant osmotic pressure, ∆Π =
RT
(
c
si
−
c
so
), and a constant
turgor pressure, ∆
P
=
P
i
−
P
o
. The KK equations for the water and solute
transport have the form
J
v
=
L
p
∆
P
−
L
p
σ
∆Π
(8.88)
j
s
=
ω
∆Π+(1
−
σ
)
c
s
J
v
(8.89)
The latter can be rewritten as the solute volume flux
J
vs
=
ωV
s
∆Π+(1
−
σ
)
c
s
V
s
J
v
(8.90)
where
V
s
is the molar volume. The total volume flux is then given as
J
v
=
J
v
+
J
vs
(8.91)
In the KK formalism, the flux
J
v
is defined as
J
v
=
J
vw
+
J
vs
; hence
J
v
=J
vw
+J
vs
+
J
vs
(8.92)
In a stationary state
J
v
=0,
J
vs
+
J
vs
= 0, and the water flux is also zero
(
J
vw
= 0). The cell does not change its volume and it does not absorb or
reject water.
8.5.2 Water Exchange Described by Mechanistic Equations
We consider a model of a cell including fluxes relevant to the ME shown in
Figure 8.5 (Kargol and Kargol 2005; Kargol et al. 2005). For illustration pur-
poses we assume that the osmotically active surface of the cell containing all
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