Biomedical Engineering Reference
In-Depth Information
equation (8.59) we get:
J
vs
=
J
vsM
=(1
−
−
σ
)
c
s
V
s
L
p
∆Π+(1
−
σ
)
c
s
V
s
L
p
∆
P
(8.95)
From (8.94) and (8.95) we see that the turgor pressure satisfies
∆
P
=
σ
∆Π
(8.96)
where
σ
=
σ
+(1
−
σ
)
c
s
V
s
(8.97)
1
−
(1
−
σ
)
c
s
V
s
8.5.3
Numerical Results for
Nitella translucens
and
Chara Corallina
In the model cell shown in Figure 8.5, the water volume influx,
J
vwa
, across
part (a) of the membrane is given as
J
vwa
=
L
p
σ
(
σ
−
1)∆Π =
L
p
σ
(
σ
−
1)
RT
(
c
si
−
c
so
)
(8.98)
where we used equation (8.96) and the volume flux equation (8.43). Similarly,
the volume flux through part (b) can be expressed as
J
vwb
+
J
vsb
=
J
vb
=
L
pb
∆
P
(8.99)
Using equation (8.96) and the solute flux equation (8.59) we can find the
following expression for the water volume eux:
J
vwb
=(1
−
σ
)[(1
−
c
s
V
s
)
σ
−
c
s
V
s
]
L
p
RT
(
c
si
−
c
so
)
(8.100)
Equations (8.98) and (8.100) show that in a stationary state the cell
can simultaneously absorb and reject water through different parts of the
membrane. In Table 8.2 we show numerical results for two particular plants,
Nitella translucens
and
Chara Corallina.
Values of transport parameters were
obtained from available literature. The table shows values of water influx and
eux calculated from equations (8.98) and (8.100), respectively. Water influx
is osmotically driven and takes place in part (a) of the membrane and water
eux is driven by the turgor pressure and occurs through pores in part (b) of
the membrane.
8.6 Passive Transport through Cell Membranes
of Human Erythrocytes
Fundamental functions of human erythrocytes are related to transport of oxy-
gen throughout the organism and removal of carbon dioxide. Contrary to most
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