OSMOSIS
Important Quantities and their units:
x position [m]
t time [sec]
c
i
(x,t) concentration of solute i
[
3
m
mole
]
c
e
(x,t)
osmolarity
[
33
m
mole
m
osmole
= ]
r
m
density
[
3
m
kg
]
V volume [m
3
]
F
osmotic flux
[
sec
m
msec
m
2
3
=
?
]
k
hydraulic permeability
[
secPa
m
2
?
]
L
v
hydraulic conductivity
[
secPa
m
?
]
p hydraulic pressure [Pa]
p
osmotic pressure [Pa]
R molar gas constant
8.314
Kmol
mN
?
?
T temperature [K]
Gene ral Equations:
c
S
=
∑
n
i
c
i
(where the i
th
solute dissociates into n
i
particles) Definition of Osmolarity
i
p = RTc
S
van’t Hoff’s Law
F
v
( x , t ) = -k
?
( p - p ) Darcy’s Law
?x
-
?
(r
m
? F
v
) = -
?
r
m
Continuity equation
?x ?t
2- Co mpartment Model (water incompressible so always at SS):
V
1
(t) F
v
V
2
(t)
c
1
(t) c
2
(t)
A =cross- section area
d
1 d
F = - ? V Definition of volumetric flux
v 1
A dt
k
L = Hydraulic conductivity
v
d
F
v
= L
v
(( p
1
-p
1
) - ( p
2
-p
2
) ) Darcy’s Law
1 2 1 2 1 2
c
S
( 0 ) V
1
( 0 ) + c
S
( 0 ) V
2
( 0 ) = c
S
( t ) V
1
( t ) + c
S
( t ) V
2
( t ) = c
S
( ∞) V
1
( ∞) + c
S
( ∞) V
2
( ∞) conservation of solute closed
V
1
( 0) + V
2
( 0) = V
1
( t ) + V
2
( t ) = V
1
( ∞) + V
2
( ∞) conservation of solvent
only
system
