Delphine’s handy dandy units and formula sheet
DIFFUSION
Important Quantities and their units:
x position [ cm]
t time [s ec]
c(x,t) concentration
[
3
cm
mole
]
f
diffusive flux
[
2
cmsec
mole
?
]
D diffusivity
[
sec
cm
2
]
k p artitioning coefficient [ unitless]
P permeability
[
sec
cm
]
t
SS
steady state time constant [ sec]
t
EQ
equilibrium time constant [s ec]
General Equations:
f ( x , t ) = -D
?
(c ( x , t ) ) Fick’s First Law
?x
-
?
f ( x , t ) =
?
(c ( x , t ) ) Continuity Equation
?x ?t
combine to get:
?
?
t
(c ( x , t ) ) = D
?
?
x
2
2
(c ( x , t ) ) Diffusion Equation
if you have a partition coefficient, k , then stick k with D in the above equations.
2- Compartment Model:
V
1
V
2
c
1
(t)
d
c
2
(t)
kD
P =
d
Membrane Permeability
d
2
t
SS
=
2
Steady State Time Constant
p D
1
t
EQ
= Equilibrium Time Constant
? 1 1 ?
AP
?
?
?
V
1
+
V
2 ?
?
?
if t
SS
<<t
EQ
(thin membrane) and at steady state then:
f = P ( c
1
( t ) - c
2
t )) Fick’ s Law for membranes
