Civil Engineering Reference
In-Depth Information
5.2.6 Moisture Transport: Molecular Diffusion
Molecular diffusion is the transport of molecules from a region of higher con-
centration to one of the lower concentrations. Gases such as water vapour and air
in fibrous media can move by molecular diffusion. Analogous to the heat con-
duction, the molecular diffusion is described mathematically by the second Fick's
law. The macroscopic mass flux of gases is
J
gas
diffusion
¼
D
gas
r
C
gas
ð
16
:
8
Þ
where
C
concentration
D
diffusivity
subscript
gas or liquid
superscript
gas or liquid
The molecular diffusivity D can be related to the molecular diffusivity of gas in
bulk in that
D
gas
¼
D
bulk
s
e
ð
16
:
9
Þ
where
D
bulk
diffusivity in bulk
So the mass conservation equation can be expressed as
o
C
gas
ot
¼rð
D
gas
r
C
gas
Þ
ð
16
:
10
Þ
which is the second Fick's law.
5.2.7 Moisture Transport: Darcy Flow
In pressure-driven gas transport, Darcy's law is often used in calculating the mass
flux in the form of
k
gas
l
gas
J
gas
pressure
¼
q
gas
r
P
ð
16
:
11
Þ
where
k
gas
¼
k
:
k
gas
relative
