8.3 Concentration of Matter for Molecular and Turbulent Diffusion
261
a y
b y
x
x
c y
d y
.. ~-; :,: ~ :.
~:d~~:'~~~'~:~:~>;'i'> .
x
x
Fig. 8.3: Advective and diffusive processes involved in the transport of particles
on plane (x, y): a initial stage, b advection by velocity U only, c diffusion only,
d advection and diffusion
and diffusion terms, i.e .::
ae
e
u -
UUL
~~-...iL=_
D\l2e
D~
D'
L2
(8.20)
where U is the characteristic velocity of the transporting fluid , L is the characteristic length of the flow domain and D is the diffusion coefficient. The
ratio
UL
Pe=V'
(8.21 )
is known as the Peclet number Pe. Values of Pe greater than one demonstrate
that advection dominates over diffusion. In the case of molecular diffusion,
when coefficient D is very small, the Peclet number is much greater than one
and advection dominates over diffusion.
To solve Eq. (8.16), boundary conditions have to be specified. Firstly, the
concentration at a given time instant, t = to, has to be known; usually to = 0
261
a y
b y
x
x
c y
d y
.. ~-; :,: ~ :.
~:d~~:'~~~'~:~:~>;'i'> .
x
x
Fig. 8.3: Advective and diffusive processes involved in the transport of particles
on plane (x, y): a initial stage, b advection by velocity U only, c diffusion only,
d advection and diffusion
and diffusion terms, i.e .::
ae
e
u -
UUL
~~-...iL=_
D\l2e
D~
D'
L2
(8.20)
where U is the characteristic velocity of the transporting fluid , L is the characteristic length of the flow domain and D is the diffusion coefficient. The
ratio
UL
Pe=V'
(8.21 )
is known as the Peclet number Pe. Values of Pe greater than one demonstrate
that advection dominates over diffusion. In the case of molecular diffusion,
when coefficient D is very small, the Peclet number is much greater than one
and advection dominates over diffusion.
To solve Eq. (8.16), boundary conditions have to be specified. Firstly, the
concentration at a given time instant, t = to, has to be known; usually to = 0