WOLFRAM|DEMONSTRATIONS PROJECT

Convection-Diffusion in a Semi-Infinite Region

​
x
t
v
D
k
xmax
value
0.1
x = 0.01 t = 0.1 v = 1 D = 4 k = 0.2 xmax = 20
-1.0
-0.5
0.0
0.5
1.0
-1.0
-0.5
0.0
0.5
1.0
x
C
C(0.01, 0.1) = 1[0.01,0.1,1,4,0.2]
C(0.01, ∞) = 1[0.01,∞,1,4,0.2]

The dimensionless concentrations
C=c/c
0
(
c
0
is surface concentration [
ML
-3
]) in a semi-infinite region are plotted (steady state in orange, transient in blue) up to the space coordinate
x=x
max
[
L
].

Only one slider is used to adjust the parameters: space
x
[
L
], time
t
[
T
], the flow velocity
v
[
LT
-1
], the hydrodynamic dispersion coefficient
D=vα
[
L
2
T
-1
] (
α
is dispersivity [
L
]), the first-order reaction rate
k
[
T
-1
], and the frame length
x
max
[
L
].

The model is described by the partial differential equation
∂
t
C(x,t)+v∂
x
C(x,t)=D∂
x,x
C(x,t)-kC(x,t),
subject to the conditions
C(0,t)=1
,
C(∞,t)=0
,
C(x,0)=0
.

For a fixed time parameter, the space
x
determines black points on the orange curve
C(x,∞)
and on the blue curve
C(x,t)
, so that you can see the corresponding numerical values. Smilarly for any parameter
​
the precise values of the steady state and transient dimensionless concentrations are available.