Biomedical Engineering Reference
In-Depth Information
C
0.160
0.159
0.157
0.155
0.153
0.152
0.150
5
5
0
0
0
0
5
10
15
X
20
25
30
5
10
15
X
20
25
30
t = 15,400
C
0.160
0.159
0.157
0.155
0.153
0.152
0.150
5
5
0
0
0
0
5
10
15
X
20
25
30
5
10
15
X
20
25
30
t = 30,750
C
0.160
0.159
0.157
0.155
0.153
0.152
0.150
5
5
0
0
0
0
5
10
15
X
20
25
30
5
10
15
X
20
25
30
t = 46,100
FIGURE 7.9
Snapshots of the distribution of precipitates (the dark gray circles) and the
concentration of solute
C
(the quasicontinuous gray scale) at three differ-
ent times. The medium gray circles denote particles representing soil grains.
The left and right columns depict results of the pore-scale and hybrid
simulations, respectively (Tartakovsky et al. 2008b). (Tartakovsky, A. M.,
Tartakovsky, D. M., Scheibe, T. D., and Meakin, P.,
SIAM J. Sci. Comput.
,
30, 6, 2008b. Copyright 2008 Society for Industrial and Applied Mathematics.
Reproduced/modified by permission of Society for Industrial and Applied
Mathematics.)
production and precipitation of the reaction product,
C
, are governed by equa-
tions (7.36-7.39) subject to the boundary conditions:
∂C
A
∂x
(
L,y, t
)=
∂C
B
∂x
C
A
(0
,y,t
)=
C
B
(
L, y, t
)=1
,
(0
,y,t
)=0
∂C
C
∂x
(0
,y,t
)=
∂C
C
∂x
(
L, y, t
) = 0
(7.57)
and the initial conditions
C
A
(
x, y,
0) =
1
,x
C
B
(
x, y,
0) =
0
,x
16
0
,x>
16
,
≤
16
16
,x>
16
≤
C
C
(
x, y,
0) =
0
,x
16
0
,x>
16
≤
(7.58)
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