Biomedical Engineering Reference
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C
Ab
C
AS
C
A,0
C
Ab
0
R
p
C
AS
r
C
A,0
X
r
r
= 0
d
C
A
d
r
Bulk fluid phase
Wall
= 0
X=0
X=
p
C
A
= C
AS
d
C
A
d
X
C
A
=C
AS
=0
r
=
R
p
“
S
S
p
i
c
a
(a)
(b)
FIGURE 17.4
Schematic ofmass transfer and reactiongeometries for (a) an infinite slab and (b) a spherical particle.
concentration gradient) hold. Therefore, along the direction of
x
, one can effectively think of A
is the transporting though a conduit centered along the
x
-axis. The cross-sectional area of the
conduit may not be constant (as in the case of
Fig. 17.4
b). Mass balance at pseudo-steady state
inside the particle,
Fig. 17.5
with mass transfer flux
N
A
from
x
þ
d
x
to
x
, leads to
d
n
A
N
A
Sj
xþ
d
x
N
A
Sj
x
þ r
A
S
d
x ¼
d
t
¼ 0
(17.19)
where
n
A
is the number of moles of A in the differential volume (between
x
and
x
d
x
)of
particle,
S
is the cross-sectional area perpendicular to the path of diffusion/transport
x
.
þ
N
A
x + dx
x
x
Outer surface
x
=
p
Inpenetratable
wall or center on
the diffusional path
x
= 0
FIGURE 17.5
Diffusion and reaction along a curved path with variable cross-sectional area.
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