Biomedical Engineering Reference
In-Depth Information
which is reduced to
h
s
¼
ðr
0
AS
Þa
i
h
þðr
0
AS
Þa
e
ðr
0
AS
Þa
c
a
i
h
þ a
e
a
c
¼
(17.90)
That is, the overall surface effectiveness factor is given by
a
e
a
i
h
þ
h
þ a
r
1 þ a
r
h
s
¼
¼
(17.91)
a
e
a
i
1 þ
If the external surface area to the internal surface area ratio is known, the overall surface
effectiveness factor can be determined through
Eqn (17.91)
. Eqn
(17.91)
indicates that the
effectiveness factor with higher fraction of external surface area (or small particle sizes) gives
rise to higher values.
The overall effectiveness factor can then be defined as
r
A
;
obs
r
A
;
b
¼
h
þ a
r
1 þ a
r
h
o
¼
h
e
h
s
¼
h
e
(17.92)
The external surface area can be more important in solid catalysis, especially when particle
size is small.
17.8. THE SHRINKING CORE MODEL
The shrinking core model as it states that deals with available reactants leaving the solid
particle and thus causing the solid particle to “shrink.”
Fig. 17.10
shows a schematic of the
“shrinking” solid in a porous matrix. The shrinking core model is applicable in areas ranging
from pharmacokinetics (e.g. dissolution of pills in the stomach), to biomass gasification (solid
to gas phase), to biomass extraction (solid to liquid phase), to porous catalyst regeneration
(solid to gas phase), to coal particle combustion (solid to gas phase), to pulping and bleaching
of fibers (solid to liquid phase), to pyrolysis.
N
A
x +
d
x
x
=
x
x
Outer surface:
Initial fluid-solid
reactive interface
x
=
p
Fluid-solid
reactive interface
at
t
x
=
t
= 0
Fluid-solid reactive interface
retreats as time increases
x
= 0
FIGURE 17.10
A schematic of a retreating fluid
e
solid reactive interface in a porous matrix.
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