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number, is set appropriately, desorption kinetics can be predicted accurately by modeling only
mass transport in P. Such kind of reasoning can be also extended to other situations, where the
contact surface area or the composition of the interface (e.g. due to exudation, phase
separation...) is not known accurately or may vary with time. All these complex phenomena can
be simulated by taking into account uncertainty of h
F
.
5.2.1.2
Principle
It is worth to notice that the dimensionless formulation proposed in section 3.2 does not use
directly D
P
and h
F
in the transport equations but the dimensionless numbers Fo and Bi. From the
statistical point of view, both descriptions are not equivalent since D
P
and h
F
are assumed to be
independent quantities when Fo and Bi cannot (i.e. D
P
and h
P
appear in the expression of Bi).
The corresponding random model is:
( )
(
)
*
*
2
2
*
*
*
,
*
*
D
D
h
P
P
P
s
p
Fo
p
F
P
F
P
F
s
s
P
P
P
Bi
D
t
D
t
Fo
D
Fo Fo
l
l
h
l
h
l
h
Bi
Bi Bi
D
D
D
=
=
=

=
=
=

(34)

Since
( )
*
D
s
Fo
and
(
)
*
,
D
h
s
s
Bi
are not independently distributed, the distribution of the resulting
dimensionless concentration
(
)
*
,
,
,
D
h
v
Fo Bi s
s
is calculated iteratively (mixture rule) from the
marginal distribution
(
)
*
,
D
i
v
Fo s
B
f
:
(
)
(
)
*
,
,
,
*
,
0
D
h
D
Bi
v
Fo Bi s
s
v
Fo s
Bi
f
f
f
dBi
+
=
(35)

where
(
)
*
,
D
v
Fo s
Bi
f
is the distribution of
*
v calculated for a given Bi value as depicted in Figure
11.
Bi
f is the expected distribution of Bi.

5.2.1.3
Detailed example
The results plotted in Figure 11 (
0.5
Fo
=
, s
D
=0.1) are extended to an arbitrary distribution of Bi
defined by:
(
)
(
)
0,
min
max
,
10
Bi
Norm
s
Bi
Bi
Bi
(36)
where the parameter s
Bi
accounts for the uncertainty on both D and h.