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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*.