(23)
The boundary conditions for the solution of equations (21) and (23) are:
(24)(25)
The effectiveness factor for internal mass transfer effects is defined as the ratio between
the overall rate of substrate consumption inside the particle roverall (S), and the rate
evaluated for the surface concentration of the substrate, r(Ss). At steady state the substrate
does not accumulate inside the support particle, thus:
(26)where Vp is the catalyst particle volume and J is the diffusive flow of substrate at the
support surface given by Fick’s law:
(27)
where A is the superficial area of the catalyst. Thus, the effectiveness factor will be given
as:
(28)or, in a dimensionless form:
(29)It can be easily shown that,
(30)
thus substituting this in equation (29) yields:
(31)
Design and modelling of immobilised biocatalytic reactors 105