concentration difference between the surface and the bulk concentration of substrate and
product.
For instance, the rate of flow of substrate rdif from the bulk solution to the biocatalyst
surface is given by
(5)where is the substrate mass transfer coefficient; a is the particle surface area per unit
volume, and SB and SS are the bulk and surface concentrations of the substrate
respectively. In a surface reaction, the flow of substrate to the biocatalyst surface and the
biocatalytic reaction take place consecutively. At steady state the rate of external mass
transfer of substrate, rdif, will be equal to its removal by reaction. Hence, the overall rate
of reaction, robs, will be
(6)where r(SS, PS) is the reaction rate for the immobilised biocatalyst and PS is the surface
concentration of the product.
Consider the reaction S → vP, where v is the stoichiometric coefficient relating
substrate and product. In the case of steady state behaviour, no accumulation of substrate
or product in the stagnant film occurs. Thus,
(7)
where PB is the bulk concentration of the product and is the product mass transfer
coefficient.
Rearranging this equation and defining a transport parameter as results in an
expression for the product concentration at the surface of the support:
(8)which can be substituted in the expression for r(SS, PS) to obtain an equation with SS as
the only unknown.
The kinetics of biocatalytic irreversible reactions may include substrate inhibition, like
the -carboxybenzylpenicillin towards the β-lactamase enzyme produced by Pseudomonas
aeruginosa (Fullbrook 1983); competitive product inhibition, as L-DOPA inhibition of
the tyrosinase ortho-hydroxylation of L-tyrosine (Pialis and Saville, 1998); non-
competitive product inhibition like the cellobiose and glucose inhibition of cellulase (Fan
and Lee, 1983); and simultaneous substrate and competitive product inhibition, as the
case of sucrose hydrolysis by invertase (López-Santín et al., 1982). All cases can be
expressed by a Michaelis-Menten type equation and r(SS, PS) can be defined as
(9)Design and modelling of immobilised biocatalytic reactors 95