Multiphase Bioreactor Design

These differences in the equilibrium concentrations of charged soluble compounds
may be described by the partition coefficient, P given by

(1)

where Ci and Co are the local and bulk concentrations, respectively.
The main consequences of these partition effects is a shift in the optimum pH, with a
displacement of the pH-activity profile of the immobilised enzyme towards more alkaline
or acidic pH values for negatively or positively charged carriers, respectively. Assuming
the Boltzmann distribution, the partitioning of hydrogen ions between the local activity

( ) and the bulk activity ( ) is given by

(2)

or by the definition of pH

(3)

where e is the electronic charge, ψ is the electrostatic potential, k is the Boltzmann
constant, T is the absolute temperature, and pHi and pHo are the local and the bulk pH
values. This equation shows that the local pH is higher if the support is negatively
charged.
By similar considerations, the partitioning of charged compounds, substrate or
product, between a charged enzyme particle and the bulk solution can be represented in
the following form:

(4)

where Ze is the substrate charge.
Thus for positively charged substrate, when using a negatively charged enzyme
particle, a higher concentration of substrate is obtained in the local environment or
microenvironment than in the bulk solution, and a higher value of relative activity is
obtained than with a neutrally charge matrix. However, when effects other than
partitioning are present, it is possible to have no shift of the enzyme’s pH optimum on
charged supports.

External mass transfer effects

When a biocatalyst is immobilised on or within a solid matrix, mass transfer effects may
exist because the substrate must diffuse from the bulk solution to the active site of the
immobilised biocatalyst. If the biocatalyst is attached to nonporous carriers there are only
external mass transfer effects on the catalytically active outer surface; in the reaction
solution, being surrounded by a stagnant film, substrate and product are transported
across the Nernst layer by diffusion. The driving force for this diffusion is the

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