Simultaneous External and Internal Mass Transfer

In practice, both external and internal mass transfer resistances are significant and they simultaneously influence global reaction rate in an immobilized enzyme (or cell reactor). Additionally, substrate partitioning can also affect the observed kinetics.

The analysis of the combined effect of these factors begins with the steady state intraparticle mass balance for substrate in a spherical immobilized enzyme pellet :

In this case, the boundary conditions become :

where:

Thus, the Biot number is representative of the relative degree to which the two resistances control mass transfer.

In the presence of partitioning effects, equilibrium concentration of the substrate in the pellet will differ from that in the bulk liquid. This results in an abrupt change in concentration at the solid-liquid interface which is given by:

where,

S_i^* : substrate concentration “just within” the surface

K_p : partition coefficient

Thus, the second boundary condition becomes:

We then define an overall effectiveness factor which is given as :

As Bi decreases, external film resistance becomes more significant. So the dependence of h₀ on b decreases. Generally if Bi is on the order of 100 or more, the effects of external resistance are not significant.

Page created by Asif Ladiwala and Shripad Gokhale.

Last modified : 13 December, 2000.