Internal Mass Transfer : Derivation

In this analysis, we assume that the enzyme is immobilized within a pellet that has approximately spherical shape, a shell of differential thickness is considered so that all conditions within the shell may be considered independent of position.

  Steady state material balance on shell between r and (r + dr) gives:

  Assuming D_eff within the permeable pellet is constant, we rewrite as:

  Taking limit dr 0 :

whence,

Presuming that the intrinsic, local kinetics of the immobilized enzyme catalyzed reactions are of Michaelis-Menten form:

Therefore, at steady state:

Boundary Conditions:

Since the concentration profile through the pellet is symmetrical about the centerline of the sphere,

Further, we shall assume that the surface concentration at the external surface of the pellet is equal to the bulk substrate concentration S₀ ie.we neglect the effect of film mass transfer resistance. Consequently,

Dimensionless Form: 

Dimensionless form of equation (15):

where;

  The dimensionless parameters f and b are defined by –

  The dimensionless boundary conditions associated with equation (16) are:

Page created by Asif Ladiwala and Shripad Gokhale.

Last modified : 13 December, 2000.