Effect of external diffusion limitation

If the activity of the immobilised catalyst is sufficiently high, the reaction which it mediates occurs essentially at the interface between the catalyst and the substrate solution. In the case of the surface immobilised enzyme or a thin microbial film this will, of course, occur irrespective of the level of activity. Under these conditions the limiting process for transporting substrate from the bulk of the solution to the immobilised enzyme is molecular or convective diffusion through the layer of solution immediate to the carrier. Under steady-state conditions, the rate of reaction at the active sites is equal to the rate at which substrate arrives at the site. This 

9C is the rate of reaction per unit surface area of catalyst 

Assuming that the local rate of enzyme reaction follows Michaelis-Menten kinetics, or that the microbe film follows Monod kinetics regardless of immobilisation, then equation 5.86 becomes  

The dimensionless substrate concentration may be defined by p = — so that substitution in equation 5.87 and rearranging gives x 

If the rate of reaction obtained with no diffusional restrictions is denoted by the symbol l then an effectiveness factor may be defined as  

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