cous substrates. The substrate diffusion across the thin film from the bulk mixture to
the surface of the support follows Fick’s law. For a system where the substrate diffu-
sion coefficient is independent of substrate concentration, the mass transfer rate at
steady state will be equal to the reaction rate:
kLaðSbSSÞ¼VmaxSS
KmþSSð 17 ÞwherekLis the substrate mass transfer coefficient,ais the external surface area,Sb
andSsare the bulk and surface substrate concentrations,Vmaxis the maximum reac-
tion rate, andKmis the Michaelis constant. When the left-hand term is smaller than
the right-hand term, the reaction rate is decided by the substrate diffusion. In such a
situation, external diffusional limitations occur.kLrelates to theSherwood number
which, in turn, corresponds with Reynolds number and Schmidt number. These num-
bers can be calculated at certain experimental conditions and, therefore,kLcan be
determined for stirred-tank reactors as well as packed-bed reactors. For packed-bed
reactors with the commercial immobilized lipase, Lipozyme IM, it was reported that
the external diffusional limitations could be neglected when the linear flow rate of
the substrate was higher than 5 10 -5ms-1in a packed-bed reactor for a reaction of
ester – ester exchange between triolein and trimyristin (Jung and Bauer, 1992). Fig-
200 11 Modification of Oils and Fats by Lipase-Catalyzed Interesterification
Figure 6. Influence of linear flow rate u (m s–1) on the packed-bed conversion (X’) for constant re-
sidence time (sR) under the constant particle diameter and pore size, for the Lipozyme IM-catalyzed ester
- ester exchange between triolein and trimyristin. (From Luck et al., 1988.)