Food Lipids: Chemistry, Nutrition, and Biotechnology

of substrate to product, the reaction is diffusion-limited, as there is not enough substrate
available for the amount of enzyme present (86). A diffusion coefficient for
internal mass transfer in immobilized enzyme systems compared to free enzyme
systems is defined as:
D�
D e =
�
where De is the effective diffusion coefficient inside the support particles, D is the
diffusion coefficient in free solution, � is the porosity of the particles, and � is the
tortuosity factor, defined as the distance of the pathlength traveled by molecules
between two points in a particle.
The effective diffusion coefficient varies inversely with the molecular weight
of the substrate (80). Internal diffusional limitations can be recognized if the activity
increases when the support particles are crushed, since crushing would decrease the
length of the pathway that the substrate would have to travel to reach the enzyme.
The Thiele modulus, �, can be used to evaluate the extent of internal mass transfer
limitations:
1/2
Vmax � = L� = L�K D�
m e
where L is the half-thickness of the support particles. Internal mass transfer limitations
can also be identified by measuring the initial velocity of the reaction at increasing
enzyme concentrations. If the rate of the reaction remains constant at increasing enzyme
concentrations (amount of enzyme per gram of support), the reaction is mass transfer–
limited. If the rate of reaction increases linearly with increasing enzyme concentration,
the reaction is kinetically limited. Internal diffusion limitations can be reduced by decreasing
the support particle size, increasing pore size and smoothness, using low molecular
weight substrates, and using high substrate concentrations (80). The difficulty
with using smaller support particles in fixed bed reactors where internal mass transfer
limitations are high is that it tends to increase the back pressure of the system (84).
External mass transfer limitations are the resistance to transport between the
bulk solution and a poorly mixed fluid layer surrounding each support particle. External
mass transfer can occur in packed bed and membrane reactors and is affected
by both convection and diffusion (84). If the reaction is faster than the rate of
diffusion of substrate to the surface or product from the surface, this can affect the
availability of substrate for lipase catalysis. If inadequate substrate quantities reach
the enzyme, the rate of reaction will be lower than that of free enzyme. An increasing
external mass transfer coefficient can be identified during kinetic analysis by an
increasing slope of a Lineweaver–Burk plot (87). In stirred reaction systems, external
mass transfer limitations have been eliminated when there is no increase in the
reaction rate with increasing rates of stirring. External mass transfer limitations can
be reduced in packed bed reactors by increasing the flow rate, reducing the viscosity
of the substrate, and increasing substrate concentration (80). Changing the heightto-diameter
ratio of a fixed bed reactor can also reduce external mass transfer limitation
as it increases the linear velocity of the substrates.
2. The Nernst Layer and Diffusion Layer
Immobilized lipases are surrounded by two different layers, which can create differences
in substrate concentration between them and the bulk phase. The Nernst layer
Copyright 2002 by Marcel Dekker, Inc. All Rights Reserved.