ure 6 illustrates the conversion (X^0 ) under same residence time (sR) and various
linear flow rates higher than 5 10 -5ms-1(u).
Internal diffusional limitationsare more crucial for immobilized enzymes. Sub-
strate mass transfer within the enzyme particles is limited because of the small size
and tortuosity of the pores in the enzyme support. It relates to the particle radius (r),
porosity of the particle (e), and the tortuosity of the pores (s), which are described by
a inclusive factor, theThiele modulus(f), as follows:
f¼r
3ffiffiffiffiffiffiffiffiffiffiffiffi
Vmaxp
KmDesð 18 ÞwhereVmaxis the maximum reaction rate,Kmis the Michaelis constant, andDis the
substrate diffusion coefficient in free solution. Effectiveness factor (g), with regard
to internal mass transfer limitations, directly relates to the Thiele modulus (f) and
bulk substrate concentration relative toKm(Sb/Km). The lessfand largerSb/Km, the
highergwill be obtained and less internal mass transfer limitations will be caused.
This effect is illustrated in Figure 7 (Luck et al., 1988; Abraham, 1988). Thes/Kmin
the figure is equivalent to theSb/Kmin the text. Internal diffusional limitations can be
recognized if the activity of an immobilized enzyme is increased when it is crushed,
i.e. when the length of the diffusion pathway is reduced. Internal diffusional limita-
tions can be minimized by using a low molecular weight substrate, a high substrate
concentration, a low biocatalyst concentration, and small highly porous enzyme
particles in which the pores are as large, nontortuous, and interconnected as possi-
ble, or by immobilizing the enzyme only to the outside surface of the support. Thus,
there is a compromise whether forming a very active immobilized preparation with a
low effectiveness factor or a less active preparation with a higher effectiveness fac-
tor. In fact, the effectiveness factor will vary throughout the support particles, being
higher near the surface and lower near the center of the particles. For Lipozyme IM,
the internal diffusional limitations did occur as studied by Jung and Bauer (1992) and
11.4 Immobilized lipases 201
Figure 7. The relationship between internal effectiveness factor (g) and the Thiele modulus (U) for
values ofs/Kmand two geometries of enzyme particles. (From Abraham, 1988.)