456
Chapter 10
D a8
7.4 ■
10 8
-—^
(Note: Units cm2 s"1)
(3)
nB
where <
t>
is the so-called association factor for the solute (=2.26 for water), MB
is the molar mass of solvent,
VA
is the molar volume of A at its normal boiling point (Units: cm3/mol), and "Hs is the viscosity of the
solvent (Units: cP, where 1 cP = 10° kg m'1
s'1). This correlation can be used for liquid solutes, e.g. ethanol
or glycerol diffusing in a solvent, but is of no use for predicting diffusivities of dissolved solid compounds,
such as sugars. Both Eq. (1) and (3) predict that DA
varies inversely proportional to the viscosity of the
solvent and proportional to the absolute temperature._____________________________________________
10.2. Mass Transfer To and Into Solid Particles
The mass transfer of substrates from the bulk liquid to the cells is normally rapid compared to the
cellular consumption rates for a suspended cell culture (see e.g. Example 10.6). However, as is the
case for many enzymatic processes, it is also for some microbial processes advantageous to apply
immobilized cells
. The cells are in such cases attached to the surface of a solid particle or are
entrapped within a matrix structure, e.g. an alginate gel, forming either spherical pellets or
immobilized films. Mass transfer from the bulk liquid will now occur to larger particles. Since a
larger particle size gives a decreased specific surface area (cf. Eq. 10.17), the maximum obtainable
volumetric mass transfer rate will be lower than for suspended cells. Furthermore, the rate of
internal mass transfer processes
, i.e. the diffusion of substrates and products within the pellet,
becomes an important factor to consider. The transport processes will interact with the microbial
conversion processes, and the overall conversion rates may, in fact, often be determined by the
physical transport processes.
In this section we will therefore take a closer look at mass transfer processes in connection with the
application of microorganisms present in a more or less solid matrix. This is also of interest in
connection with the application of filamentous fungi, which have the ability to form pellets
consisting of many individual hyphal elements. Our discussion of the mass transfer processes is
divided into two parts: External mass transfer and intraparticle diffusion.
10.2,1. External Mass Transfer
External mass transfer carries the reacting species from the bulk liquid to the pellet surface. The
treatment of mass transfer to the pellet is completely analogous to the treatment of mass transfer
from a bubble. The concept of a stagnant film (often called the
Nernst diffusion layer
in the
biochemistry literature) is thus used also for this transport process. The flux to the pellet surface is
given by
J A = K (ca ~Ca.,)
(10.34)
cAj
is the concentration of A at the more or less well defined interface between liquid and e.g. a gel
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