depending on the initial particle size. Wheat bran particles of initial flake length
of 1 mm completely disappeared, and the decrease in flake length during the
fermentation was described well by the model. As flake length increased there
was a greater residual length. Particles of initial flake length of 2 mm and above
were degraded to only 50% of this initial length in the 96 h of fermentation. In
this case the model did not describe the degradation curve well. Nandakumar
et al. [128] pointed out that smaller wheat bran particles contain mainly starch,
while larger particles contain significant amounts of hemicellulose and cellulose, which cannot be degraded by B. coagulans.
A more sophisticated model was proposed for growth of biofilms of B. coagulans on reducing particles by Rajagopalan et al. [114], describing many other
phenomena occurring such as oxygen reaction within the biofilm, expansion of
the biofilm during growth, release of enzyme into the substrate, and diffusion
of glucose through the substrate and biofilm. Their model also agreed well with
the data of Nandakumar et al. [128]. They argued that the explanation of different compositions for particles of different sizes is not the only possible
explanation. Instead, they suggested that the limited diffusion of glucoamylase
into a particle, combined with the “clearing effect” noted by Mitchell et al. [84],
could account for the different consumption rates for different particles sizes.
Late in the fermentation, almost all the glucoamylase could be located in
regions cleared of starch, preventing further particle degradation. However,
they did not clearly propose a mechanism by which particle shrinkage was
related to starch utilization.
4.6
Potential to Develop a Microscale Model of Growth
The preceding sections have highlighted the complexity of the microscale
phenomena occurring during SSF, and our current understanding of how these
phenomena can influence the process. Before describing approaches to
modeling bioreactors, it is worthwhile to consider how these microscale phenomena might be handled in bioreactor models. There are basically two approaches – either to use empirical growth equations which ignore microscale
mass transfer, or to attempt to incorporate the microscale mass transfer
processes into the bioreactor model.
Due to the complexity of describing transfer phenomena at both the intraparticle and supraparticle scale, most bioreactor models use empirical equations, such as the logistic equation (Eq. 5), with the specific growth rate being
expressed as an empirical function of temperature. However, if this is done the
parameters of the empirical model must be determined for each small change
in the system. The model may simply fail to describe data under different
operating conditions where the factor limiting growth may be different.
Additionally, the values of the fitted kinetic parameters will have no biological
significance, although it still might be useful to compare values (e.g., of m max or
X max in the logistic equation) for different fermentations.
Combined intraparticle and interparticle diffusion of oxygen has been taken
into account in a model of a tray bioreactor [122]. A “complete” bioreactor
96
D.A. Mitchell et al.
of 1 mm completely disappeared, and the decrease in flake length during the
fermentation was described well by the model. As flake length increased there
was a greater residual length. Particles of initial flake length of 2 mm and above
were degraded to only 50% of this initial length in the 96 h of fermentation. In
this case the model did not describe the degradation curve well. Nandakumar
et al. [128] pointed out that smaller wheat bran particles contain mainly starch,
while larger particles contain significant amounts of hemicellulose and cellulose, which cannot be degraded by B. coagulans.
A more sophisticated model was proposed for growth of biofilms of B. coagulans on reducing particles by Rajagopalan et al. [114], describing many other
phenomena occurring such as oxygen reaction within the biofilm, expansion of
the biofilm during growth, release of enzyme into the substrate, and diffusion
of glucose through the substrate and biofilm. Their model also agreed well with
the data of Nandakumar et al. [128]. They argued that the explanation of different compositions for particles of different sizes is not the only possible
explanation. Instead, they suggested that the limited diffusion of glucoamylase
into a particle, combined with the “clearing effect” noted by Mitchell et al. [84],
could account for the different consumption rates for different particles sizes.
Late in the fermentation, almost all the glucoamylase could be located in
regions cleared of starch, preventing further particle degradation. However,
they did not clearly propose a mechanism by which particle shrinkage was
related to starch utilization.
4.6
Potential to Develop a Microscale Model of Growth
The preceding sections have highlighted the complexity of the microscale
phenomena occurring during SSF, and our current understanding of how these
phenomena can influence the process. Before describing approaches to
modeling bioreactors, it is worthwhile to consider how these microscale phenomena might be handled in bioreactor models. There are basically two approaches – either to use empirical growth equations which ignore microscale
mass transfer, or to attempt to incorporate the microscale mass transfer
processes into the bioreactor model.
Due to the complexity of describing transfer phenomena at both the intraparticle and supraparticle scale, most bioreactor models use empirical equations, such as the logistic equation (Eq. 5), with the specific growth rate being
expressed as an empirical function of temperature. However, if this is done the
parameters of the empirical model must be determined for each small change
in the system. The model may simply fail to describe data under different
operating conditions where the factor limiting growth may be different.
Additionally, the values of the fitted kinetic parameters will have no biological
significance, although it still might be useful to compare values (e.g., of m max or
X max in the logistic equation) for different fermentations.
Combined intraparticle and interparticle diffusion of oxygen has been taken
into account in a model of a tray bioreactor [122]. A “complete” bioreactor
96
D.A. Mitchell et al.