and three times (Karamanev et al., 1992). The effect of the Ad/Ar ratio was also studied
and a maximum kLa was obtained for a ratio value of three.
The assessment of kLa in different zones of a bioreactor is also important, as it may
give insight into the limitations that a given reactor design might have. During the
fermentation of a flocculating S. cerevisiae strain in a 5.4 L concentric tube airlift
bioreactor with an aeration rate of 0.1 v.v.m., the value of kLa was significantly higher in
the downcomer zone (0.12 min−^1 ), when compared with the riser (0.1 min−^1 ) and the gas-
liquid separator (0.085 min−^1 ) (Sousa et al., 1994b). Lübbert et al. (1988) suggest that the
enhanced mass transfer in the downcomer is a consequence of the bigger difference
between the gas and the liquid phase velocities in this zone, which means that a longer
period of time is available for the bubbles to transfer oxygen into the liquid phase.
Mass Transfer of Solutes in the FlocsDiffusion is probably the most important mechanism of solute transport through cell
aggregates and it is generally described using a single parameter, the effective diffusivity
(De) which relates the gradient of the characteristic concentration (c(r,t)) along the
coordinate r at time t to the average diffusive solute flux (JD) across the volume of the
object in study, which is expressed by Fick’s law:
(2)There are two distinct approaches for the calculation of effective diffusion coefficients,
which are widely employed. In the first one, the effective diffusivity in the aggregates can
be determined analysing the data by means of a reaction-diffusion model, knowing the
consumption rate of the solute of interest and either the size of the aggregate or the
solute’s concentration profile in it; in the second, the assessment is made in steady state
using Equation 2 in the absence of reaction. The techniques used in both approaches have
advantages but also some limitations (Libicki et al., 1988; Tanaka, et al., 1984). In the
first case, it is not necessary to destroy the flocs but some assumptions about the solutes
consumption or production must be made, which can affect significantly the obtained
results. In the second case, as no reaction is taking place, there is no need for assumptions
about the kinetics of the solute consumption or production but, on the other hand, cell
aggregates must usually be formed artificially or confined within a matrix (both
procedures are likely to affect the results) and it is difficult to ensure that the solute does
not react during the course of the experimental run. The option for either approach
depends, therefore, on the system in question and on the experimental methods available.
In general, the diffusion coefficient of a component in a solvent is taken as a function
of parameters such as temperature (Onuma et al., 1985), pressure (in gaseous systems)
and medium composition (Kurillová et al., 1992). Very little work has been done in this
area with flocs (Ananta et al., 1995, Sousa and Teixeira, 1991; Teixeira and Mota, 1990)
and the existing data on the diffusivity of glucose and oxygen do not usually refer to the
case of cell aggregates (biofilms not included) (Libicki et al., 1988). A very simple, yet
valid, reason for this situation, already pointed out before, is their very fragile nature: in
fact, flocs are very difficult to handle, as they are easily destroyed; further, this problem
becomes more acute with the size increase, namely when dealing with diameters between
Flocculation bioreactors 399