Parameter Tramper et al. (1988) Wu and Goosen (1995a)
Vd0(m^3 ) −5 (−176+166) 10−^13 −1 (−360+358) 10−^13
k 0.001 (−0.005+0.008) 0.0001 (−0.0005+0.0008)
p 3.0 (2.0 4.1) 2.4 (1.4 3.3)
r^2 0.988 0.995
F-value 257 302
Data points 9 6
for the two data sets. The difference between the power coefficients is not significant and
the values of 2 and 3 fall within the 95% confidence intervals for both sets.
Consequently, on the basis of these data sets it is not possible to determine whether the
killing volume is proportional to the bubble surface or bubble volume. The killing
volumes of Wu and Goosen (1995a) are higher than those of Tramper et al. (1988) due to
the fact that Tramper et al. (1988) used 10% FCS and 0.1% methyl-cellulose, while Wu
and Goosen (1995a) only used 5% FBS. The data of Orton (1992) (taken from Meier et
al. 1999) follow the curve of the data of Wu and Goosen (1995a) quite well, except for
the last two points. In contrast to the above studies, which all showed that larger bubbles
are more detrimental in the range of 0.5–5 mm, Handa et al. (1985) found that smaller
bubbles (1 mm) were more damaging than larger bubbles (1.6 mm) on a per bubble basis.
This difference may originate from the differences in experimental set-up. Handa et al.
(1985) quantified cell damage from the maximum attained cell density in bubble columns
operated in batch mode during three to four days at moderate sparging rates (10−^4 –10−^3
vvm). The other authors studied the decrease in viable cells in small bubble columns for
three to six hours at intense sparging conditions (5 10−^3 –10−^2 vvm).
Wang et al. (1994) presented a theory that is comparable in approach to the
hypothetical-killing-volume theory. They defined an inactivation zone, χ (m^3 .m−^3 ),
around each bubble with a thickness s (m). Cells in this zone have a probability q of
being inactivated. This resulted in the next Michaelis-Menten-like expression describing
cell death:
(7)
where k 2 (cells.m−^3 .s−^1 ) is the maximum inactivation rate reflecting the probability of a
cell in the inactivation zone becoming inactivated, K (cells.m−^3 ) is the saturation constant
expressing more or less the affinity for cells to be in the inactivation zone, and a is the
specific surface area (m−^1 ). When the unoccupied inactivation volume is much larger then
that occupied by cells equation (7) can be simplified to
(8)
For the case of a bubble column without coalescence and bubble break-up the specific
surface area can be substituted giving
Multiphase bioreactor design 460