reactor diameter. In Figure 15.1 an example is shown on the relation between the first-
order death-rate constant and the gas-flow rate and reactor height (Martens et al. 1992).
Furthermore, Tramper et al. (1988) showed that the hypothetical killing volume is
proportional to the bubble volume.
Wu and Goosen (1995 a) derived an equation correlating the hypothetical killing
volume of a gas bubble to its surface. They assumed that cell death occurs only at the
medium surface, where bubble escape takes place. Furthermore, they made a distinction
between the part of the bubble that is above the liquid level at burst (the bubble cap) and
the part that is below the surface (the bubble cavity). Next, they proposed that the
Table 15.2 Small-scale bubble-column (BC) and
air-lift (AL) experiments
Reactor Additives Cell F/V s−^1 db mm vd 10 –10m^3 Ref.
BC 0.1%MC10%FBS Sf-21 0.016 3.5 0.4 Tramper 1988
BC 5% FCS Hybridoma 0.001 1.6 0.06 Handa 1987
BC none Sf-21 7.0 Trinh 1994
BC 5%FBS Sf-21 0.005 3.5a 1.9 Wu 1995a
BC 1% FCS Hybridoma 0.028 5 b 4.8 Jobses 1991
BC none Hybridoma 0.020 3.5a 8.6 Pol 1992
BC 5% FCS Hybridoma 0.020 3.5a 1.7 Pol 1990
BC 5% FCS Hybridoma 0.005 1.1 1.7 Orton 1992
AL 5% FCS Vero 0.11 3.5a 0.5 Martens 1992
AL 0.5% FCS Hybridoma 0.028 3.5° 2.1 Martens 1996
BC 0.1% Pluronic F68 Sf-21 0.20 5 c 1.4 Cherry 1992
aValue for the bubble diameter not given and arbitrary set at 3.5 mm.
bAverage bubble diameter.
cSmallest measured bubble diameter.
Lethal effects of bubbles in animal-cell culture 457