(9)
This equation equals equation (3) for the hypothetical-killing-volume theory, with the
killing volume being proportional to the bubble surface (Vd=(k 2 /K)db^2 s). Thus the main
difference with the model of Tramper et al. (1988) is that the model of Wang et al.
(1994) is proportional to the square of the bubble diameter instead of to the third power.
MECHANISM OF CELL DEATH AND LOCATION OF THE KILLING
VOLUME
The hypothetical-killing-volume theory of Tramper et al. (1988) does in fact not specify
where the hypothetical killing volume is located. Although Wang et al. (1994) and Wu
and Goosen (1995 a) suggested that the volume is located in a thin liquid layer around the
bubble, experimentally a correlation is shown to exist only between their killing volume
and the bubble diameter. A number of studies have been conducted to reveal the
mechanism of cell damage and thereby the location of the killing volume. In the
following section, first the mechanical properties of cells and the interaction of cells with
air bubbles will be discussed. Next, possible mechanisms of cell death are reviewed for
different zones in a bioreactor; the sparger zone, the zone of bubble rise, the zone of
bubble escape and the foam layer. Finally, it is discussed whether bubble break-up and
coalescence may contribute to cell death and a summary on the protection mechanism of
different additives is given.
Mechanical Properties of Animal CellsIn order to study the fragility of cells a number of authors have used simple shear devices
like viscometers and capillary tubes. Table 15.4 gives an overview of the different
methods used and the sensitivity of the cells. Abu-Reesh and Kargi (1989) exposed
hybridoma cells for 30–180 minutes and found that cell damage in the turbulent-flow
regime is more damaging than comparable shear stresses in the laminar-flow regime. To
cause 50% loss of viable cells after one hour of shear, a shear level of about 30 N.m−^2
was required for turbulent stress, while for laminar stress a level of 55 N.m−^2 was
required. McQueen and Bailey (1989) used hybridoma cells in a capillary system,
wherein the flow was turbulent, and found a threshold wall shear stress of 180 N.m^2
below which no cell damage occurred. Tramper et al. (1986) found significant cell death
in a viscometer after 3 hours at 1 N.m^2 in the presence of 0.1% methylcellulose
(Methocel). After one hour only a small effect could be seen at 55 N.m^2. For exposure
times of 10 minutes Petersen et al. (1990) found already cell death at 1 N.m−^2. They
observed that the shear sensitivity of cells in a batch culture is dependent on the phase of
the culture and that this is not a consequence of changes in growth rate (Petersen et al.
1988, 1990). Michaels et al. (1991b) studied cells in viscometers in the presence of shear
protecting agents. They
Lethal effects of bubbles in animal-cell culture 461