Combining this with equation (31) for the first-order death-rate constant gives
(35)From this equation it is clear that increasing the reactor height decreases the death-rate
constant until a certain plateau value given by the second part of equation (35). The effect
of bubble diameter is difficult to deduce because it affects the following parameters:
The bubble rise velocity. For the creeping-flow regime the bubble rise velocity decreases
with decreasing bubble diameter below diameters of 1 mm, which would also decrease
the death-rate constant if the projected radius is not affected. However, the projected
radius increases making the net effect difficult to predict.
The combination “kh”: This factor in fact represents the amount of cells killed per unit
bubble area. Garcia-Briones and Chalmers (1994) showed that the burst of smaller
bubbles causes higher hydrodynamic forces. Therefore, a decrease in bubble diameter
would be expected to lead to an increase in this factor and in the death-rate constant.
Projected radius. The projected radius is a function of the bubble and cell diameter, the
bubble rise velocity and the required contact time. The relation is shown in Figure 15.4,
where one can see that up to a bubble diameter of 0.2 mm the killing volume decreases
with bubble diameter.
In conclusion, high reactors should be used to minimise cell death. For the bubble size
many of the processes and parameters affecting cell death are not exactly known making
it difficult to predict which bubble diameter should be used.
CONCLUSIONS
Cell death due to sparging occurs at bubble break-up at the surface during retraction of
the bubble film and the subsequent collapse of the bubble cavity. Numerical calculations
modelling collapse of the cavity show that the hydrodynamic forces liberated are
sufficient to kill the cells and increase with decreasing bubble diameter. When
elucidating the exact mechanism of cell death and protection it is important to model the
interaction of these forces with the cells. This might also give more insight into the effect
of bubble diameter on cell death
Cell death during bubble rise is highly unlikely. However, adsorption of cells occurs
during bubble rise, which causes an increase of the number of cells in the danger zone at
bubble break-up and thus an increase in cell death.
Although there is no clear proof of cell death at the sparger, this in principle may
occur due to liquid flows at bubble formation and the contact between a cell and newly
formed bubble surface that contains no surfactants. Modelling the flow patterns and
hydrodynamic forces at the sparger as well as modelling the formation of new bubble
surface in combination with adsorption of cells and surfactants would be of great
importance for understanding events at the sparger.
With respect to the effect of bubble diameter, most observations on cell death show
that the killing volume increases with bubble diameter in the range of 0.5 to 6 mm, which
contradicts with the decrease of hydrodynamic forces for increasing bubble diameters.
For larger bubbles a larger volume of medium and thus more cells are involved in the
Lethal effects of bubbles in animal-cell culture 485