exponentially when the bubble diameter increases from 0.77 to 6.3 mm. This is in
accordance with the finding of Handa et al. (1985) that smaller bubbles are more
detrimental than larger bubbles. Table 15.6 shows maximum values for the flow
parameters proposed by Garcia-Briones and Chalmers (1994) for different bubble sizes.
Table 15.6 Flow parameters for three different
bubble sizes, (adapted from Garcia-Briones and
Chalmers 1994)
Bubble diameter
(m)
State of stress
(N.m−^2 )RD Time at maximum state of
stress (s)Total break-up
time (s)0.77 10−^3 479.7 0.02 0.43 10−^3 0.55 103
1.70 10−^3 199.8 0.02 1.4 10–3 2.0 10−^3
6.32 10−^3 17.5 0.01 5.6 10−^3 10 10–3
Comparing these values to the values known to damage cells as given in Table 15.3, they
concluded that cells would be destroyed in a fraction of a second. Dey et al. (1997)
experimentally studied and numerically calculated the effect of additives on the bubble
burst process. The severity of the rupture process was assessed by measuring the Height
of the Axis Node (HAN=depth of the cavity/initial bubble radius) as a function of time.
Addition of surfactants resulted in a slower, less high jet with a wider base and narrower
tip as opposed to the situation without surfactants, where a long, slender jet was formed.
In addition, in the absence of surfactants four to five droplets were formed, whereas in
the presence of 0.1% Pluronic only one droplet was formed and no droplets were formed
at all when 5% serum was added. Thus, the presence of Pluronic clearly decreases the
severity of the bubble burst, which may at least in part be the mechanism by which
Pluronic offers protection. From the numerical simulation of the rupture process the most
important parameter influencing this process was the surface dilatational viscosity.
However, in order to obtain good agreement with the experimental data, the value of this
parameter had to be made an order of magnitude higher than the experimentally
determined value. It is stated that this may be due to the fact that the experimental
method used to measure the surface dilatational viscosity may not give the correct value.
Trinh et al. (1994) tried to quantify the number of insect cells killed per bubble rupture
as well as the location of cell death. From sparging experiments they found that at a cell
concentration of about 2 10^6 cells per ml about 1150 insect cells were killed per burst of a
3.5 mm bubble, which corresponds to a killing volume of 6 10−^10 m^3. Comparing this to
other literature data, only van der Pol et al. (1992) present data obtained in a serum-free
medium. From their data, assuming a bubble diameter of 3.5 mm, a hypothetical killing
volume of 8.6 10^10 m^3 can be calculated. At a cell concentration of 2 10^6 cells per ml this
means that about 1700 cells would be killed per bubble. Although of the same order of
magnitude, these numbers are higher than those found by Trinh et al. (1994), which may
be caused by the difference in cell types. Trinh et al. (1994) used insect cells, whereas
van der Pol et al. (1992) used hybridoma cells. Trinh et al. (1994) also collected the
liquid from the upward jet and found that in the absence of Pluronic about 1400 cells
were present in this jet. Compared to the bulk liquid the viability in the jet was reduced
Lethal effects of bubbles in animal-cell culture 477