PVA 0.1 47 65 2 1.24 Michaels 1995b
0.1 48.7 71.5 Chattopadhyay
1995bPVP 0.1 53 61.1 41600 0.25 Michaels 1995b
PEG 8000 0.1 52 62.3 77 <0.1 Michaels 1995b
PEG 4000 0.1 45.9 65.7 Chattopadhyay
1995b
sparger zone, the zone of bubble rise, the zone of bubble escape and the foam layer. The
section on the mechanism of bubble-related cell death ends with a discussion on whether
bubble break-up and coalescence may contribute to cell death and a summary of the
protection mechanism of different additives. Finally, the chapter ends with a discussion
on the possibility of reducing bubble-related cell death through proper reactor design.
OVERALL THEORIES
Damaging effects of sparging were reported as early as 1965 (Telling and Elsworth
1965). Since then numerous studies have been devoted to the relation between air bubbles
and cell death. Tramper et al. (1988) were the first to describe the amount of cell death
due to sparging as a function of design parameters in their hypothetical-killing-volume
theory. The main hypothesis of the theory is that a hypothelial volume, Vd (m^3 ),
associated with each air bubble during its life time exists, in which all viable cells are
killed. A balance over the viable cells in the reactor assuming cell growth is negligible
gives
(1)
where V(m^3 ) is the reactor volume, Cv (cells.m−^3 ) is the concentration of viable cells, t (s)
is the time, (s−^1 ) is the number of bubbles generated per second, F (m^3 .s−^1 ) is the gas-
flow rate, and db (m) is the bubble diameter.
Assuming next that the hypothetical killing volume, the gas-flow rate, reactor volume,
and bubble diameter are time independent, equation (1) can be written as
(2)
where kd (s−^1 ) is the first-order death-rate constant given by
(3)where T (m) is the reactor diameter and H (m) the reactor height. The model has been
verified at lab scale by different authors. Table 15.2 summarises this work. Thus, it was
shown that the killing volume is independent from the gas-flow rate, reactor height, and
Multiphase bioreactor design 456