Figure 15.3 Schematic drawing of the
projected radius for a rising bubble
(Adapted from Meier et al. (1999).
where τ(s) is the minimal contact time required for attachment of a cell to a bubble, Rb
(m) is the bubble radius, Rc (m) is the cell radius, and v∞ (m·s−^1 ) is the terminal rising
velocity. In the creeping-flow regime, the Reynolds number for flow around the bubble is
less than 1. For potential flow the Reynolds number is typically larger than 1000. In the
absence of surfactants potential flow occurs at bubble diameters of 0.7 mm and higher.
However, in the presence of surfactants the bubble surface becomes more rigid and also
the larger bubbles fall within the creeping-flow regime. Michaels et al. (1995a)
experimentally determined the required contact time needed for attachment of a cell to a
bubble in the presence of protective compounds. Figure 15.4 shows the effect of reactor
height and bubble diameter on the rise-dependent killing volume for a situation without
Multiphase bioreactor design 470