Figure 15.1 First-order death-rate
constant in a small bubble column as a
function of the air-flow rate and
reciprocal column height (Martens et
al. 1992).
killing volume consists of the liquid present in the liquid film of the cap and in a thin
liquid layer surrounding the bubble cavity. This led to the following equation for the
killing volume:
(4)where hf, hc (m) are the thickness of, respectively, the film and cavity layer, Af, Ac (m^2 )
are the surface areas of respectively the bubble cap and bubble cavity and k 1 (–) is a
dimensionless constant. Assuming a spherical bubble and an equal thickness of the
bubble-cap film and the liquid layer around the cavity, this equation was simplified to
(5)where k 2 (m) is a constant. If the film thickness in the bubble cap is different from that in
the bubble cavity, it is necessary to calculate the surfaces of the cap and cavity separately.
Wu and Goosen (1995a) derived equations for this on the basis of spherical bubbles,
which, as they stated, is valid only for bubbles smaller then 2 mm. For bubbles between 2
and 5 mm the calculations are only approximate. Up to a bubble diameter of 3.5 mm they
showed that less than 10% of the surface area belongs to the bubble cap and death is
mainly attributed to the cavity. For bubbles larger than 5 mm a substantial part of the
surface is located in the bubble cap, meaning that this cap becomes more important for
cell death. They showed experimentally that the killing volume is proportional to the
bubble surface area for bubble diameters ranging from 0.5–4.5 mm. This is different from
Multiphase bioreactor design 458