432
Chapter 10
Bubble
break-up
Coalescence
O
o
o
o
Bubble
break-up
Coalescence
O
o
o
o
o
o
° o o o
o
O o
o
o
Figure 10.3 Factors influencing the dynamic bubble-size distribution in a bioreactor.
When the bubbles have been formed at the orifices of the sparger, they circulate in the gas liquid
dispersion until finally leaving the dispersion for the
head space.
The gas liquid dispersion is
normally vigorously agitated, resulting in the formation of a
turbulent flow field,
in which there is a
maximum bubble size
db max
determined by the balance of opposing forces:
1.
Shear forces acting on the bubble tend to distort the bubble into an unstable shape so that
the bubble disintegrates into smaller bubbles.
2.
The surface tension force acting on the bubble tends to stabilize the spherical shape of the
bubble.
3.
In the dispersed phase, there is viscous resistance to deformation o f the bubble.
In gas liquid dispersions, the viscous resistance on the gas side is negligible compared to the surface
tension contribution, and at equilibrium we therefore have:
(
10
.
21
)
where
rs
is the
shear stress,
i.e. force per unit area acting parallel to the surface (N m 2), and
k,
is a
dimensionless constant. If
db > dhmia
the shear force acting on the bubble is larger than the surface
tension forces, and the result is bubble breakup. In order to calculate
dbmax
we need to determine a
value for the shear stress. According to the statistical theory of turbulence, the dynamic shear stress
acting on bubbles with diameter
db
is given by Eq. (10.22) for a turbulent flow field (see Note
10.1):
3
3
d*
(10.22)
is the power dissipation per unit volume (W m‘3), and
k2
is a dimensionless constant In a
low viscosity medium (like water), the dynamic shear stress given by Eq. (10.22) is much larger
than the viscous shear stress. In such a case, a combination of Eqs. (10.21) and (10.22) will give the
following expression for the maximum stable bubble diameter
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