Biomedical Engineering Reference
In-Depth Information
stirred tank operates at turbulent conditions, the input power only would depend on the
agitation rate.
Substitution of the above in equation (3) leads to the following expression:
1
⎛
μ
·
·
N
3
·
d
5
·
N
⎞
2
⎜
i
p
⎟
τ
=
(7)
V
⎝
⎠
Bubble column and airlift bioreactors are also reactors widely used for the biological
treatment of wastewaters because of their high mass transfer rates and simplicity of design. In
systems where hydraulic stress is generated by gas, the power input per unit volume of liquid
is related with the superficial gas velocity u
g
(m/s), as follows (Sánchez Pérez et al., 2006):
P
⎛
⎞
=
g
·ρ
·
u
⎝
⎠
(8)
g
V
Then the combination of equations (5) and (8) gives the shear stress as a function of the
superficial gas velocity for no-Newtonian fluids:
(
(
)
)
( )
n
n
τ
=
K
·
g
·
ρ
·
u
n
+
1
(9)
g
In packed bed reactors where hydraulic stress is caused by the liquid flow rate, the shear
stress can be calculated according to the following equation (Rittmann and McCarty, 2001):
C
·
μ
·
u
·(
1
−
ε
)
2
τ
=
1
l
(10)
d
2
·
ε
3
·
a
p
where C
1
is an empirical coefficient, u
l
is the superficial liquid velocity (m/s), ε is the porosity
of the bed, d
p
is the equivalent diameter of the carrier (m) and a is the specific surface of the
biofilm carrier (1/m).
Iaconi et al. (2005) also developed a simple methodology to calculate hydrodynamic
shear forces in a fixed bed system with granular biomass. According to such a procedure, the
shear stress was calculated by equation (11):
2
C
·
μ
·
u
·(
1
−
ε
)
C
·
ρ
·
u
τ
=
2
l
+
3
l
(11)
2
2
d
·
ε
ε
p
where C
2
and C
3
are empirical coefficients.
Correlations given in literature for the prediction of mass transfer coefficients are
generally expressed as a function of the power input of the impeller and the superficial gas
and/or liquid velocities and can be related to shear stress by equations (7), (9), (10) and (11).
Several correlations are available for the calculation of the gas-liquid mass transfer
