Biology Reference
In-Depth Information
For a pulse injection,
Η
can be quantified by replacing the relative breakthrough concentration in
equation (1.6)
with relative mass breakthrough (
/
) (Abudalo et al., 2005, Kretzschzmar
M
M
eff
inf
et al., 1997) where
and
are the total number of cells in the effluent and influent,
M
M
eff
inf
respectively.
The sticking efficiency is then obtained by
Η
(1.7)
Α
=
Η
0
Tufenkji and Elimelech (2004a) developed a correlation equation to predict the single collector
efficiency by summing the individual transport mechanisms to a collector surface as
(1.8)
Η
=
Η
+
Η
+
Η
0
D
I
G
where
Η
(-)
,
Η
(-) and
Η
(-)
are theoretical values for the SCCE when the sole transport
mechanisms are diffusion, interception and sedimentation, respectively, and defined as
Η
=
2.4
A
1/3
N
−
0.081
N
−
0.715
N
0.052
(1.9a)
S
R
Pe
vdW
D
Η =
0.55
A N
1.675
N
0.125
(1.9b)
R
A
I
S
−
0.24
1.11
0.053
Η
=
0.22
N
N
N
(1.9c)
R
G
vdW
G
where
A
(-) in
equations (1.9a)
and (
1.9b
)
is a porosity dependent parameter defined as
5
5
6
1/3
d
A
=
2(1
−
Γ
)
/
(2
−
3
Γ
+
3
Γ
−
2
Γ
)
and
Γ
=
(1
−
Θ
)
,
N
=
d
/
d
interception number (-),
is the
p
c
p
R
mean particle diameter (m).
Ρ Ρ− / 9 Π is for sedimentation where
g
is the
acceleration due to gravity (m/s
2
),
Ρ
is the particle density (kg/m
3
) Ρ is the fluid density
(kg/m
3
), Π is the absolute fluid viscosity (Pa.s) and
U
is the fluid approach velocity (m/s). The
Peclet number (-),
=
2
d
(
)
g
N
2
G
p
P
f
v
Θ
/
D
for the sum of convection and diffusion. The van der Waals
number expresses the ratio of van der Waals interaction energy to the particle's thermal energy
=
N
Pe
C
ΠΠ Θ gives
the attraction number (-) and expresses the combined influence of van der Waals attraction forces
and fluid velocity on particle deposition rate due to interception. The description of the
methodology for obtaining the correlation equation for each transport mechanism can be found
in Tufenkji and Elimelech (2004a).
=
H
/
kT
where
H
is the Hamaker constant (J). The expression
=
H
/
12
d v
N
N
2
vdW
A
1.3. Deviation of bacteria transport from the colloid filtration theory
The classical colloid filtration theory is based on the assumption that the attachment of
biocolloids to collector surfaces in saturated porous media is invariable and results in a log-linear
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