Page 343 - Fundamentals of Water Treatment Unit Processes : Physical, Chemical, and Biological

298 Fundamentals of Water Treatment Unit Processes: Physical, Chemical, and Biological

10 –1
10 –2
10 –3
10 –4
10 –5
10 –6 k S
k ij (cm 3 ) 10 –7 k SH
–8
10
10 –9
10 –10 k B
10 –11
10 –12
10 –13
10 –14
10 –15
10 –2 10 –1 10 0 10 1 10 2 10 3
(a) Particle size (μm)
10
10 –1
10 –2
10 –3
k SH
10 –4
–5
k ij (cm 3 /s) 10 –6 k S
10
–7
10
10 –8
10 –9
k B
10 –10
10 –11
10 –12
10 –2 10 –1 10 0 10 1 10 2 10 3
(b) Particle size (μm)

FIGURE 11.3 Effect of target particle size on collision rate constants for conditions indicated. (a) Settling basins. (b) Flocculation basins.
(Adapted from O’Melia, C.R., Coagulation in wastewater treatment, in: Ives, K.J. (Ed.), The Scientific Basis of Flocculation, Sijthoff &
Noordhoff International Publishers, Alphen aan den Rijn, the Netherlands, p. 228, 1978.)
g is the acceleration of gravity ¼ 9.806650 m=s 2
SG p is the specific gravity of solid particles (dimensionless) Conditions
n is the kinematic viscosity of water at temperature, Parameter Settling Tank Flocculation Tank
2
T (m =s)
Tank Settling Flocculation
Reference O’Melia (1978, p. 228)
Figure 11.3a and b shows how the three rate coefficients,
Figure 11.3a 11.3b
i.e., k B (i, j), k SH (i, j), k S (i, j) vary with particle diameter for
d i (mm) 1 10
the conditions of a settling tank and a flocculation basin, 2 2 2 3
d j (mm) 10 –10 10 –10
respectively. As seen in Figure 11.3a, Brownian motion is
T (8C) 5 20
dominant for d(particle) < 10 mm but for d(particle) > 10 mm,
SG 1.02 1.02
settling becomes dominant. For a flocculation basin, Figure
1
G (s ) 0.1 10
11.3b shows that shear is dominant for all particle sizes, but
settling is equally important for d(particle) > 100 mm. Also, Subscript Motion Equation Reference
as noted in Section 10.3.1.2, e.g., Figure 10.11, for ‘‘mixing’’ B Brownian motion 11.4
and reaffirmed for flocculation, shear is effective in causing SH Fluid shear 11.5
collisions only for eddies that are about the same size as the S Settling 11.6
particles (Casson and Lawler, 1990).