Page 339 - Fundamentals of Water Treatment Unit Processes : Physical, Chemical, and Biological

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

To filters

+

58.8 m Inlet channel Grit basin Sed. basin #3: 13,251 m 3 Sed. basin #2: 6,436 m 3 Sed. basin #1: 3,218 m 3 + Four flocculation tanks, each 13.4 m dia. 7.0 m depth

+

+

Raw 0.91mpipe
water
Alum injection
15.5m 68.9m
FIGURE 11.1 Schematic of filtration plant at Sacramento, California, showing paddle-wheel flocculation basins and sedimentation basin
3
(Langelier, 1921). Q(design) ¼ 2.2 m =s (50 mgd); q(flocculation basins) 30 min; q(sedimentation basins) 63 h.

11.3.1.4 Flocculation Practice, c. 1940 11.3.2.2 Smoluchowski’s Collision Equations
Table 11.1 gives data from Camp (1955) for 14 flocculation The equations of Smoluchowski are referenced frequently in
basins, c. 1940. He computed tip velocity, v; detention time, the literature as the starting point for discussion of kinetic
u; headloss, h L , for baffled systems (or power consumed, P=Q, theory of particle collisions. The Smoluchowski equation on
for paddle-wheel basins); power per unit volume, P=V; G; and orthokinetic motion was referenced by Harris et al. (1966,
Gu. Of the 14 plants, most had end-around baffles; only four p. 96) who credited its introduction into water treatment theory
were paddle-wheel basins. The baffled basins were not satis- to Camp and Stein (1943, Equation 23). They derived the
factory according to Camp (1955, p. 5) because the gradients equation from fundamentals, however, and did not cite Smo-
were excessive at the bends and deficient in the straight luchowski, i.e., probably they were not aware of his papers.
portions. Camp’s 1955 paper was the basis for rational design The enumeration of Smoluchowski’s equations here is from
of floc basins, adopted widely in practice. Argaman and Kaufman (1968, p. 5), which were described
previously in Section 10.2.3.1; the numbering is retained.

11.3.2 EVOLUTION OF THEORY
11.3.2.2.1 Perikinetic Motion
Three ‘‘milestones’’ in flocculation theory were (1) the equations
of Smoluchowski for ‘‘perikinetic’’ and ‘‘orthokinetic,’’ fluid The first equation of Smoluchowski (1916) was for the condition
motion in 1916 and 1918, respectively; (2) the observations of that collisions were due to Brownian motion (called ‘‘periki-
Langelier, c. 1919, on the effect of slow stirring on the formation netic’’ motion) calculated as the diffusion flux of particles in
of settleable floc; and (3) the work of Camp in formulating the the radial direction around a single stationary particle:
basis for the theory and practice in 1943 (Camp and Stein, 1943)
3
and in 1955 (Camp, 1955), respectively. N(diffusion) ij ¼ 4pD ij (r i þ r j ) n i n j (10:1)
11.3.2.1 Langelier where
As applied to water treatment practice, Langelier’s floccula- N(diffusion) ij is the number of contacts per unit time per
tion experiments as related to the Sacramento plant, c. 1919, unit volume between i and j particles due to diffusion
3
was the basis for an initial descriptive theory. Langelier flux (collisions=m =s)
2
recognized the role of stirring in causing the growth of floc D ij is the combined diffusion coefficient, D i þ D j (m =s)
particles and used his jar-test apparatus as the means for r i is the radius of particle i (m)
investigating the effects of other independent variables. r j is the radius of particle j (m)
3
Colloid chemistry entered the picture, c. 1941, through an n i is the number concentration of particles of radius r i (#=m )
MS thesis by H. Ludwig (Ludwig, 1942) under Langelier; n j is the number concentration of particles of radius
3
the basis was Professor Hans Jenny’s course on the topic. r j (#=m )