Page 349 - Fundamentals of Water Treatment Unit Processes : Physical, Chemical, and Biological

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

pp. 252, 255). Note that the SI system favors joules over the tensile force induced, i.e., the strand is not broken. The
calories, but the ‘‘kcal’’ is common in the literature prior maximum size stable floc is that size where the tensile
to about 1980. strength of the filament stands equals the eddy-induced tensile
stress (Parker et al., 1972, p. 89).
Figure 11.9a shows empirical data that relates average floc
11.4.2.2 Floc Breakup size to velocity gradient for both alum and ferric floc. The
The net effect of the flocculation process is the aggregation sizes are compared with Kolmogorov’s microscale; the latter
rate minus breakup rate (Parker et al., 1972, p. 79). Two kinds is generally smaller than the floc sizes, except as G increases.
of breakup are (1) surface erosion of primary particles and (2) By comparison, floc sizes are smaller in the study summarized
deformation and floc fragmentation (Parker et al., 1972, p. 81; in Figure 11.4 by Spicer and Pratsinis (1996a, p. 1051).
Gregory, 1989, p. 221). Surface shearing of primary particles Figure 11.9b shows the maximum length of activated sludge
is a function of the scale of turbulence (Parker et al., 1972, floc observed for different velocity gradients for three acti-
p. 82). Eddies that are sufficiently large to fully entrain the vated sludges, one with sludge age markedly less than the
floc produce zero relative velocity and no surface shear. other two. As seen, the biological floc size is generally larger
Eddies much smaller than the floc result in little surface than the chemical floc.
shear. Eddies of a scale approximating the floc diameter In general, and as seen in Figure 11.9, the relationship
would impart the maximum relative velocity and maximum between d(floc) and G plotted on a log–log scale is linear
surface shear (see Figure 10.11). Therefore, there will be a (François, 1987b, p. 1024), i.e.,
maximum stable floc size in which the maximum stress
imposed upon the floc will just equal the surface shear g
d(floc) ¼ KG (11:12)
strength (Parker et al., 1972, pp. 82, 85). A force balance on
a floc particle equates viscous drag and acceleration relative to
the fluid with buoyancy and gravity. where
In Figure 11.8a, the structural backbone is the filamentous d(floc) is the floc diameter (m)
network. Such filaments rupture by tensile failure. The K is the empirical constant
essence of this structure represented in Figure 11.8b shows g is the empirical exponent
two spherical clusters connected by a strand of filaments.
For the floc to rupture, two eddies must act on the floc A theoretical analysis by some investigators have
entraining each end and causing stress in opposite directions shown that g ¼ 2 for the inertial range of turbulence and
on the clusters, thereby causing tensile stress on the filament- g ¼ 1 for the viscous range (François, 1987b, p. 1024).
ous strand (Parker et al., 1972, p. 89). If the floc is ‘‘stable,’’ Flocs with dimensions of the order of magnitude of the
the tensile strength of the filamentous strands is greater than turbulence scale for inertial advection will be ruptured into
large fragments. Those subjected to viscous forces will be
ruptured by erosion of small particles from the floc surface
(François, 1987b, p. 1029). The empirical coefficient, g,isan
index of floc strength against hydraulic shear. Some values
from different experimenters are seen in Table 11.4 for
different G values and for different coagulants and chemical
conditions.

11.4.2.3 Bioflocculation
The aggregation of microbes is called ‘‘bioflocculation.’’ Such
(a) aggregation, in the form of settleable flocs, is an essential part
of the activated sludge process.
The ‘‘glue’’ that binds the bacteria cells to form an aggre-
d(floc) d(floc) gate is thought to be exocellular biopolymers produced by
the bacteria. They can be attached to the cell as a capsule or
excreted into the surrounding medium as a slime (Higgins and
Novak, 1997, p. 479). Exocellular polysaccharides have been
l(floc)
thought to play the major role in flocculation but Higgins and
(b)
Novak (1997, p. 479) have indicated that exocellular proteins,
FIGURE 11.8 Depictions of activated sludge floc with filaments. i.e., lectin in particular, may have an important role as well,
(a) Characterization of actual floc. (b) Structural characterization of with divalent cations being necessary to provide bridging
floc. (Adapted from Gorczyca, B. and Gahczarczyk, J., The AWWA between negatively charged sites within the biopolymer.
Annual Conference, Vancouver, BC, p. 5, 1992.) The model they proposed is illustrated in Figure 11.10; it