Page 217 - Fundamentals of Water Treatment Unit Processes : Physical, Chemical, and Biological

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

The transport may be by turbulence, diffusion, interception, spacing to give a uniform blanket of rising bubbles increasing
sedimentation, etc. The most likely transport mechanism is the probability of particle–bubble contacts, i.e., by ‘‘intercep-
probably interception as the bubbles rise, aided by turbulence. tion’’ (a component of the transport function). In forming
After contact, the bubble may ‘‘attach’’ to a solid particle, larger bubbles, the repulsive energy must be overcome, e.g.,
usually a ‘‘floc.’’ The ‘‘floc’’ is a particle created by coagula- by turbulence.
tion (Chapter 9) and flocculation (Chapter 11), which precede
the ‘‘contact zone.’’ Since the bubbles are negatively charged, 8.3.3.3 Parameter Values
the floc particle must be positively charged. Their size is Table 8.1 gives size ranges for bubbles and particles, concen-
controlled by coagulant dose, flocculation intensity, and trations of bubbles and particles, and other values. The par-
detention time with a goal of 10–30 mm, but not larger than ticle diameter, d p , and particle density, N p , are controlled for a
50 mm (Edzwald, 1995, p. 20). As indicated, the floc particle given water by the coagulant concentration, polymer usage,
is not large relative to the bubble. and flocculation turbulence intensity. As noted, the bubble
Figure 8.9b illustrates the mechanism of entrapment, diameter, d b , is dependent upon the saturator pressure. The
which is more likely if the floc particles are larger in size, bubble number concentration, N b , is dependent upon the
i.e., d p > 100 mm. Of the two bubble–particle interactions, the ‘‘released’’ (or ‘‘excess’’) dissolved gas concentration, i.e.,
first is felt to predominate in water treatment. that available to form bubbles.
8.3.3.2 Bubble–Particle Contact
The rate of particle–bubble adhesions is proportional to the 8.3.4 SEPARATION ZONE
respective concentrations of bubbles and particles, and other The particles rise in the ‘‘separation zone,’’ i.e., as illustrated
factors, as described in Equation 8.9 (Edzwald, 1995, p. 9): in Figure 8.8. The ‘‘overflow velocity,’’ v o (Section 6.3.1.2), is
the basis for determining the plan area, i.e., v o ¼ (Q þ R)=A
dN p
¼ a pb h A b v b N b N p (8:9) (plan). In principle, the value of v o is based upon a character-
T
dt
istic rise velocity of the particle–bubble agglomerate.
in which
3
N p is the particle number concentration (# particles=m ) 8.3.4.1 Rise Velocity of Bubbles
N b is the bubble concentration in contact zone For reference, the rise velocity of a bubble may be calculated
3
(# particles=m ) by Stoke’s law, Equation 6.8, applied to a bubble, i.e.,
t is the elapsed time (s)
a pb is the adhesion efficiency, i.e., ratio of particle–bubble gd (r r )
2
b w b
adhesions to particle–bubble contacts (dimensionless) v b ¼ 18m (8:10)
h T is the transport function is the ratio of the number of
particle–bubble contacts to the number of bubbles being in which
transported to the vicinity of a given particle (dimen- d b is the diameter of bubble (m)
sionless) v b is the rise velocity of bubble (m=s)
2
3
A b is the projected area of bubble (m ) r w is the density of water (998.2063 kg=m at 208C, Table
v b is the rise velocity of bubble relative to water as calcu- B.9)
lated by Stoke’s law (m=s) r b is the density of air bubble (1.2038 kg=m at 1.00 atm
3
pressure and 208C)
2
As stated in a previous paragraph, the transport function, g is the acceleration of gravity (9.8066 m=s )
h T ,is influenced mostly by turbulent diffusion and intercep- m is the viscosity of water at stated water temperature
tion; sedimentation and molecular diffusion have smaller (1.002 10 3 NS=m at 208C)
2
effects. All have been evaluated quantitatively by theoretical
equations (see Edzwald, 1995, p. 9). 8.3.4.2 Rise Velocity of Particle–Bubble
On adhesion efficiency, a pb decreases as the bubbles
The buoyant force on a particle–bubble agglomerate equals
attach, taking up more area. Concerning attachment, floc
the weight of the volume of water displaced, i.e., Archimedes
particles are a matrix of positively charged coagulant hydrox-
principle (Section 6.2.2). The associated rise velocity may be
ides and negatively charged suspended solids (Fukushi et al.,
calculated by Stoke’s law (Section 6.2.2), derived in the steps
1998, p. 80). A bubble, which is negatively charged ( 100
outlined (Edzwald, 1995, p. 13) as follows:
zeta-potential for oxygen and 150 mV for precipitated air
bubbles at pH 7), must attach at a positively charged site.
1. Determine the density for a particle–bubble agglom-
Values of a pb were estimated at 0.35 for 2.5 mg=L alum and
erate:
a pb ¼ 0.40 for 5.0 mg=L alum (Fukushi et al., 1998). The
particle–bubble attachment can be increased further by adding h 3 3 i
polymers (de Rijk et al., 1994, p. 467). r d þ B r d
b b
p p
r h i (8:11)
Another result of the negative charges on the bubbles is pb ¼ 3 3
d þ Bd
that they repel one another. Thus, the bubbles maintain their p b