Page 297 - Fundamentals of Water Treatment Unit Processes : Physical, Chemical, and Biological

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

C o

C

• Alum hydrolysis products
• Dissolved oxygen ΔC
• Organic carbon j= • Activated carbon
δ
• Chlorine, ozone, etc. • Ion-exchanger
δ
• Ions • Microorganism
• Viruses • Virus
• Bacteria • Gas–liquid interface
(a) (b) (c)

FIGURE 10.12 Reactions requiring diffusion, facilitated by turbulence. (a) Diffusing substance. (b) Diffusion to surface. (c) Surface
material.

terms, and the kinds of ‘‘sinks’’ that take up molecules where
or particles that diffuse. As seen in Figure 10.12a, diffus- J pk is the rate of change of total particles in suspension by
3
ing substances include aluminum hydrolysis products, dis- perikinetic transport (particles=m =s)
solved oxygen, organic carbon, a disinfectant (such as N is the total concentration of particles in suspension at
3
chlorine or ozone), ions, etc. The reacting sites, or time, t (particles=m )
‘‘sinks,’’ include discrete particulate surfaces such as acti- t is the elapsed time since initial measurement of N (s)
vated carbon, an ion-exchanger (resin or green sand), a a is the collision efficiency factor (fraction of collisions
microorganism, a virus, a gas–liquid interface, etc. As in producing aggregates=collision)
Figure 10.12b, the flux density, j, to a sink is governed by k is the Boltzman’s constant (10 23 J=K)
Fick’s first law, i.e., j ¼rDC), where r is the operator for the T is the absolute temperature of suspension (K)
total differential, D is the diffusion constant, and C is the m is the dynamic viscosity of the water suspension (Pa s
2
solution concentration at a given point in space, and is or N s=m )
approximated as, j ¼ D(C o C)=d, with terms illustrated in
Figure 10.12b. 10.3.1.3.2 Orthokinetic Transport
The role of turbulence is threefold: (1) to reduce the
The frequency of particle contacts caused by turbulence
film thickness, d; (2) to maintain the concentration at near
(orthokinetic transport) was given also by O’Melia (1970) as
the level of the bulk of solution, C o ; and (3) to increase
the total surface area across which diffusion may occur, i.e.,
3
dN 2aGd N 2
SA i , which is relevant where creation of an interface is
J ok ¼ ¼ (10:18)
involved (such as causing smaller bubbles in gas transfer). dt 3
With respect to the (1) and (2), reducing d and maintaining C o
increases the concentration gradient, which, of course, where
increases j. J ok is the rate of change of total particles in suspension by
3
orthokinetic transport (particles=m =s)
d is the diameter of colloidal particles (m)
10.3.1.3 Transport Regime
The parameters that define the relative roles of turbulence- 10.3.1.3.3 Ratio of Turbulent Transport
transport and diffusion transport are delineated here. From to Diffusion Transport
this, we can see the approximate ranges of G and particle
The ratio of contact rate by turbulence (orthokinetic transport)
sizes that define each respective regime, i.e., turbulence and
to such rate by diffusion (perikinetic transport), J ok =J pk , is,
diffusion.
dividing Equation 10.18 by Equation 10.17,
10.3.1.3.1 Perikinetic Transport 3
J ok mGd
The frequency of particle contacts caused by diffusion (peri- ¼ 2kT (10:19)
J pk
kinetic transport) was given by O’Melia (1970) as
Figure 10.13 was plotted from Equation 10.19, and
dN 4akT 2 shows how the ratio J ok =J pk is influenced by G for
N (10:17)
J pk ¼ ¼
dt 3m particle diameters of d ¼ 0.1, 1, and 10 mm, respectively