Page 432 - Fundamentals of Water Treatment Unit Processes : Physical, Chemical, and Biological

Rapid Filtration 387

States, the former were called ‘‘English filters,’’ and Flocculant: The implication is that a polymer is added after
the latter, ‘‘American filters.’’ coagulation and preceding flocculation. The term is
Field: The idea of a ‘‘field’’ refers to the distribution of some not strictly defined except that the use of a polymer is
quantity throughout a given geometric bounded vol- implied. Some persons may use the term inter-
ume or area. The quantity could be a force (electrical, changeably with coagulant aid. Others may intend
gravity, centrifugal), velocity, acceleration, potential that a flocculent in intended to aid in binding micro-
(e.g., hydraulic head), concentration of suspended flocs and floc particles to become larger and
solids or dissolved solids, etc. A change in geometry ‘‘tougher’’ floc particles.
changes the configuration of the field, but a change Fluidize: Water flow with velocity vertical and up will at a
in input level has no effect. A flow net is a combin- certain point cause a bed of granular media to be
ation of a potential field and streamlines; a velocity maintained in suspension caused by the drag on the
field and a convective acceleration field are each particles; when this occurs the bed is ‘‘fluidized.’’
derivatives of the streamline configuration. Gravity: The effect of gravity on a particle trajectory may
Filter aid: Polymer added prior to filtration. The premise is cause deviation from the advective transport along
that one part of the polymer will attach to the media its streamline to cause impingement against a col-
with strands extending into the flow which, in turn, lector surface. The effect becomes more significant
may provide attachment sites for coagulated par- as particle size approaches about 100 mm. The
ticles. idea was suggested by Allen Hazen who described
Filter coefficient: The coefficient, l, in the Iwasaki relation, the pores of a slow sand filter as miniature
qC=qZ ¼ lC. settling basins. (see Ives, 1975b, p. 189). In typical
The filter coefficient can be related to the several rapid filter with v ¼ 2mm=s, P ¼ 0.4, T ¼ 208C,
transport mechanisms, shown as dimensionless num- v i ¼ 5mm=s and applying Stoke’s law to a 10 mm
bers, that is, (Ives, 1975b, p. 196) clay particle, v s ¼ 0.1 mm=s, which is 2% effect.
Near the surface of a granular media the local vel-
a
b c
ld(grain) ¼ K(d=D) (1=P) S (1=R) d ocities may be near 0.2 mm=s indicating that par-
ticles close to the surface may be transported to the
This shows a minimum at d(particle) 1 mm. collector surface. Experiments have shown, how-
Filter medium: The granular material that comprises a filter ever, that particles deposit on the top of the granular
bed is called a filter medium. The plural is ‘‘media.’’ media giving a dome effect on top.
Filtration: Filtration is a unit process for achieving a separ- Hamaker constant: A constant associated with calculation
ation between a fluid and its suspended matter by of intermolecular forces (see, for example, Myers
passage of the suspension through a porous medium. (1991, p. 65). A more complete explanation was
Filtration efficiency: A common definition is simply the given by Gregory (1975, pp. 78–79). In 1937, H.C.
ratio of particle concentration leaving the filter, C, Hamaker published a paper that extended the con-
divided by the particle concentration entering the cept of van der Waals forces to include the energy of
filter, C o , i.e., the ratio, C=C o . interaction between finite particles of various shapes,
Filtration mode: The filtration ‘‘mode’’ as used here refers to separated by distance, d. His mathematical relations
whether the treatment train is in-line, direct, or con- for the bonding energy between two flat plates and
ventional, illustrated in Figure 12.1a,b, and c,
two spheres were, respectively, U(flat plates) ¼
respectively. These terms are defined subsequently. A 12 =12pd 2 and U(two spheres) ¼ A 12 a 1 a 2 =6d
When the term ‘‘rapid filtration’’ is used, one of these (a 1 þ a 2 ), in which A 12 is the Hamaker constant for
modes must be specified. materials 1 and 2 in a vacuum. For a sphere and a flat
Filtration process: See filtration. surface, the model used in filtration for a particle-
Filtration technology: The filtration process and the support-
grain surface attachment is U(sphere=flat plate) ¼
ing components to make it work is called here, A 12 a 1 =6d. Gregory (p. 79) extended the idea to
‘‘filtration technology.’’ The ‘‘process’’ occurs within the case in which water is a medium. The magnitude
the media bed. The supporting components include: of the Hamaker constant for materials in water is
an under-drain system, pipes, valves, controls, and about 0.1–10 10 –20 J (Gregory, 1975, p. 81), with
various instruments. Numerous variations exist the exact magnitude depending on the materials.
which are both generic and proprietary. Hamaker constant: Hamaker showed how interactions
Filtration theory: The quest of filtration theory is to provide between molecules could be integrated to give the
a means to understand how the three dependent energy of interaction between particles of various
functions in filtration, that is, the effluent turbidity= shapes. The results for parallel flat plates and for
particle concentration versus time, the solids concen- spheres are of special interest and are given below.
tration depth profile, and the rate of clogging head- These expressions are based on the assumption of
loss with time, is affected by the most important of complete additivity of intermolecular interactions
the independent variables. and contain a constant A12, which depends only