Page 431 - Fundamentals of Water Treatment Unit Processes : Physical, Chemical, and Biological

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

tubes, constricted cell, sphere, or a sphere within cell deposit causes a particle or aggregate of particles to
of Happel (1958). be detached and entrained in the flow; thus it
Collision: A ‘‘collision’’ between a particle and a filter grain behaves like any other particle and is subject to
occurs when the particle trajectory brings the particle attachment at some distance downstream. Such
into the proximity of the force field of the filter grain deposits also cause a higher local pressure gradient,
where it may be either repulsed or attracted. A ‘‘col- which is another manifestation of the higher shear
lision’’ may also be defined as a ‘‘contact.’’ stresses. The exact detachment point depends upon
Contact: See collision. the shear stress of the attached floc, which is inde-
Conventional filtration: The ‘‘conventional’’ filtration mode terminate.
is rapid-mix=coagulation followed by flocculation, Deterministic: The sense of usage is that a variable outcome
followed by settling, followed by filtration. Conven- is due to predictable factors. A ‘‘deterministic’’
tional filtration is the most common mode and is model has the characteristics that a given dependent
essential when floc load must be reduced prior to variable may be a function of certain independent
filtration. variables. In a given model if the dependent and
d 10 size: In a sieve analysis of a filter media, the d 10 size is the independent variables are identified and if the math-
size of which 10% of the media is smaller by weight. ematical functions are proposed, the model is ‘‘deter-
The d 60 size is also noted and sometimes the d 90 size ministic.’’ If the model is tested experimentally and
is used. Usually when one refers to a media size of if the dependent variables behave as predicted by
say 0.9 mm, the implicit reference is to the d 10 size. changes in selected independent variables, then the
Declining-rate filtration: A means to distribute water to a model is ‘‘verified.’’ The antithesis of ‘‘determinis-
group of filters is to apply the coagulated water to all tic’’ is ‘‘stochastic’’; ultimately, most stochastic vari-
without control valves. The water levels are the same ables have deterministic characteristics if they are
for each filter of the group. At the same time the understood well.
effluent flow from the under-drain system of each Diffusion: The random motion of particles due to thermal
filter is not restricted by a control valve. Thus energy, that is, Brownian motion, may bring par-
the headloss across each filter is constant and is the ticles into proximity with a collector. For particles
same at the start of the filter run as at the end of the larger than 1 mm diameter, the mean-free-path of
run. The filtration velocity declines, however, as the particles is at the most one or two particle diameters
filter clogs. and so diffusion is not important. An important par-
Deep bed filtration: See depth filtration. ameter is the coefficient, B, in the Stokes-Einstein
Deposit: The particles-to-be-removed attach to the collectors equation, B ¼ kT=(3pmd c ). The ratio, Brownian
and are termed deposits. Also we may call these velocity=Advective velocity ¼ B=(d c v), which is 1=P
deposits, in aggregate, ‘‘solids’’ as distinguished (P is the Peclet number)
from the same material as comprising the suspension.
Depth filtration: In depth filtration, the suspended particles where
penetrate into the porous medium and attach to ‘‘col- B is the Stokes-Einstein diffusion coefficient
2
lectors,’’ that is, filter grains, at different depths. The (m =s)
process involves ‘‘transport’’ of particles to a col- d c is the diameter of granular media particle (m)
lector (grain of granular media) and then ‘‘attach-
5
ment’’ on the collector surface. Ives (1975a, p. 1) In water filtration, 10–8 < 1=P < 0.5 10 .
and Tien and Payatakes (1979, p. 733) state simply Direct filtration: The ‘‘direct’’ filtration mode is rapid-
that depth filtration is filtration through a deep bed of mix=coagulation followed by flocculation, followed
granular media. The particles interact with each other by filtration.
and with the filter media in a manner involving Electro-osmosis: Flow of liquid through a porous plug (or
colloid and interfacial forces at various depths in tube) under the influence of an applied electric field
the filter bed. The term ‘‘deep bed’’ filter is used (Gregory, 1975, p. 65).
often in chemical engineering to distinguish the pro- Electrophoresis: Migration of charged particles in an electric
cess from ‘‘cake’’ filtration. field (Gregory, 1975, p. 65).
Detachment: Ives (1975b, p. 199) states that experimental Electrophoretic mobility: Velocity of a particle in an electric
evidence indicates that increasing the flow in a deep field per unit of field strength, that is,
bed filter, when deposited particles are present in the U ¼ V e =E ¼ ez=h; and, a quick conversion between
pores, leads to detachment of some of these particles z an U is, z 12.8U (Gregory, 1975, p. 65).
causing locally increased suspension concentration. English filter: During the early days of the rapid filtration
Mints of the USSR believes that such detachment technology, the prevailing filtration technology in
occurs even at constant flow because the deposits Europe was slow sand, which had its inception in
cause local increases in interstitial velocity with con- London in 1929. To distinguish slow sand filtration
sequent increase in shear. Rupture of a part of the from the rapid filters being developed in the United