Page 332 - Fundamentals of Water Treatment Unit Processes : Physical, Chemical, and Biological

Mixing 287

referring to any form of flocculation caused by fluid (1) A mixer in water treatment intended to promote
motion. (2) Greek: Rectangular, upright (Aa Diction- the coagulation process. (2) The function is to dis-
ary, Apple, Inc., 2007); the rationale of Smolu- perse the applied coagulant or other chemicals
chowski could have been that the collision rate in throughout the water to be treated.
laminar flow is normal to the velocity vector, i.e., the Recycle reactor: The product stream from a plug-flow
velocity gradient is dv=dy. reactor is recycled back to the entrance (Levenspiel,
Paddle: Flat-blade impeller with surface normal to flow- 1999, p. 136). As the recycle flow increases, the
inducing radial flow. Sometimes, blades are pitched. behavior of a plug flow reactor approaches a
Otherwise, there is no axial flow. They rotate at slow CSTR. Recycle is a means to obtain various
to moderate speeds, e.g., 20–150 rpm, with axis degrees of ‘‘backmixing’’ with a plug-flow reactor
located in the center of a vessel. The diameter is (p. 136).
about 0.5–0.8 times the diameter of the vessel with Rushton: The ‘‘Rushton’’ impeller and mixing basin system
width 0.17–0.1 times the impeller diameter. Baffles became a standard reference for mixing systems. The
are necessary to prevent rotation of the fluid mass proportions of such a basin are given by McCabe
and the development of a vortex (McCabe et al., et al. (1993, p. 242) and Rushton et al. (1950a,b).
1993, p. 237). Table G10.1 gives nomenclature and proportions for
Perikinetic: (1) Collision of suspended particles due to their a Rushton basin.
motion as induced by Brownian motion (Langelier
and Ludwig, 1949, p. 165; Argaman and Kaufman,
1968, p. 5). (2) Greek: prefix; around, about (Aa
TABLE G10.1
Dictionary, Apple, Inc., 2007).
Proportions for Rushton Basin
Plug-flow reactor: An ‘‘ideal’’ reactor characterized by
orderly flow with no element overtaking or mixing Proportion Fraction Proportion Fraction
with any other ahead or behind; the necessary and Tank shape is round Round Baffles ¼ 4
sufficient condition is for the residence time in the D(impeller)=T ¼ 0.33 W(blade)=D(impeller) ¼ 0.20
reactor to be the same for all elements of the fluid C=T ¼ 0.33 L(blade)=D(impeller) ¼ 0.25
(Levenspiel, 1972, p. 97). For a ‘‘plug-flow’’ reactor, H(water)=T ¼ 1.0 J(baffle)=H(tank) ¼ 0.083–0.10
the average residence time is u ¼ V(reactor)=Q.
Power number: A dimensionless number, defined as, Nomenclature
3 5 D(impeller) is the diameter of impeller (m)
P ¼ P=(rn D ). The power number is an identity
T is the diameter of tank (m)
with the drag coefficient.
C is the distance from floor of tank to mid-point of impeller blade (m)
Pressure field: The description of pressures at points in space
D(water) is the depth of water in tank (m)
for a given system at a given time.
H(tank) is the depth of water in tank (m)
Primary particles: The particles that are the target of coagu-
W(blade) is the height of impeller blade, i.e., vertical dimension (m)
lation as contrasted with the product particles formed
L(blade) is the length of blade, i.e., horizontal dimension (m)
as a result of coagulation. J(baffle) is the width of baffle (m)
Propeller: Axial flow, high speed, 1150–1750 rpm or 400–
800 rpm for larger sizes, impeller that causes cur-
rents in an axial direction that continue until
deflected by a floor or wall. The flow plume is helical Scale-up: The idea of a model is to predict some portion of
and entrains adjacent stagnant fluid. Because of the behavior of the prototype and, at the same time,
the persistence of the currents, propellers are effect- to try to scale up in terms of geometry, turbulence,
ive for large vessels. A standard, three-blade marine power required, etc.
impeller is most common; size rarely exceeds 457 Shear: Hydraulic shear is given as t ¼ mdv=dy; units are
2
mm (18 in.) regardless of the size of the vessel. In a N=m .
deep tank, two or more impellers may be mounted on Shear rate: Shear divided by viscosity, i.e., t=m ¼ dv=dy;
1
the same shaft. Shear is high at the surface of the units are s .
impeller (McCabe et al., 1993, p. 237). Short-circuiting: The residence time of a portion of the fluid
Prototype: The term prototype means a full-scale version is much less than the average, i.e., t p u, where, t p is
of a system that was previously simulated by a the residence time of any given parcel of fluid. See
model. The terms ‘‘model’’ and ‘‘prototype’’ go also, dead-zone.
together. Similarity: The idea of similarity applies to modeling as a
Pumping number: Same as flow number, Q. primary application. Three kinds of similarity are as
Rapid mix: Mixing of coagulant chemicals, usually associ- follows (Rushton, 1952, p. 34):
ated with high-intensity turbulence generated, as a 1. Geometric similarity: Two systems of different
rule, by an impeller–basin system. Synonymous with size have the same ratio of length for all corre-
flash mixing, initial mixing. Related definitions are: sponding boundaries and positions.