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Ethiopian Defence University
College of Engineering
Department of Chemical Engineering
MECHANICAL UNIT OPERATIONS
(ChEg 3331)
by
Ashagrie L. (MSc, Chem.Eng.)
Chapter Five
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Mixing and Segregation
Contents:
• Liquid-Liquid Mixing
• Solid-Solid Mixing
• Solid-Liquid Mixing
• Segregation causes, mechanisms, and its reduction
Introduction
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 Many operations depend upon effective agitation and mixing
of fluid or solid particles (components).
 Though often confused, agitation and mixing are not
synonymous of each other, both having different meaning.
 Mixing is defined as:
 The reduction of inhomogeneinty in order to achieve a
desired process result. Any operation used to change a non-
uniform system into a uniform one (i.e., the random
distribution of two or more initially separated phases).
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 A unit operation that aims to treat two or more components,
initially in an unmixed or partially mixed state, so that each unit
(particle, molecule, etc.) of the components lies as nearly as
possible in contact with a unit of each of the other components.
 Main aim of the mixing process is the production of a blend
whose sample reflects exactly, or at least by pre-defined accuracy,
the ratio of the added base materials.
 In industrial process engineering, mixing is a unit operation that
involves manipulation of a heterogeneous physical system with
the intent to make it more homogeneous.
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 A single homogeneous material such as water in a tank can
be agitated but not mixed until another material is added to
tank.
 Concerned with all combinations of phases of which the most
frequently occurring ones are:
 Gases with Gases.
 Gases into Liquids: Dispersion.
 Gases with Granular solids: fluidization, pneumatic
conveying; drying
 Liquids into Gases: Spraying.
 Liquids with Liquids: Dissolution, Emulsification,
Dispersion.
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 Liquids with Granular solids: Suspension.
 Pastes with each other and with Solids.
 Solids with Solids: Mixing of powders.
Objectives of Mixing:
 Simple Physical Mixture: Simply the production of a blend of
two or more miscible liquids or two or more uniformly divided
solids.
 Physical Change: Mixing may aim at producing a change that is
physical. The solution of a soluble substance. Lower efficiency of
mixing will often be acceptable.
 Dispersion: dispersion of two immiscible liquids to form an
emulsion or the dispersion of a solid in a liquid to give a suspension
or paste.
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 Promotion of Reaction: Mixing will usually encourage (and
control at the same time) a chemical reaction, so ensuring
uniform products.
 Products or processes where accurate adjustment to pH is
required and the degree of mixing will depend on the process.
 Usually good mixing is required to ensure stability.
 Agitation refers to:
 The induced motion of a material in a specified way, usually in
a circulatory pattern inside some sort of container.
 whereby mixing of phases can be accomplished and by which
mass and heat transfer can be enhanced between phases and with
external surfaces.
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 Forcing a fluid by mechanical means to flow in a circulatory or
other pattern inside a vessel.
 Whereby mixing of phases can be accomplished and by which
mass and heat transfer can be enhanced between phases or with
external surfaces.
 Agitation of Liquids
 Purposes of Agitation: Liquids are agitated for a number of
purposes, depending on the objectives of the processing step.
These purposes include:
1. Suspending solid particles
2. Blending miscible liquids, e.g., methyl alcohol and water.
3. Dispersing a gas through the liquid in the form of small
bubbles
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4.
Dispersing a second liquid, immiscible with the first, to form
an emulsion or suspension of fine drops.
5.
Promoting heat transfer b/n the liquid and a coil or jacket.
Agitation Equipment
 Generally, liquids are agitated in a cylindrical vessel which can be
closed or open to the air. The height of liquid is approximately
equal to the tank diameter. An impeller mounted on a shaft is
driven by an electric motor.
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Three-blade Propeller Agitator. The propeller can be a
side-entering type in a tank or be clamped on the side of an
open vessel in an off-center position. These propellers turn at
high speeds of 400 to 1750 rpm and are used for liquids of low
viscosity. The flow pattern in a baffled tank with a propeller
positioned on the center of the tank shown below. This type of
flow pattern is called axial flow since the fluid flows axially
down the center axis or propeller shaft and up on the sides of
the tank as shown.
2. Paddle agitator. Various types of paddle agitators are often
used at low speeds b/n about 20 and 200 rpm. Two-bladed &
four-bladed flat paddles are often used, as shown in fig. 5.2(a).
1.
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Fig. (5.1) Baffled tank and 3-blade propeller agitator with axial-flow pattern:
(a) Side view, (b) bottom view,
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 The total length of the paddle impeller is usually 60 to 80 % of
the tank diameter and the width of the paddle 1/6 to 1/10 of its
length.
 At low speeds mild agitation is obtained in unbaffled vessel. At
higher speeds baffles are used, since, without baffles, the liquid is
simply swirled around with little actual mixing. The paddle
agitator is ineffective for suspending solids since good radial flow
is present but little vertical or axial flow. An anchor or gate
paddle (Fig. 5.2b), is often used. It sweeps or scraps the tank
walls and sometimes the tank bottom. It is used with viscous
liquids where deposits on walls can occur and to improve heat
transfer to the walls. However, it is a poor mixer. These are often
used to process starch pastes, paints, adhesives, and cosmetics.
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Fig. (5.2) various types of agitators: (a) four-blade paddle, (b) gate or anchor
paddle, (c) six-blade open turbine, (d) pitched-blade (45o) turbine.
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3.
Turbine Agitators. Turbines that resemble multibladed
paddle agitators with shorter blades are used at high speeds for
liquids with a very wide range of viscosities. The diameter of a
turbine is normally b/n 30 and 50 % of the tank diameter.
Normally, the turbines have 4 or 6 blades. The turbines with
flat blades give radial flow. They are also useful for good gas
dispersion where the gas is introduced just below the impeller
at its axis and is drawn up to the blades and chopped into fine
bubbles.
 In the pitched-blade turbine with the blades at 45o, some axial
flow is imparted so that a combination of axial and radial flow is
present. This type is useful in suspending solids since the
currents flow downward and then sweep up the solids.
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Fig. (5.3) Baffled tank with 6-blade turbine agitator with disk showing flow patterns:
(a) side view, (b) bottom view, (c) dimensions of turbine and tank.
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4. Helical-ribbon agitators. This type of agitator used in
highly viscous solutions and operates at a low RPM in the
laminar region. The ribbon is formed in a helical path and is
attached to a central shaft. The liquid moves in a tortuous
flow path down the center and up along the sides in a
twisting motion. Similar types are the double helical ribbon
and the helical ribbon with a screw.
5. Agitator selection and viscosity ranges. The viscosity
of the fluid is one of several factors affecting the selection of
the type of agitator. Indications of the viscosity ranges of
these agitators are as follows.
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 Propellers
are used for viscosities of the fluid below
about 3 Pa.s; turbines can be used below about 100
Pa.s, modified paddles such as anchor agitators can be
used above 50 Pa.s to about 500 Pa.s; helical and
ribbon-type agitators are often used above this range
to about 1000 Pa·s and have been used up to 25000
Pa·s.
 For viscosities greater than about 2.5 to 5 Pa·s and
above, barnes are not needed since little swirling is
present above these viscosities.
Flow Patterns in Agitation
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 The flow patterns
in an agitated tank depend upon the
fluid properties,
the geometry of the tank, types of
barnes in the tank, and the agitator itself.
 If a propeller or other agitator is mounted vertically in
the center of a tank with no barnes, a swirling flow
pattern usually develops.
 Generally, this is undesirable, because of excessive air
entrainment, development of a large vortex, surging, and the
like, especially at high speeds.
 To prevent this, an angular off-center position can be
used with propellers with small horsepower. However, for
vigorous agitation at higher power, unbalanced forces can
become severe and limit the use of higher power.
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 For vigorous
agitation with vertical agitators, barnes
are generally used to reduce swirling and still promote
good mixing. Barnes installed vertically on the walls of
the tank are shown in Fig. 5.3.
 The turbine impeller drives the liquid radially against
the wall, where it divides, with one portion flowing
upward near the surface and back to the impeller from
above and the other flowing downward.
 Sometimes, in tanks with large liquid depths much
greater than the tank diameter, two or three impellers
are mounted on the same shaft, each acting as a
separate mixer.
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 The bottom impeller is about 1.0 impeller diameter above
the tank bottom.
 In an agitation system, the volume flow rate of fluid
moved by the impeller, or circulation rate, is important
to sweep out the whole volume of the mixer in a
reasonable time.
 Also, turbulence in the moving stream is important for
mixing, since it entrains the material from the bulk
liquid in the tank into the flowing stream. Some
agitation systems require high turbulence
with low
circulation rates, and others low turbulence and high
circulation rates. This often depends on the types of
fluids being mixed and on the amount of mixing needed.
Typical “Standard" Design of Turbine
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 The turbine
agitator
shown in Fig. 8.3 is the most
commonly used agitator in the process industries. For
design of an ordinary
agitation system, this type of
agitator is often used in the initial design.
 The geometric proportions of the agitation system which
are considered as a typical "standard"
design are
given in Table 1. These relative proportions are the basis
of the major correlations
of agitator performance
in
numerous publications (See Fig.5.3c for nomenclature).
 In some cases W/ DA = 1/8 for agitator correlations. The
number of Barnes is 4 in most uses.
Power Used in Agitated Vessels
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 In the design of an agitated vessel, an important factor is the
power required to drive the impeller. Since the power
required for a given system cannot be predicted theoretically,
empirical correlations have been developed to predict the
power required.
 The presence or absence of turbulence can be correlated
with the impeller Reynolds number NRe defined as:
NRe = DA2Nρ/μ
 Where D. is the impeller (agitator) diameter in m, N is rotational
speed in rev/s ρ is fluid density in kg/m3 and μ is viscosity in
kg/m·s.
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 The clearance or gap between the baffles and the wall is
usually 0.10 to 0.15 J to ensure that liquid does not form
stagnant pockets next to the baffle and wall. In a few
correlations the ratio of baffle to tank diameter is J /DT = 1/10
instead of 1/12.
 Geometric proportions for a “standard” Agitation system,
DA/DT = 0.3 to 0.5, H/DT = 1, C/DT = 1/3, W/DA = 1/5, L/DA
= 1/4, J/DT = 1/12.
 H: Depth of liquid, DT: Tank diameter, DA: Impeller diameter,
L: Blade length, W: Impeller width, J: Width of baffle, C:
Clearance.
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 The flow is laminar in the tank for Nre < 10, turbulent for NRe >
104, and for a range between 10 and 104, the flow is transitional,
being turbulent at the impeller and laminar in remote parts
of the vessel.
 Power consumption is related to fluid density ρ, fluid viscosity, μ
rotational speed N and impeller diameter DA by plots of power
number NP versus NRe.
 The power number is:
NP = P/ρN3DA5
Where, P = power in J/s or W.
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 Figure 5.4 is a correlation for frequently used impellers with
Newtonian liquids contained in baffled, cylindrical vessels.
 Dimensional measurements of baffle, tank, and impeller sizes
are given in Fig. 5.3c. these curves may also be used for the
same impellers in unbaffled tanks when NRe is 300 or less.
 When NRe is above 300, the power consumption for an
unbaffled vessel is considerably less than for a baffled Vessel.
Curves for other impellers are also available.
 Curve 1. Flat six-blade turbine with disk (like Fig.8.3 but six
blades); DA/W = 5; four baffles each DT/J = 12.
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Fig 5.4: Power correlations for various impellers and baffle
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 Curve-2. Flat six-blade open turbine (like Fig.5.2e); DA/W = 8;
four baffles each DT/J =12.
 Curve-3. Six-blade open turbine bile blades at 45° (like
Fig.8.2d); DA/W = 8; four baffles each DT/J = 12.
 Curve-4. Propeller (like Fig.5.1); pitch = 2DA; four baffles each
DT/J=10; also holds for same propeller in angular off-center
position with no baffles.
 Curve-5. Propeller; pitch = DA; four baffles each DT/J = 10;
also holds for same propeller in angular off-center position with
no baffles.
Examples
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1.
A flat-blade turbine agitator with disk having six blades is installed
in a tank similar to fig. 8.3. The tank diameter, DT is 1.83 m, the
turbine diameter, DA is 0.61 m, DT = H, and the width, W is 0.122
m. The tank contains four baffles, each having a width J of 0.15 m.
The turbine is operated at 90 rpm and the liquid in the tank has a
viscosity of 10 cp and a density of 929 kg/m3.
(a) Calculate the required kW of the mixer.
(b) For the same conditions, except for the solution having a viscosity
of 100,000 cp, calculate the required kW.
Solution
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The following data are given: D = 0.61 m, W = 0.122 m, DT = 1.83
m, J = 0.15 m, N = 90/60 = 1.50 rev/s, ρ = 929 kg/m3, and μ = (10
cp) (1x10-3) = 0.01 kg/m.s = 0.01pa.s.
 The Reynolds number is
(a)
NRe = DA2Nρ/μ = (0.61)2(1.5)929/0.01 = 5.185 x 104
 Using curve 1 in Fig. 5.4 since DA/W = 5 and DT/J = 12, NP = 5 for
NRe = 5.185 x 104. Solving for P in, NP = P/ρN3DA5 and substituting
known values,
P = (NP) (ρN3DA5)
= 5(929) (1.5)3(0.61)5
= 1324 J/s = 1.324 kW
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(b)
μ = 100,000(1 x 10-3) = 100 kg/m.s
NRe = (0.61)2(1.5)929/100 = 5.185
 This is in the laminar flow region, from fig. 8.4, NP = 14
P = 14(929) (1.5)3(0.61)5 = 3707 J/s = 3.71 kW
 Hence, a 100,000 fold increase in viscosity only increases the power
from 1.324 to 3.71 kW
 Variations of various geometric ratios from the standard design can
have different effects on the power number NP in the turbulent region of
the various turbine agitators as follows
 For the flat six-blade open turbine, NP ≈ (W/DA)
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 For the flat, six-blade open turbine, varying DA/DT from 0.25
to 0.50 has practically no effect on NP.
 With two six-blade open turbines installed on the same shaft
and the spacing b/n the two impellers (vertical distance b/n
the bottom edges of the two turbines) being at least equal to
DA, the total power is 1.9 times a single flat-blade impeller.
 For two six-blade pitched-blade (45o) turbines, the power is
also about 1.9 times that of a single pitched-blade impeller.
 A baffled vertical square tank or a horizontal cylindrical tank
has the same power number as a vertical cylindrical tank.
However, marked changes in the flow patterns occur.
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 The power number for a plain anchor-type agitator similar to
fig. 8.2b but without the two horizontal cross bars is as follows
for NRe < 100:
NP = 215(NRe)-0.955
 Where DA/DT = 0.90, W/DT = 0.10, and C/DT = 0.05
 The power number for a helical ribbon agitator for very viscous
liquids for NRe < 20 is as follows:
NP = 186(NRe)-1 (agitator pitch/tank diameter = 1)
NP = 290(NRe)-1 (agitator pitch/tank diameter = 0.5)
 The typical dimensional ratios used are DA/DT = 0.95, with
some ratios as low as 0.75, and W/DT = 0.095.
Mixing of Solids
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 The mixing of solids, whether
free flowing or cohesive,
resembles to some extent the mixing of low-viscosity
liquids. Both processes intermingle two or more separate
components to form a more or less uniform product.
Some of the equipment normally used for blending liquids
may, on occasion, be used to mix solids.
 Yet there are significant differences between the two
processes. Liquid blending depends on the creation of flow
currents, which transport unmixed material to the mixing
zone adjacent to the impeller. In heavy pastes or masses of
particulate solids no such currents are possible, and mixing is
accomplished by other means.
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 In consequence, much more power is normally required in
mixing pastes and dry solids than in blending liquids.
 Another difference is that in blending liquids a "well-mixed"
product usually means a truly homogeneous liquid phase,
from which random samples, even of very small size, all have
the same composition. In mixing pastes and powders the.
product often consists of two or more easily identifiable
phases, each of which may contain individual particles of
considerable size.
Power Requirements
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 Large amounts of mechanical energy are needed to mix heavy
plastic masses.
 In continuous mixers the material must also be moved through
the machine. Only part of the energy supplied to the mixer is
directly useful for mixing, and in many machines the useful part is
small.
 Probably mixers that work intensively on small quantities of
material, dividing it into very small elements, make more effective
use of energy than those that work more slowly on large quantities.
Machines that weigh little per pound of material processed waste
less energy than heavier machines.
 Regardless of the design of the machine, however, the power
needed to drive a mixer for pastes and deformable solids is
many times greater than that needed by a mixer for liquids.
Criteria of Mixer Effectiveness
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 The energy supplied appears as heat, which must ordinarily be
removed to avoid damaging the machine or the material.
 The performance of an industrial mixer is judged by the
time required, the power load, and the properties of the
product. Both the requirements of the mixing device and the
properties desired in the mixed material vary widely from one
problem to another.
 Sometimes a very high degree of uniformity
is required;
sometimes a rapid mixing action; sometimes a minimum
amount of power. The degree of uniformity of a mixed product,
as measured by analysis of a number of spot samples, is a valid
quantitative measure of mixing effectiveness.