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UNIT OPERATIONS IN FOOD PROCESSING
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Contents > Mechanical Separations > Sedimentation
CHAPTER 10
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MECHANICAL SEPARATIONS (cont'd)
SEDIMENTATION
Gravitational Sedimentation of Particles in a Liquid
Flotation
Sedimentation of Particles in a Gas
Settling Under Combined Forces
Cyclones
Impingement separators
Classifiers
Sedimentation uses gravitational forces to separate particulate material from
fluid streams. The particles are usually solid, but they can be small liquid
droplets, and the fluid can be either a liquid or a gas. Sedimentation is very
often used in the food industry for separating dirt and debris from incoming raw
material, crystals from their mother liquor and dust or product particles from air
streams.
In sedimentation, particles are falling from rest under the force of gravity.
Therefore in sedimentation, eqn. (10.1) takes the familiar form of Stokes' Law:
vm = D2g(p - f)/18
(10.2)
Note that eqn.(10.2) is not dimensionless and so consistent units must be employed throughout. For example,
in the SI system D would be m, g in m s-2, in kg m-3 and in N s m-2, and then vm would be in m s-1.
Particle diameters are usually very small and are often measured in microns (micro-metres) = 10-6 m with the
symbol m.
Stoke's Law applies only in streamline flow and strictly only to spherical particles. In the case of spheres the
criterion for streamline flow is that (Re) = 2, and many practical cases occur in the region of streamline flow, or
at least where streamline flow is a reasonable approximation. Where higher values of the Reynolds number
are encountered, more detailed references should be sought, such as Henderson and Perry (1955), Perry
(1997) and Coulson and Richardson (1978).
EXAMPLE 10.1. Settling velocity of dust particles
Calculate the settling velocity of dust particles of (a) 60 m and (b)10 m diameter in air at 21C and 100 kPa
pressure. Assume that the particles are spherical and of density 1280 kg m-3, and that the viscosity of air = 1.8
x 10-5 N s m-2 and density of air = 1.2 kg m-3.
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For 60 m particle:
vm = (60 x 10-6)2 x 9.81 x (1280 - 1.2)
(18 x 1.8 x 10-5)
= 0.14 m s-1
For 10 m particles since vm is proportional to the squares of the diameters,
vm = 0.14 x (10/60)2
= 3.9 x 10-3 m s-1.
Checking the Reynolds number for the 60 m particles,
(Re) = (Dvb/)
= (60 x 10-6 x 0.14 x 1.2) / (1.8 x 10-5)
= 0.56
Stokes' Law applies only to cases in which settling is free, that is where the motion of one particle is
unaffected by the motion of other particles. Where particles are in concentrated suspensions, an appreciable
upward motion of the fluid accompanies the motion of particles downward. So the particles interfere with the
flow patterns round one another as they fall. Stokes' Law predicts velocities proportional to the square of the
particle diameters. In concentrated suspensions, it is found that all particles appear to settle at a uniform
velocity once a sufficiently high level of concentration has been reached. Where the size range of the particles
is not much greater than 10:1, all the particles tend to settle at the same rate. This rate lies between the rates
that would be expected from Stokes' Law for the largest and for the smallest particles. In practical cases, in
which Stoke's Law or simple extensions of it cannot be applied, probably the only satisfactory method of
obtaining settling rates is by experiment.
Gravitational Sedimentation of Particles in a Liquid
Solids will settle in a liquid whose density is less than their own. At low concentration, Stokes' Law will apply
but in many practical instances the concentrations are too high.
In a cylinder in which a uniform suspension is allowed to settle, various quite well-defined zones appear as
the settling proceeds. At the top is a zone of clear liquid. Below this is a zone of more or less constant
composition, constant because of the uniform settling velocity of all sizes of particles. At the bottom of the
cylinder is a zone of sediment, with the larger particles lower down. If the size range of the particles is wide,
the zone of constant composition near the top will not occur and an extended zone of variable composition will
replace it.
In a continuous thickener, with settling proceeding as the material flows through, and in which clarified liquid is
being taken from the top and sludge from the bottom, these same zones occur. The minimum area necessary
for a continuous thickener can be calculated by equating the rate of sedimentation in a particular zone to the
counter-flow velocity of the rising fluid. In this case we have:
vu = (F - L)(dw/dt)/A
where vu is the upward velocity of the flow of the liquid, F is the mass ratio of liquid to solid in the feed, L is the
mass ratio of liquid to solid in the underflow liquid, dw/dt is the mass rate of feed of the solids,
of the liquid and A is the settling area in the tank.
If the settling velocity of the particles is v, then vu = v and, therefore:
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is the density
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A = (F - L)(dw/dt)/v
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(10.3)
The same analysis applies to particles (droplets) of an immiscible liquid as to solid particles. Motion between
particles and fluid is relative, and some particles may in fact rise.
EXAMPLE 10.2. Separating of oil and water
A continuous separating tank is to be designed to follow after a water washing plant for liquid oil. Estimate the
necessary area for the tank if the oil, on leaving the washer, is in the form of globules 5.1 x 10-5 m diameter,
the feed concentration is 4 kg water to 1 kg oil, and the leaving water is effectively oil free. The feed rate is
1000 kg h-1, the density of the oil is 894 kg m-3 and the temperature of the oil and of the water is 38C.
Assume Stokes' Law.
Viscosity of water = 0.7 x 10-3 N s m-2.
Density of water = 1000 kg m-3.
Diameter of globules = 5.1 x 10-5 m
From eqn. (10.2),
vm = D2g(p - f)/18
vm = (5.1 x 10-5)2 x 9.81 x (1000 - 894)/(18 x 0.7 x 10-3)
= 2.15 x 10-4 m s-1 = 0.77 m h-1.
and since F = 4 and L = 0, and dw/dt = flow of minor component = 1000/5 = 200 kg h-1, we have from eqn.
(10.3)
A = 4 x 200/(0.77 x 1000)
= 1.0 m2
Sedimentation Equipment for separation of solid particles from liquids by gravitational sedimentation is
designed to provide sufficient time for the sedimentation to occur and to permit the overflow and the sediment
to be removed without disturbing the separation. Continuous flow through the equipment is generally desired,
so the flow velocities have to be low enough to avoid disturbing the sediment. Various shaped vessels are
used, with a sufficient cross-section to keep the velocities down and fitted with slow-speed scraper-conveyors
and pumps to remove the settled solids. When vertical cylindrical tanks are used, the scrapers generally rotate
about an axis in the centre of the tank and the overflow may be over a weir round the periphery of the tank, as
shown diagrammatically in Fig. 10.1.
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Figure 10.1 Continuous-sedimentation plant
Flotation
In some cases, where it is not practicable to settle out fine particles, these can sometimes be floated to the
surface by the use of air bubbles. This technique is known as flotation and it depends upon the relative
tendency of air and water to adhere to the particle surface. The water at the particle surface must be displaced
by air, after which the buoyancy of the air is sufficient to carry both the particle and the air bubble up through
the liquid.
Because it depends for its action upon surface forces, and surface forces can be greatly changed by the
presence of even minute traces of surface active agents, flotation may be promoted by the use of suitable
additives. In some instances, the air bubbles remain round the solid particles and cause froths. These are
produced in vessels fitted with mechanical agitators, the agitators whip up the air-liquid mixture and overflow
the froth into collecting troughs.
The greatest application of froth flotation is in the concentration of minerals, but one use in the food industry is
in the separation of small particles of fat from water. Dissolving the air in water under pressure provides the
froth. On the pressure being suddenly released, the air comes out of solution in the form of fine bubbles which
rise and carry the fat with them to surface scrapers.
Sedimentation of Particles in a Gas
An important application, in the food industry, of sedimentation of solid particles occurs in spray dryers. In a
spray dryer, the material to be dried is broken up into small droplets of about 100 m diameter and these fall
through heated air, drying as they do so. The necessary area so that the particles will settle can be calculated
in the same way as for sedimentation. Two disadvantages arise from the slow rates of sedimentation: the
large chamber areas required and the long contact times between particles and the heated air which may lead
to deterioration of heat-sensitive products.
Settling Under Combined Forces
It is sometimes convenient to combine more than one force to effect a mechanical separation. In consequence
of the low velocities, especially of very small particles, obtained when gravity is the only external force acting
on the system, it is well worthwhile to also employ centrifugal forces. Probably the most common application
of this is the cyclone separator. Combined forces are also used in some powder classifiers such as the rotary
mechanical classifier and in ring dryers.
Cyclones
Cyclones are often used for the removal from air streams of particles of about 10 m or more diameter. They
are also used for separating particles from liquids and for separating liquid droplets from gases. The cyclone is
a settling chamber in the form of a vertical cylinder, so arranged that the particle-laden air spirals round the
cylinder to create centrifugal forces which throw the particles to the outside walls. Added to the gravitational
forces, the centrifugal action provides reasonably rapid settlement rates. The spiral path, through the cyclone,
provides sufficient separation time. A cyclone is illustrated in Fig. 10.2(a).
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Figure 10.2 Cyclone separator: (a) equipment (b) efficiency of dust collection
Stokes' Law shows that the terminal velocity of the particles is related to the force acting. In a centrifugal
separator, such as a cyclone, for a particle, rotating round the periphery of the cyclone:
Fc = (mv2)/r
(10.4)
where Fc is the centrifugal force acting on the particle, m is the mass of the particle, v is the tangential velocity
of the particle and r is the radius of the cyclone.
This equation shows that the force on the particle increases as the radius decreases, for a fixed velocity.
Thus, the most efficient cyclones for removing small particles are those of smallest diameter. The limitations
on the smallness of the diameter are the capital costs of small diameter cyclones to provide sufficient output,
and the pressure drops.
The optimum shape for a cyclone has been evolved mainly from experience and proportions similar to those
indicated in Fig. 10.2(a) have been found effective. The efficient operation of a cyclone depends very much on
a smooth double helical flow being produced and anything which creates a flow disturbance or tends to make
the flow depart from this pattern will have considerable and adverse effects upon efficiency. For example, it is
important that the air enters tangentially at the top. Constricting baffles or lids should be avoided at the outlet
for the air.
The efficiency of collection of dust in a cyclone is illustrated in Fig. 10.2(b). Because of the complex flow, the
size cut of particles is not sharp and it can be seen that the percentage of entering particles which are retained
in the cyclone falls off for particles below about 10 m diameter. Cyclones can be used for separating
particles from liquids as well as from gases and also for separating liquid droplets from gases.
Impingement separators
Other mechanical flow separators for particles in a gas use the principal of impingement in which deflector
plates or rods, normal to the direction of flow of the stream, abruptly change the direction of flow. The gas
recovers its direction of motion more rapidly than the particles because of its lower inertia. Suitably placed
collectors can then be arranged to collect the particles as they are thrown out of the stream. This is the
principle of operation of mesh and fibrous air filters. Various adaptations of impingement and settling
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separators can be adapted to remove particles from gases, but where the particle diameters fall below about 5
m, cloth filters and packed tubular filters are about the only satisfactory equipment.
Classifiers
Classification implies the sorting of particulate material into size ranges. Use can be made of the different
rates of movement of particles of different sizes and densities suspended in a fluid and differentially affected
by imposed forces such as gravity and centrifugal fields, by making suitable arrangements to collect the
different fractions as they move to different regions.
Rotary mechanical classifiers, combining differential settling with centrifugal action to augment the force of
gravity and to channel the size fractions so that they can be collected, have come into increasing use in flour
milling. One result of this is that because of small differences in sizes, shapes and densities between starch
and protein-rich material after crushing, the flour can be classified into protein-rich and starch-rich fractions.
Rotary mechanical classifiers can be used for other large particle separation in gases.
Classification is also employed in direct air dryers, in which use is made of the density decrease of material on
drying. Dry material can be sorted out as a product and wet material returned for further drying. One such
dryer uses a scroll casing through which the mixed material is passed, the wet particles pass to the outside of
the casing and are recycled while the material in the centre is removed as dry product.
Mechanical separations > CENTRIFUGAL SEPARATIONS
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Unit Operations in Food Processing. Copyright 1983, R. L. Earle. :: Published by NZIFST (Inc.)
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