An object moving in a circular path is subjected to an outward centrifugal force, which balances the centripetal force moving the object toward the center of rotation.
THE CENTRIFUGE
An
object moving in a circular path is subjected to an outward centrifugal force,
which balances the centripetal force moving the object toward the center of
rotation. This principle is used in the mechanical separations called
centrifugal filtration and centrifugal sedimentation. In the former, a material
is placed in a rotating perforated basket, which is lined by a filter cloth.
This is used to sep-arate a solid, which is retained at the cloth, from a liquid.
It is essentially a filtration process in which the driving force is of
centrifugal origin. It, in no way, depends on a difference in the densities of
the two phases.
In
centrifugal sedimentation, the separation is due to the difference in the
density of two or more phases. In this more important process, both
solid-liquid mixtures and liquid-liquid mixtures can be completely sepa-rated.
If, however, the separation is incomplete, there will be a gradient in the size
of the dispersed phase within the centrifuge due to the faster radial velocity
of the larger particles. Operated in this way, the centrifuge becomes a
classifier.
FIGURE 11.9 (A) Batch centrifugal filter, (B) supercentrifuge, and (C) solid-bowl
batch centrifuge.
The
principles of filtration discussed previously can be directly applied to this
process, although theoretical predictions of filtration rate and spinning time
are uncertain. The process is widely used for the separation of crystals and
granular products from other liquors, but it is less effective if the slurry
contains a high proportion of particles less than 1 x 10-4 m. The
advantages of the process are effective washing and drying. Residual moisture
after centrifugation is far less than that in cakes produced by pressure or
vacuum filtration. By this method, the moisture content of a cake of coarse
crystals can be reduced to as low as 3%. This facilitates the drying operation
that normally follows. Enclosure of the centrifuge is easy so that toxic and
volatile materials can be processed.
A
typical batch filter is shown in Figure 11.9A. It consists of a perforated
metal basket mounted on a vertical axis. The cloth used to retain solids is
often supported on a metal screen. Baskets mounted in the manner shown are
emp-tied by shoveling the cake. If, however, top suspension is used, the cake
can be more easily withdrawn through traps in the base of the basket. In batch
oper-ation, considerable time is lost during the acceleration and deceleration
of the machine. Machines operating with continuous discharge of solids are used
for separation of coarse solids when the scale of the operation is large. Such
machines are commonly constructed with a horizontal axis of rotation.
The
motion of a particle in a liquid is described by Stokes’ equation. If its
diameter is d, the rate, u, at which
it settles by gravity in a liquid of viscosity η and density ρ is given by equation (24) in
chapter 2 as
where
the acceleration due to gravity is g and the density of the particle is ρs. In the centrifuge,
the gravitational force causing separation is replaced by a centrifugal force.
If the particle has a mass m and moves at an angular velocity ω in a circle of radius r, the
centrifugal force will be ω2r·(m - m1),
where m1 is the mass of
the displaced liquid. ω2r/g is, therefore, the ratio of the
centrifugal and gravitational forces in the example described above. Its value
can exceed 10,000. The separation is, therefore, quicker, more complete, and
effective in systems containing very fine particles, which will not sediment by
gravity because of Brownian movement.
Expressing
the mass of the particle in terms of its volume and effective density, the
centrifugal force can be written as
In
streamline conditions, the opposing viscous force, given by equation (22) in
chapter 2, is 3πηdu, u
being the terminal velocity of the particle. Equating these expressions,
The
rate of sedimentation is proportional to the radius of the basket and the
square of the speed at which it rotates. Centrifugal sedimentors can be divided
into a number of types.
For
operation at very high speeds, the centrifuge bowl is tubular with a
length-diameter ratio ranging from 4 to 8. An example is the Sharples
super-centrifuge illustrated in Figure 11.9B, which operates at up to 15,000
rpm or, in turbine-driven laboratory models, up to 50,000 rpm. The machine,
which gives continuous discharge of two separated liquids, is widely used for
the separation of emulsions. It is also an effective clarifier when the
concentration of solids is very low. These are periodically discharged by
scraping the walls of the cen-trifuge tube. Uses include the cleaning of fats
and waxes, the fractionation of blood, and the recovery of viruses.
Disk-type
centrifuges introduce baffles into the bowl to decrease the dis-tance that
particles travel before settling at the wall. These split the liquid into a
number of layers in which separation occurs. The length to diameter ratio is
usually much smaller than that in tubular-bowl centrifuges, and operational
speeds are lower. In batch processes, the machine is discharged manually at
intervals. Larger machines continuously or intermittently discharge the solids
as a thick slurry through nozzles or valves at the periphery of the basket.
A
solid-bowl batch basket is shown in Figure 11.9C. In this type of machine,
liquids are discharged by weirs or skimmers. In the figure, two skimmers are
shown, each taking off a liquid phase. Solids are discharged manually at the
end of the process. In continuous models, a conveying scroll, operating at a
slightly different speed from the basket, plows the solids to one end,
discharging the material as a damp powder.
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