The Centrifuge

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.

Centrifugal Filtration

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 If, however, top suspension is used, the cake can be more easily withdrawn through traps in the base of the basket.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.

Centrifugal Sedimentation

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 ρ_s. 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.