The capacity of a shaker is measured by the mass of material that can be fed per unit time to a unit area of the screen. Capacity and effectiveness are opposing factors. To obtain maximum effectiveness, the capacity must be small, and large capacity is obtainable only at the expense of a reduction in effectiveness. In practice, a reasonable balance between capacity and effectiveness is desired. Although accurate relationships are not available for estimating these operating characteristics of screens, certain fundamentals apply, which can be used as guides in understanding the basic factors in screen operation.
Relationship of capacity and effectiveness
The capacity of a screen is controlled simply by varying the rate of feed to the unit. The effectiveness obtained for a given capacity depends on the nature of the screening operation. The overall chance of passage of a given undersize particle is a function of the number of times the particle strikes the screen surface aud the probability of passage during a single contact. If the screen is overloaded, the number of contacts is small and the chance of passage
on contact is reduced by the interference of the other particles. The improvement of effectiveness attained at the expense of reduced capacity is a result of more contacts per particle and better chances for passage on each contact.
Ideally, a particle would have the greatest chance of passing through the screen if it struck the surface perpendicularly, if it were so oriented that its minimum dimensions were parallel with the screen surface, if it were unimpeded by any other particles, and if it did not stick to, or wedge into, the screen surface. None of these conditions applies to actual screening, but this ideal situation can be used as a basis for estimating the effect of mesh size and wire dimensions on the performance of screens.
Effect of mesh size on capacity of screens
The probability of passage of a particle through a screen depends on the fraction of the total surface represented by
openings, on the ratio of the diameter of the particle to the width of an opening in the screen, and on the number of contacts between the particle and the screen surface. When these factors are all constant, the average number of particles passing through a single screen opening in unit time is nearly constant, independent of the size of the screen opening. If the size of the largest particle that can just pass through a screen is taken equal to the width of a screen opening, both dimensions may be represented by Dpc. For a series of screens of different mesh sizes, the number of openings per unit screen area is proportional to 1/D²pc. The mass of one particle is proportional to D³pc. The capacity of the screen, in mass per unit time, is, then, proportional to (1/ D²pc)D³pc = Dpc Then the capacity of a screen, in mass per unit time, divided by the mesh size should be constant for any specified conditions of operation. This is a well-known practical rule of thumb.
Capacities of actual screens
Although the preceding analysis is useful in analyzing the fundamentals of screen operation, in practice several complicating factors appear that cannot be treated theoretically. Some of these disturbing factors are the interference of the bed of particles with the motion of any one; blinding; cohesion of particles to each other; the adhesion of particles to the screen surface; and the oblique direction of approach of the particles to the surface. When large and small particles are present, the large particles tend to segregate in a layer next to the screen and so prevent the smaller particles from reaching the screen. All these factors tend to reduce capacity and lower effectiveness. Moisture content of the feed is especially important. Either dry particles or particles moving in a stream
of water screen more readily than damp particles, which are prone to stick to the screen surface and to each other and to screen slowly and with difficulty. Capacities of actual screens, in ton/ft²-h-mm mesh size, normally range between 0.05 and 0.2 for grizzlies to 0.2 and 0.8 for vibrating screens. As the particle size is reduced, screening becomes progressively more difficult, and the capacity and effectiveness are, in general, low for particle sizes smaller than about 150-mesh.