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|Introduction and Historical Background Although both sluices and devices using a simple flowing film are among the oldest known methods of concentration, they are still extensively employed in a variety of situations where they are not only efficient but also have a low operating cost. More particularly, they are valuable for making a bulk concentrate of high specific gravity minerals from alluvials and beach sand and in upgrading low value ores. The antiquity of some of the basic concepts can be seen in the fact that they are found in Agricola's De Re Metallica which was published at Basic in 1546, while in 1602, Carew114 gave a fairly clear account of tin ore dressing in Cornwall in which grass turves were used to catch the cassiterite. This is perhaps one of the forerun¬ners of the blanket strake. The planilla of Mexico, the lanchute of Malaysia and the old Cornish box huddle are also descended from these early strakes. In fact, a sluice with holes in the bottom for concentrate discharge was shown by Agricola, not unlike the principle used in the plane table and the lamflo sluice. The convex huddle for the treatment of sandy material appeared about 1848 and the concave form eight to ten years later. For the treatment of "slime" sizes, wooden dead frames which were manually worked were used in Cornwall for many years but gave way to the automatic water-operated type in 1860, and even a mechanically tilted frame was described by Henderson115 in 1857. Theoretical Considerations The behavior of solid particles in suspension depends to a great extent upon the pulp density and the size of the suspended particles. In a fairly dilute suspension, such as that normally used when dealing with small particle sizes, the behavior of particles in a flowing film results from two effects. These are the lateral displacement, which is determined by the time taken for each particle to penetrate the flowing film and reach the solid surface, and the resistance offered by each particle to further displacement after it has reached this surface. The initial penetration through the flowing film depends on the size and specific gravity of the particle and the thickness and viscosity of the film. As a result the smaller particles will migrate further before their movement is retarded relative to larger particles of the same specific gravity. The behavior on reaching the solid surface de¬pends on whether there is a single particle layer or, as is more often the case, a multiple layer or thin bed of material which is sufficiently dilated, permits the penetration of higher specific gravity grains. Thrust of Flowing Films. When a thin film of liquid flows over a plane solid surface, the layer next to the surface remains at rest but the velocity of the film increases with the distance from the surface and becomes a maximum near, but not quite at, the free surface. Therefore, a particle in suspension in such a film is acted upon by a greater force near the upper part of the film than at the lower part, resulting in an overturning effect. After a particle reaches the separating surface or an accumulated densely packed bed of other particles, the liquid flow causes it to move downstream by rolling, sliding, or by a movement involving alternating suspension and deposi¬tion (saltation). In rolling and sliding, which are brought about by a substantially noneddying stream, the large submerged particles are acted upon to the greatest extent and they move more rapidly than smaller ones, notwithstanding their greater mass. When two particles of the same size but of different specific gravity are considered, the higher density one moves more slowly by reason of its greater mass. As a result the particles tend to become arranged in the manner shown in Fig. 29. If any particle is so large as to stand above the water surface, the transporting force on such a particle, although the maximum available, will have less effect than that on a submerged one. Such large grains are therefore carried a lesser distance. Fluid Velocity in a Flowing Film It can be shown that if y is the distance within the flowing film from the interface, the fluid velocity v' at this point is given by IIn this equation p' is the fluid density, g the acceleration due to gravity, a the viscosity, a the angle made by the film to the horizontal, and 0 the film thickness (in cgs units). Furthermore, the volume Q of fluid per unit time and unit width is related to the film thickness and can be calculated, since which upon integration gives Consideration of the velocity v' (Eq. l) and the terminal falling velocity µ derived from Stokes law enables the horizontal travel dz in time dt to be calculated as follows: Again integration and substitution of Eq. 3 gives In this equation, z is the distance travelled before a particle of density p at the top of the fluid film has settled on the concentrating surface. From these expressions it can be seen that the depth of the flowing film varies as the cube root of the volume of fluid and inversely as the cube root of the sine of the plane surface inclination. Similarly the distance a particle can travel before reaching the surface is directly related to the quantity of fluid and its viscosity. The viscosity of pulp is greatly increased by the presence of near colloidal particles and consequently the penetration of the somewhat larger grains through the flowing film is retarded, resulting in them being carried further across the concentrator deck. Obviously this effect can be reduced by prior removal of some or all of the ultra¬fine particles. The detrimental effect of kaolin on the separation of fine ferrosilicon from quartz has also been demonstrated by Johnston,116 the relationship between viscosity and efficiency of separation being shown in Fig. 30. The pH value also has a very marked influence on the viscosity and the use of acid mine water, for example, can increase viscosity materially and thereby result in lower efficiency. Dilation of Multi-Particle Systems Except during washing (when a single particle layer may exist) concentration usually takes place in a bed of particles which is partially dilated or stirred by eddy currents. The extreme case is seen in various forms of the sluice where the flow of water and the presence of riffles combine to create a fluid bed in which reverse classification takes|