Organization: Society for Mining, Metallurgy & Exploration

Pages: 6

Publication Date:
Jan 1, 1985

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Abstract

HINDERED SETTLING CONCENTRATION In the free settling of mineral particles in a liquid, the falling particles are at a distance from each other so that no particle is affected by its neighbor. In hindered settling, the concentration of particles is sufficiently high so that each particle is affected by its proximity to other particles in the suspension. Richards and Locke86 have described the hindered settling phenomenon as the condition “.. where particles of mixed sizes, shapes and densities in a crowded mass, yet free to move along themselves, are sorted in a rising current of water, the velocity of which is much less than the free-falling velocity of the particles but yet fast enough so the particles are in motion." This is the condition normally encountered in mineral con¬centration processes. The well known Newton equation for free settling of coarse (ap proximately +10-mesh, 1/16-in. or -- 2000-µm) spherical particles is:87 where v," is free settling velocity, cm/sec; p' is density of the fluid; p is density of the particle, g/cm3; d is particle diameter, cm; g is acceleration due to gravity, cm/sec2; and Q is coefficient of resistance, dimensionless, ~0.4. For the settling of fine spheres in water (approximately 150 mesh or 100 µm) the equation of Stokes pertains:87 where µ is viscosity of the fluid in poises and the other symbols have the same meaning as those in Eq. 1. For particles whose size lies between about 10 mesh (--2000 µm) and 150 mesh (100 µm), their settling velocity can be determined from experimental data. These data are available in convenient form in the text by Taggart88 based on the original work of Richards. Alternatively, a Reynolds number-coefficient of resistance plot may be used to determine the settling rate of such particles.87 The settling rate of spherical particles under hindered settling conditions can also be calculated from Eqs. I and 2 by replacing p', the density of the fluid, by p" the apparent density of the suspen¬sion. The concentration of particles in the fluid thus imparts an appar¬ent density to the composite fluid or suspension greater than that of the liquid alone, resulting in a buoyant effect on the larger particles. Particle shape affects the settling rate of both coarse and fine particles. The general effect is to reduce their settling velocities and the effect is greater for coarse particles and for those settling under hindered settling conditions than for fine particles or free settling ones. For two particles of differing densities but settling at the same velocity under Newtonian conditions, the ratio of their diameters from Eq. 1, called the free settling ratio is: where L signifies the lighter particle and H, the heavier particle. Under Stokesian conditions the exponent would be 0.5. For hindered settling conditions the fluid density p' is replaced by the apparent density of the suspension, p", to obtain a generalized equation for the hindered settling ratio: assuming both particles settle in approximately the same regime. The free settling ratio as given by Eq. 3 has been called by Taggart88 the "concentration criterion" and is used to predict the effectiveness of any gravity concentration process (see Introduction to this section). Based on Eqs. 3 and 4, if two particles of densities pH and p,, settle at the same velocity, the diameter of the lighter particle will be larger than that of the heavier particle. For example, in the case of galena (pH = 7.5) and quartz (pL = 2.65) settling in water (p =1.0) under free settling, Newtonian conditions 3.9. Thus, a quartz particle nearly four times as large as a galena particle will settle at the same velocity. Any quartz particle just slightly less than four times the diameter of the largest galena particle may be separated from it. Under hindered settling, Newtonian condi¬tions in a suspension where p" = 1.65, dL/dH = 5.85 or any quartz particle just slightly less than about six times the largest galena particle may be separated from it. Reference to Eq. 4 indicates that a superior separation between two minerals of differing densities is favored by: (1) coarse particles settling under Newtonian conditions, (2) a large difference in (pa - PL), and (3) separation under hindered settling conditions where p" is high. Of course, there are practical limits to increasing p" excessively because at very high percent solids suspen¬sion fluidity would be lost and the hindered settling separation process defeated. Examples of hindered settling separators are the Dorrco-Fahren¬wald sizer,89 the Rheolaveur box 90 the Spitzkasten,89 and the Willoughby washer.91 These devices make a mineral separation on the basis of both specific gravity and size and all of them are essentially obsolete except for the Dorrco-Fahrenwald sizer and similar devices which still find application for the removal of coarse particles from a much finer particle assemblage and for preconcentration ahead of shaking tables. However, nearly all gravity concentration processes (jigs, tables, flowing film concentrators, heavy media separators) and many sizing devices (sizing classifiers, clarifiers, thickeners, hydrosepa¬rators) make use of the hindered settling phenomenon during the separation of particles. JIGGING Introduction In jigging, a mixture of ore particles, supported on a perforated plate or screen in a layer or "bed" with a depth many times the thickness of the largest particle, is subjected to an alternating rising and falling (pulsating) flow of fluid with the objective of causing all |

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