One of the promising ways of improving the efficiency of enrichment processes for economic minerals including those with different strengths is use of selective conmlinution in the preliminary stage of enrichment and in obtaining intermediate or final enrichment products.Recently in our country and abroad research has been carried out into the kinetics of comminution for two-component mineral mixtures including those with different strength characteristics [I-6].This work has developed in two main directions:-a study of the kinetics of combined comminution of minerals of different strengths with the aim of obtaining a prescribed range of size fractions for the charge going on to subsequent processing [1-2].-selective comminution of ores in order to obtain one of the final enrichment products [4,5].Results are presented in our work for a study of selective comminution of two-components mixtures in ball mills.The main factors which determine the process of selective comminution for the weak component of an ore are strength properties of the components, the ratio of component sizes, and the ratio of the energy of the grinding bodies to the energy required for breaking the particles of both components.We consider the various energy combinations with selective comminution of two-component mineral mixtures.We introduce the following notation (in J):E is the energy of grinding bodies at the instant of impact;Emax is the energy required in order to break particles of the strong component of the --S. C -maximum size;Emin is the energy required in order to break particles of the strong component of the s.c minimum size; E~? x is the energy required in order to break Particles of the weak component of the maximum size;Emin is the energy required in order to break particles of the weak component of the W.C minimum size.
An effective way of increasing mill output of the first crushing stage is to reduce the size of the initial feed.The expected increase in ball mill output can be calculated frown equations derived on the basis of equations of crushing kinetics. However, owing to the particular features of material preparation for crushing, it was necessary to derive special kinetic equations.The size characteristic of the whole crushed product with respect to residue on a specific sieve [1-3] is sufficient in ordinary ore grinding and crushing schemes, when the material being crushed exhibits awhole r~nge of size classes, including those virtually the same as the final product.This grain-size composition is usually satisfactorily represented by the Rozin-l~mler equation. However, in practice, e.g., in laboratory crushing of narrow classes 8-3 and 5-1 nun, the standard size class distribution in the initial feed is sometimes impaired. In the additional fractionation of + 16-, + 12-, and + 10-rnTn material in cone breakers operating in a closed cycle with sieves, the content of the -0.074-and, 0.050mm classes, taken as the characteristic ones in the crushed product, varies little in comparison with the grain-size composition of the mill feed. Thus in the crushing of ore to 15-0 nun the content of the -0.074-rnTn class is 3-5% ; in crushing to the 10-0-mm class, the content is 4-6%. Therefore in a number of cases we require a more general characteristic of the grain-size composition of the material, reflecting these changes.Below we give the results of a statistical analysis of possible alternatives of the size characteristics and grain-size composition of the initial product and the crushing products.
Processes involving motion of mineral suspensions in liquids or gases are widely used in various branches of technology-mineral benefieiation, chemical technology, hydraulics, etc.In the known relations, based on similarity criteria, between the liquid veloci W and the parameters of the mineral suspensions [2,3], there is no precise definition of the initial conditions of restricted motionofthe grains, and also no definiteness in the relation between the coefficients of resistance r and the Reynolds number Re for free and restricted motion with limiting dilution of the grains.This causes large errors in calculations based on the expressions given by various authors [10]. This applies particularly to the transitional region between restricted and free motion of the grains.The aim of our present investigation is to develop an expression for the Reynolds number for restricted conditions, identical with the number for free motion, and giving a continuous functional relation between the parameters of free and restricted motion.The classical relation of Rayleigh between the coefficient of resistance r and the Reynolds number Re, based on theory of dimensions and similarity, is the most complete solution to the problem of free motion of grains. Of course, in a correct assessment of the phenomena occurring during restricted motion, application of the theory of dimensions and similarity should give Rayleigh's relation for limiting dilution of the grains. This is possible with an exact definition of the initial conditions of restricted motion of the grains and with a choice of a parameter which characterizes the flow of the liquid around the body in restricted conditions in the same way as the flow is characterized for free motion.As a characteristic parameter in the similarity criterion of Reynolds for restricted motion we can take the thickness l of the layer of liquid diverted by the body (flowing around the body); in a viscous liquid this is a finite quantit3'. The presence of such a layer can be seen from the following considerations.According to present-day ideas concerlting the hydroaerodynamics of a viscous liquid flowing around a body in free conditions, next to the surface there is a boundary layer with large tangential stresses due to the high veloei.ty gradient along the normal to the surface of the body [t]. In the rear zone there is a region where either laminar or turbulent flow is possible. Outside the boundary layer and this region there is a third zone where motion of the liquid is characterized by small tangential stresses and small angular rotation velocities of the particles. In this region, with sufficient accuracy for practical purposes, the liquid can be regarded as ideal and the motion as conservative (derivable from a potential ftmction-in other words, in this zone all the laws of motion of an ideal liquid will be applicable.From the viewpoint of the geometrical characteristics of the flow, the thickness of the boundary layer in the plane of the midsection of a sphere is a small quantity [4], and ...
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