A mass-transfer equation, the solution of which for given boundary conditions makes it possible to derive in analytical form a relationship between the extraction of the solid phase of a suspension into the centrifuge effluent and the fineness of the particles, is suggested on the basis of a model; this is of particular importance in connection with the development of a new trend in the utilization of filtering centrifugesconcentration of coal slurries by extraction into the centrifuge effluent of the finest particles, the ash content of which is substantially higher than that of particles of the coarser classes. Results are presented for production studies under conditions at an active establishment (the Neryungrinskaya Enrichment Factory); these results confirmed the adequacy of the mathematical model proposed: convergence of computed and experimental data was within the limits of the experimental error (no more than 3%). The model in question can be used to predict results of suspension separation by centrifugal filtration.Widespread use of filtering centrifuges in various branches of industry (mining, chemical, foodstuff, etc.) has dictated development of a theory of centrifugal filtering in connection with the need to ascertain laws governing the process, bases for rational regimes of centrifuge operation, and prediction of indicators of centrifugal filtering.In the past decade, a deterministic approach based on manifestation of laws governing the motion of individual particles of solid phase and liquid in capillaries of the cake under the action of centrifugal force has been predominant in studies concerning centrifugal filtration.Basic trends in the mathematical modeling of centrifugal filtering are: 1) determination of conditions whereby solid-phase particles are displaced along various surface configurations of the filtering rotor;2) development of a method for production analysis of various types of centrifuges distinguished by means of off-loading of the cake;3) investigation of the kinetics of centrifugal filtering; and 4) study of the influence exerted by physical properties of the initial material on its dewatering. One of the common drawbacks of various models of centrifugal filtering is (in first approximation) a similar approach to processes involving centrifugal filtration and filtering under static conditions (in a vacuum, or under excess pres-

A mathematical model of a process enables us to control it and maintain optimum conditions, thus ensuring maximum yield and minimum cost. Such models are based on modern statistical procedures of data processing and experimental design.Statistical methods of expetimental design enable us to distinguish the governing factors among a great many possible ones, determine the optimum process conditions, assess the effects of interaction between factors using the minimum number of experiments, and construct a mathematical model of the process.An experiment can be planned if we satisfy the conditions (controllabiLity of the process, reproducibility of the results, the presence of an optimality criterion) present in a laboratory study of flotation. In the present work we used the Box-Wiison method [1,2].The aim of the work was to determine the optimum conditions for basic zinc pyrite flotation at the Zyryanov beneficiation plant under laboratory conditions. The experiments were performed on a dry sample of copper-lead flotation railings, which are the feedstock for the zinc pyrite cycle of operations.The factors, zero points and variation ranges were based on plant conditions. We selected the following factors: X I. the period of agitation with copper sulfate in min; X s, the consumption of butyl xanthate in g/t; X a, the consumption of copper sulfate in g/t; X 4, the agitation time in min; X s, the flotation time in rnin; X s, the consumption of Aerofloat in g/t. Table 1 gives the values of the zero. point and the variation ranges of the factors.We studied three optimality criteria simultaneously: Yl, the extraction; y~ the Goden selectivity index f3] = '(I> (where 8 is the extraction of the chain component into the concentrate and R is the extraction of the waste part into the concentrate); and Ys, the economic criterion [4] Y3= TIBc (13), (9.) , where 7 is the yield of concentrate in %, • is the content of the chain component in the concentrate in %, and C(S) is the cost function of the concentrate.

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