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-

Based on the analysis of ultimate stress of floccules under shear, the authors determine maximum force and stress for bridges between particles of solid to keep strong. The rheological research shows that flocculating structures in concentrate suspensions and in coal flotation suspension are kindred with liquid-like pseudo-plastic systems by nature of flow. The experimentally obtained ultimate dynamic shear stresses depending on dosing of flocculants are comparable with theoretical calculations and differ from the latter by 25% at the most.

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The energy of interaction of particles with dissimilar wettability (quartz, coal, and pyrite) and air bubbles in neutral and alkaline media are analyzed on the basis of the extended DLVO theory to assess the floatability of these minerals. It is established that for hydrophilic materials such as quartz, the formation of particle-bubble complexes (at both the primary, and also secondary potential minima) is impossible owing to existence of a high potential barrier and weak force of attraction. For coal and pyrite, the pattern of the potential curves (energy of interaction versus distance between particle and bubble) will depend largely on the pH of the medium: an increase in this parameter will lead to manifestation of a potential barrier (when pH ≈ 7.8 for coal, and pH ≈ 9.8 for pyrite), and to an increase in its height. This causes unstable flotation of the coal and pyrite even for relatively small changes in the surface potential, pH, and ionic composition of the medium. An increase in the effectiveness of flotation benefication of coal and pyrite can be achieved by hydrophobization of the minerals by reagents-collectors: the wetting angle is increased from 50-80°to 90-100°. In turn, the potential barrier is eliminated, the effect of the pH of the medium is neutralized, and stable attachment of particles of the minerals under consideration to air bubbles is ensured in the region of the secondary potential minimum. Analysis of the forces of particle-bubble interaction made it possible to determine the forces of adhesion and detachment. Computed values of the forces in question for an air-bubble/hydrophobized-pyrite-particles system are comparable to experimental values of the indicated forces for a similar system.In this paper, interaction of air bubbles with the following minerals was examined:• quartz (θ = 20°); • pit coal (θ = 50°); • pyrite (θ = 80°); and • pyrite hydrophobized by hexyl xanthate (θ = 100°). For each of these minerals, calculations were performed for a dispersion medium at two pH levels:• 7 (neutral medium); and • 9 (weakly alkaline medium). Methylisobutylcarbinol (MIBC) served as a frothing reagent: an empirical formula C 6 H 13 OH, molecular mass of 102 kg/kmole, and a concentration of (4-5)·10 -4 kmole/m 3 in the dispersion medium. According to Wang and Yoon [1], K H = 3.4·10 -19 J, A * = 1.2·10 -20 J, and σ = 0.07 N/m for the concentration in question. The medium consisted of an NaCl