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ИГД » Издательская деятельность » Журнал «Физико-технические проблемы… » Номера журнала » Номера журнала за 2008 год » JMS, Vol. 44, No. 6, 2008

JMS, Vol. 44, No. 6, 2008


A. A. Baryakh, S. B. Stazhevskii, E. A. Timofeev, and G. N. Khan

The reported data confirm applicability of the discrete element method to modeling numerically evolution of the strain state of a rock mass in the vicinity of karst cavities.

Rock mass, karst genesis, discrete element method, strain state

1. G. A. Maksimovich, Fundamentals of Karst Science. Karst Morphology, Speleology and Hydrogeology [in Russian], Vol. 1, Perm Knizhnoe Izd., Perm (1963).
2. Geographic Distribution of Karst Terrain, Cave, Encyclopedia Britannica, 2006, Encyclopedia Britannica Online, 25 Sept, 2006 / htpp://www.britannica.com/eb/article-49702/cave.
3. Construction Norms and Regulations 2.02.01–83. Foundations of Buildings and Constructions [in Russian], Moscow (2000).
4. Construction Norms and Regulations 2.01.15–90. Engineering Protection of Buildings and Constructions from Dangerous Geological Processes. Fundamentals of Planning [in Russian], Moscow (1990).
5. Monitoring Exogenic Geological Processes in the Perm Region [in Russian], GI UrO RAN, Perm (2004).
6. Monitoring Exogenic Geological Processes in the Perm Region [in Russian], GI UrO RAN, Perm (2005).
7. G. N. Khan, «Studies of caving of frozen rocks by the discrete element method,» in: Proceedings of the 3rd International Conference «High Technologies for Mineral Mining and Processing» [in Russian], IGD SO RAN, Novosibirsk (2003).
8. G. N. Khan, «Discrete element method to solve rock mechanics problems related with faults and strain localization,» in: Proceedings of the 3rd International Conference «High Technologies for Mineral Mining and Processing» [in Russian], IGD SO RAN, Novosibirsk (2005).
9. E. P. Rusin, S. B. Stazhevskii, and G. N. Khan, «Geomechanical aspects of exo- and endokarst,» Fiz.-Tekh. Probl. Razrab. Polezn. Iskop., No. 2 (2007).
10. A. F. Revuzhenko, S. B. Stazhevskii, and E. I. Shemyakin, «Structure-dilatancy strength of rocks,» Dokl. Akad. Nauk SSSR [in Russian], 305, No. 5 (1989).
11. P. A. Cundall and O. D. L. Strack, «A discrete numerical model for granular assemblies,» Geotechnique, 29 (1979).
12. G. N. Khan, «On asymmetric regime of rock mass failure in the vicinity of a cavity,» Fiz. Mezomekh. 11, No. 1 (2008).
13. A. F. Revuzhenko, S. B. Stazhevskii, and E. I. Shemyakin, «On mechanism of granular material deformation under large shears,» Fiz.-Tekh. Probl. Razrab. Polezn. Iskop., No. 3 (1974).
14. A. F. Revuzhenko, S. B. Stazhevskii, and E. I. Shemyakin, «Models of rock and soil deformation,» in: Some Problems of Computational and Applied Mathematics [in Russian], Nauka, Novosibirsk (1975).

V. P. Kosykh

The paper describes experimental results for the Savart — Masson effect in a perfect granular medium under shearing. The relationships between displacement jumps, forces, gravitation load and the medium state are determined, and the dynamics of individual jumps is analyzed.

Experiment, granular material shear, deformation diagram, displacement jumps, gravitation load, jump dynamics

1. J. F. Bell, Experimental Foundations of Solid Mechanics, Springer, Berlin, Heidelberg, New York (1973).
2. Yu. I. Golovin, V. I. Ivolgin, and M. A. Lebedkin, «Unstable plastic flow in alloy Al-3%Mg under continuous nanoindentation,» Fiz. Tverd. Tela, 44, No. 7 (2002).
3. A. P. Bobryakov and A. V. Lubyagin, «Experimental investigation into unstable slippage» Fiz.-Tekh. Probl. Razrab. Polezn. Iskop., No. 4 (2008).
4. A. Yu. Loskutov and A. S. Mikhailov, Study Guide, Introduction to Synergetics [in Russian], Nauka, Moscow (1990).
5. G. G. Kocharyan, A. A. Kulyukin, and D. V. Pavlov, «Inter-block deformation in the Earth’s crust: features of dynamics,» Geolog. Geofiz., 47, No. 5 (2006).


P. A. Martynyuk

The author shows that in case the position of an initial fracture is close to orthogonal relative to the maximum compression direction, the minimum opening of the hydraulic fracture takes place at the contour of borehole. A model problem on fracture propagation along the interface of blocks is solved, and the conditions are found when edges of fractures close.

Hydraulic fracture, compression field, fracture path, fracture opening

1. M. P. Savruk, 2D Elastic Problems for Bodies with Fractures [in Russian], Naukova Dumka, Kiev (1981).
2. G. V. Basheev, P. A. Martynyuk, and E. N. Sher, «Influence of the direction and value of the external stress field on the paths of a stellular mesh of fractures,» Prikl. Mekh. Tekh. Fiz., No. 5 (1994).
3. V. V. Panasyuk, Limit Equilibrium of Brittle Bodies with Fractures [in Russian], Naukova Dumka, Kiev (1986).
4. T. E. Alekseeva and P. A. Martynyuk, «Crack emergence trajectories at a free surface,» Fiz.-Tekh. Probl. Razrab. Polezn. Iskop., No. 2 (1991).
5. P. A. Martynyuk and E. N. Sher, «Development of a crack close to a circular opening with an external field of compressive stresses,» Fiz.-Tekh. Probl. Razrab. Polezn. Iskop., No. 6 (1996).
6. P. A. Martynyuk and E. N. Sher, «Trajectory of crack formed by hydraulic fracturing near the contact of productive stratum with enclosing rocks,» Fiz.-Tekh. Probl. Razrab. Polezn. Iskop., No. 4 (2002).
7. V. V. Zubkov, V. F. Koshelev, and A. M. Lin’kov, «Numerical modeling of hydraulic fracture initiation and development,» Fiz.-Tekh. Probl. Razrab. Polezn. Iskop., No. 1 (2007).

S. V. Muchnik

The author describes the construction of an explosion booster composed of a waveguide and a membrane. The booster is placed at the bottom of a blast hole and is initiated by detonation wave. Experimental underground tests of explosion boosters showed the qualitative ore blasting results, in particular, with fan-patterned blast hole drilling.

Explosion booster, blast hole fan, detonation wave, ore blasting

1. I. A. Krasnopol’skii, V. M. Kuznetsov, V. D. Petrenko, and A. F. Shatsukevich, «Rock failure by blast hole and bore-hole charges,» in: Blasting. Collected Works No. 83/40. Measurement Procedure and Instrumentation for Blast Action Investigation [in Russian], Nedra, Moscow (1982).
2. S. V. Muchnik and Yu. D. Chugunov, «Vibrator application to improve blasting in the periphery of bore-hole fans,» Gorny Zh., No. 12 (2001).
3. A. A. Adkhamov, T. M. Muinov, and Z. A. Kabilov, «Variation in durability of a polymer in the ultrasound field,» Dokl. Akad. Nauk, Tadzhik SSR [in Russian], 16, No. 9 (1973).
4. E. V. Shumilova, V. V. Semenov, et al., «Investigation of the ultrasound effect on the gas — coal system,» Razrab. Mest. Polezn. Iskop., No. 35, Naukova Dumka, Kiev (1974).
5. M. A. Margulis, «Relationship of the sonochemical reaction velocity and ultrasound wave intensity,» Zh. Fiz. Khim., 48, No. 9 (1974).


A. S. Kondratenko and A. M. Petreev

The paper illustrates experimental determination of the effect exerted on core removal from a pipe by the initial moisture of the core, squeeze force and impact energy. An adequate numerical model of the system «pipe — earth core» is presented to describe gradual core removal from the pipe during the principal and stages of the pipe cleaning.

Trenchless technologies, impact driving, earth core, displacement velocity, moisture, friction, calculation model

1. N. Ya. Kershenbaum and V. I. Minaev, Horizontal and Vertical Percussive Hole-Making [in Russian], Nedra, Moscow (1984).
2. A. P. Ryabakov, «Foundations of trenchless technologies,» Press-Byuro, No. 1 (2005).
3. B. N. Smolyanitskii, V. V. Chervov, V. V. Trubitsyn, I. V. Tishchenko, and I. E. Veber, «Russian Federation Patent No. 3120997. The method and device for earth core removal from pipes,» Byull. Izobret., No. 15 (1999).
4. I. I. Blekhman, What the Vibration Can Do? [in Russian], Nauka, Moscow (1988).
5. A. S. Kondratenko, «Determination of influencing variables on the capacity of pipe cleaning from earth core,» in: Proceedings of the 3rd International Conference on Problems in the Current Mechanics of Machines [in Russian], 1, VSGTU, Ulan-Ude (2006).
6. O. D. Alimov, V. P. Manzhosov, and V. E. Erem’yants, Deformation Wave Propagation in Impact Systems [in Russian], Nauka, Moscow (1985).
7. B. N. Stikhanovskii, Mechanics of Impact [in Russian], OmGTU, Omsk (2002).
8. A. M. Petreev and P. N. Tambovtsev, «Impact loading of a hard rock via plastic substance in a drill hole,» Fiz.-Tekh. Probl. Razrab. Polezn. Iskop., No. 6 (2006).
9. M. V. Kurlenya, V. N. Oparin, and V. I. Vostrikov, «Anomalously low friction in block media,» Fiz.-Tekh. Probl. Razrab. Polezn. Iskop., No. 1 (1997).
10. V. I. Vostrikov, V. N. Oparin, and V. V. Chervov, «On some features of solid-body motion under combined vibro-wave and static actions,» Fiz.-Tekh. Probl. Razrab. Polezn. Iskop., No. 6 (2000).
11. V. P. Gileta, «Design and improvement of air-percussive devices for vibro-impact driving of pipes,» Theses of Cand. Tech. Sci. [in Russian], IGD SO AN, Novosibirsk (1987).


V. N. Oparin, A. P. Tapsiev, and A. M. Freidin

The authors analyzed various criteria that are used in different classifications of mining methods and systems. It is shown that today’s complex geomechanical situation of mining at large depths and wide application of mobile machinery to mineral exploitation has brought to nothing the erstwhile practical importance of many geotechnologies. The modern trend-based classification of the underground ore mining methods is proposed.

Classification criterion, mining method, caving, backfill, combined geotechnology

1. N. I. Trushkov, Ore Mining [in Russian], 2, Metallurgizdat (1947).
2. M. I. Agoshkov, Calculating and Designing Ore Mining Methods and Technologies [in Russian], Nauka, Moscow (1965).
3. O. A. Baikonurov, Classification and Selection of Underground Mining Methods [in Russian], Nauka, Alma-Ata (1969).
4. V. R. Imenitov, Underground Ore Mining Methods [in Russian], Nedra, Moscow (1978).
5. D. M. Bronnikov, N. F. Zamesov, and G. I. Bogdanov, Deep Ore Mining [in Russian], Nedra, Moscow (1982).
6. V. N. Oparin, E. P. Rusin, A. P. Tapsiev, et al., World Experience Gained in Underground Mining Automation [in Russian], SO RAN, Novosibirsk (2007).
7. Yu. Yu. Pilenkov, A. M. Freidin, A. V. Antipov, «Estimation of natural impact of the origination of rockburst hazard at shallow depths,» in: Rock Pressure and Underground Ore Mining Technology for Large Depths [in Russian], IPKON AN SSSR, Moscow (1990).
8. R. B. Yun, V. I. Gerasimenko, and V. N. Malyshev, «Dynamic rock pressure manifestations at Zheskazgan deposit,» Gorny Zh., No. 3 (1997).
9. N. F. Zamesov, «Influence of the ground control on the design of the mining method for gentle ore formations,» in: Problems of Underground Ore Mining at Large Depths [in Russian], IPKON AN SSSR, Moscow (1979).
10. V. I. Khomyakov, Foreign Experience of Mining with Backfill [in Russian], Nedra, Moscow (1984).
11. A. M. Freidin, S. A. Neverov, A. A. Neverov, et al., «Mine stability with application of sublevel caving schemes,» J. Min. Sci. 44, No. 1 (2008).

D. R. Kaplunov and M. V. Ryl’nikova

The authors describe a new scientific-technical approach to projecting the integrated development of ore deposits with combining physico-technical and physicochemical geotechnologies. The paper generalizes the theoretical backbone of integrated subsoil development, presents the modern concept and principles of projecting the combined physico-technical and physicochemical geotechnology, and shows mining-and-engineering systems for integrated ore extraction with an expanded geotechnological cycle.

Integrated development, combined geotechnology, natural and technogenic georesources, mining-and-engineering system, projecting, open-pit mine, underground mine, leaching

1. K. N. Trubetskoy (Ed.), Mining Science. Development of Preservation of the Earth’s Bowels [in Russian], Akad. Nauk, Moscow (1977).
2. D. R. Kaplunov, V. N. Kalmykov, and M. V. Ryl’nikova, Combined Geotechnology [in Russian], «Ruda Metally» Publishing House, Moscow (2003).
3. K. N. Trubetskoy and D. R. Kaplunov (Eds.), Problems of Geotechnological Processes in Integrated Development of Super Ore Formations [in Russian], IPKON RAN, Moscow (2005).
4. K. N. Trubetskoy and D. R. Kaplunov (Eds.), Challenges of Comprehensive Development of Super Strategic Mineral Deposits [in Russian], IPKON RAN, Moscow (2006).

E. V. Freidina, A. A. Botvinnik, and A. N. Dvornikova

The paper sets forth scientific foundations and organizational-technical environment offered by ISО 9000 standards that are oriented to product quality management and, thus, product quality planning. The authors describe the results of coal product quality planning with using the QFD methodology, present a model of coal quality control through the coal product life cycle and mining technologies. It is proposed to evaluate the quality management efficiency by the coefficient of concordance between the product quality and consumer’s demands.

Quality management, quality index, product life cycle, production charting, quality management model, concordance of quality and consumer’s demands

1. Russian State Standard R ISO 9001 — 2001, Quality Management System. Requirements [in Russian], Gosstandart Rossii, Moscow (2001).
2. Russian State Standard R 9004 — 2001, Quality Management System [in Russian], Gosstandart Rossii, Moscow (2001).
3. E. V. Freidina, «Selecting a coal energy valuation index,» Fiz.-Tekh. Probl. Razrab. Polezn. Iskop., No. 6 (1997).
4. O. P. Gludkin, N. M. Gorbunov, A. I. Gurov, and Yu. L. Zorin, Total Quality Management. Study Guide [in Russian], INFRA-M, Moscow (2000).
5. S. George and A. Weimerskirch, Total Quality Management: Strategy and Techniques Proven at Today’s Most Successful Companies, John Wiley&Sons, New York (1994).
6. V. Alekseev, «Using QFD in product development,» Met. Mened. Kach., No. 8 (2004).
7. Yu. V. Bragin and V. F. Korol’kov, QFD: Product Planning and Production as Judged by Consumers’ Expectations [in Russian], NNOU «Tsentr Kachestva,» Yaroslavl (2003).
8. K. N. Trubetskoi, A. A. Peshkov, and N. A. Matsko, «Cost-effectiveness evaluation methods for mining enterprises,» Ekonomika Mat. Metody, 31, No. 2 (1995).
9. W. J. Stevenson, Production/Operations Management, 4th Edition, Irwin, Boston, MA (1993).
10. A. A. Botvinnik and A. N. Dvornikova, «Mineral structuring methods based on geoinformation techniques,» Gorn. Inform.-Analit. Byull., No. 9 (2005).
11. E. V. Freidina, A. S. Tret’yakov, and A. N. Dvornikova, «Principles of organization and operational planning of extraction operations with quality control,» Fiz.-Tekh. Probl. Razrab. Polezn. Iskop., No. 3 (1981).
12. E. V. Freidina, A. S. Tret’yakov, and S. G. Molotilov, Current Planning Methods for Surface Mining [in Russian], IGD SO AN SSSR, Novosibirsk (1989).
13. M. I. Shchadov, E. V. Freidina, A. A. Botvinnik, and A. N. Dvornikova, «System quality control in open mining and processing of coals,» Ugol, No. 3 (2002).
14. E. V. Freidina and A. N. Dvornikova, «Conditioning of large open cast coal mines to consumership,» Otkryt. Raboty, No. 2 (2002).
15. E. V. Freidina, A. N. Dvornikova, and A. S. Tret’yakov, «Evaluating the utilization of coking coal reserves,» Fiz.-Tekh. Probl. Razrab. Polezn. Iskop., No. 5 (1997).

А. S. Tanaino

A multifactor classification of rocks by drillability is proposed based on canonical representation of the mechanical and structural properties of rocks by the dimensionless characteristics of rock fracture resistance.

Drillability, canonical scale of failure, mechanical and structural properties of rocks

1. K. N. Trubetskoi, M. G. Potapov, K. E. Vinitskii, N. N. Mel’nikov, et al., Open-Pit Mining. Handbook [in Russian], Gornoe Byuro, Moscow (1994).
2. N. M. Fedorovskii, Classification of Minerals by Energy Parameters [in Russian], Izd. AN SSSR, Moscow, Leningrad (1935). 3. V. V. Rzhevsky and G. Ya. Novik, Fundamentals of Rock Physics [in Russian], Nedra, Moscow (1985).
4. B. A. Simkin, B. N. Kutuzov, and V. D. Butkin, Drilling at Open-Pits. Handbook [in Russian], Nedra, Moscow (1990).
5. www. drillings.ru.
6. N. I. Lyubimov, Principles of Classification and Efficient Rock Breaking in Exploration Drilling [in Russian], Nedra, Moscow (1967).
7. A. S. Tanaino, «Rock classification by drillability. Part I: Analysis of available classifications,» Fiz.-Tech. Probl. Razrab. Polezn. Iskop., No. 6 (2005).
8. G. V. Artsimovich, Mechanophysical Fundamentals of Development of Rock Breaking Drilling Tools [in Russian], Nauka, Novosibirsk (1985).
9. Yu. F. Alekseev, Use of the Data on Mechanical and Abrasive Rock Properties in Drilling Operations [in Russian], Nedra, Moscow (1968).
10. M. R. Mavlyutov, Rock Failure in Hole-Making Process [in Russian], Nedra, Moscow (1978).
11. L. A. Shreiner, Hardness of Brittle Bodies [in Russian], Izd. AN SSSR, Moscow, Leningrad (1949).
12. GOST 12288–66. Rocks. Method for Evaluation of Mechanical Properties by Indenting a Die.
13. L. I. Baron, Rock Hardness Indexes [in Russian], Nauka, Moscow (1972).
14. L. I. Baron and L. B. Glatman, Contact Rock Strength [in Russian], Nedra, Moscow (1966).
15. A. S. Tanaino, «Classification of half-rocks and hard rocks by strength parameters,» Vest. KuzGTU, No. 2 (2008).
16. V. N. Oparin, A. S. Tanaino, and V. F. Yushkin, «Discrete properties of entities of a geomedium and their canonical representation,» Fiz.-Tekh. Probl. Razrab. Polezn. Iskop., No. 3 (2007).
17. M. V. Ratz, Heterogeneity of Rocks and Their Physical Properties [in Russian], Nauka, Moscow (1968).
18. V. Ryka and A. Malishevskaya, Lithological Dictionary, Tr. from Polish, Nedra, Moscow (1989).
19. M. A. Solodukhin and I. V. Arkhangel’skii, Handbook for Engineering-Geology and Hydrogeology Technicians [in Russian], Nedra, Moscow (1982).
20. M. V. Kurlenya and V. N. Oparin, «Scale factor of phenomenon of zonal disintegration of rock and canonical series of atomic and ionic radii,» Fiz.-Tekh. Probl. Razrab. Polezn. Iskop., No. 2 (1996).
21. V. N. Oparin, V. F. Yushkin, A. A. Akinin, and E. G. Balmashnova, «A new scale of hierarchically structured representations as a characteristic for ranking entities in a geomedium,» Fiz.-Tekh. Probl. Razrab. Polezn. Iskop., No. 5 (1998).
22. www. siams.com
23. I. Kh. Bikbulatov, R. A. Maksutov, G. S. Abdrakhmanov, and B. P. Mikhailov, «Evaluation of rock porosity by mechanical drilling speed,» in: TatNIPIneft Transactions [in Russian], Issue XXXVII, Bugulma (1977).
24. A. I. Spivak, Rock Abrasiveness [in Russian], Nedra, Moscow (1972).
25. I. A. Tangaev, Drillability and Blastability of Rocks [in Russian], Nedra Moscow (1978).
26. I. A. Tangaev, Energy Intensity of Mineral Mining and Processing [in Russian], Nedra, Moscow (1986).
27. D. B. Simakov, «Substantiation of rational crushing grade in open pit mining,» Thesis of Cand. Tech. Sci. [in Russian], Magnitogorsk (2007).
27. Z. T. Bieniawski, «The geomechanics classification of rock engineering applications,» in: Proceedings of the 4th Congress on Rock Mechanics, 2, ISRM, Montreux (1979).
29. Z. T. Bieniawski, Engineering Rock Mass Classification, John Wiley&Sons (1989).


A. E. Krasnoshtein, B. P. Kazakov, and A. V. Shalimov

The paper presents the methods for the numerical modeling of complex air-gas-heat dynamic processes that take place in underground mines. It is shown that modeling the condensate moisture migration, air movement due natural draft as well as heat and smoke propagation during fire may be based upon the earlier developed conjugate model of heat exchange between mine air and a rock mass. The qualitative and quantitative analysis of the effect exerted by thermal compressions of air in shafts on the air movement in mines is performed.

Air distribution, heat exchange, condensation, evaporation, natural draft thermal depressions, mine microclimate, heat transfer coefficient, reversal, Laplace transform

1. G. A. Maksimovich and G. V. Bel’tyukov, «Formation and migration of condensate brains in the potassium mine workings,» in: Geology and Hydrogeology of Salt Deposits [in Russian], Leningrad (1972).
2. A. E. Krasnoshtein, B. P. Kazakov, and A. V. Shalimov, «Modeling phenomena of non-stationary heat exchange between mine air and a rock mass,» Fiz.-Tekh. Probl. Razrab. Polezn. Iskop., No. 5 (2007).
3. O. A. Kremnev, «Heat exchange between ventilation air and rock masses in old mines and workings,» in: Trudy ITE AN USSR, No. 10 (1954).
4. A. F. Voropaeva, Theory of the Heat Exchange Between Mine Air and Rocks in Deep Mines [in Russian], Nedra, Moscow (1966).
5. Yu. P. Ol’khovikov, Supporting Permanent Workings in the Potassium and Salt Rock Masses [in Russian], Nedra, Moscow (1984).
6. A. E. Krasnoshtein, B. P. Kazakov, and A. V. Shalimov, «Modeling non-stationary gas admixture flow in excavations under recirculating airing,» Fiz.-Tekh. Probl. Razrab. Polezn. Iskop., No. 1 (2006).
7. A. M. Krasyuk and I. V. Lugin, «Ventilation modes in inflammation of train in a subway,» Fiz.-Tekh. Probl. Razrab. Polezn. Iskop., No. 4 (2005).
8. A. E. Krasnoshtein, B. P. Kazakov, and A. V. Shalimov, «Mathematical modeling of heat exchange between mine air and rock mass during fire,» Fiz.-Tekh. Probl. Razrab. Polezn. Iskop., No. 3 (2006).

A. M. Krasyuk and I. V. Lugin

The in situ test data on the evaluation of temperatures in tunnel lining and lining-adjacent soil are presented for shallow subways located in the severe continental climate conditions. The procedure for calculating heat balance in the tunnels is proposed.

Shallow subway, tunnel, soil, temperature, heat exchange

1. A. M. Krasyuk, Metro Tunnel Aeration [in Russian], Nauka, Novosibirsk (2006).
2. Construction Standards and Regulations 32–02–203: Metros [in Russian], Gosstroi Rossii, Moscow (2004).
3. D. V. Zedgenizov and I. V. Lugin, «Airing effect on temperature conditions in linings of shallow subway tunnels,» Gorn. Inform.-Analit. Byull. MGGU, Appendix on Safety (2005).
4. A. M. Krasyuk, «Calculation of tunnel ventilation in shallow subways,» Fiz.-Tekh. Probl. Razrab. Polezn. Iskop., No. 3 (2005).


S. A. Kondrat’ev

It is demonstrated that the basic factor, identifying the capability to form a flotation complex, is the availability of a reagent sorbed physically on a particle surface and promoting the thinning-down of water interlayer between a mineral particle and a bubble at final stages of their approach. The numerical evaluation of the effect of physically sorbed collector on variations in the velocity of water discharge from an interlayer, partitioning a mineral particle and a gas bubble at the moment of their meeting is given.

Flotation, mineral particle, gas bubble, water interlayer, water discharge velocity

1. A. A. Abramov, Fundamentals of Optimization of Selective Sulfide Ore Flotation [in Russian], Nedra, Moscow (1978).
2. P. F. Whelan and D. J. Brown. «Particle-bubble attachment in froth flotation,» Bulletin of the Institute of Mining and Metallurgy, No. 591 (1956).
3. S. S. Dukhin, N. N. Rulev, and D. S. Dimitrov, Coagulation and Dynamics of Thin Films [in Russian], Naukova Dumka, Kiev (1986).
4. S. A. Kondratiev and A. S. Izotov, «Effect of apolar reagents and surfactants on the stability of a flotation complex,» Fiz.-Tech. Probl. Razrab. Polezn. Iskop., No. 4 (2000).
5. B. T. Emtsev, Technical Hydromechanics [in Russian], Mashinostroeniye, Moscow (1987).
6. A. F. Taggart, Mineral Processing. Handbook [in Russian], Vol. 2, Gos. Nauchno-Tekhn. Izd., Moscow (1933).
7. D. G. Suciu., O. Smigelschi, and E. Ruckenstein, «The spreading of liquids on liquids,» J. Colloid and Interface Sci., 33, No. 4 (1970).
8. B. V. Zhelezny, «Allowance for rheological peculiarities of thin layers of Newtonian fluids in motion equations,» Colloid. Zh., 38, No.5 (1976).
9. I. A. Kakovskii and V. M. Apashkevich, «Studies of organic disulfide properties,» in: Proceedings of the 8th International Mineral Processing Congress [in Russian], Leningrad (1969).
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