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The particle settling velocity is the feature of separation in such processes as flowing classification and jigging. It characterizes material forwarded to the separation process and belongs to the so-called complex features because it is the function of particle density and size. i.e. the function of two simple features. The affiliation to a given subset is determined by the values of two properties and the distribution of such feature in a sample is the function of distributions of particle density and size. The knowledge about distribution of particle settling velocity in jigging process is as much important factor as knowledge about particle size distribution in screening or particle density distribution in dense media beneficiation.

The paper will present a method of determining the distribution of settling velocity in the sample of spherical particles for the turbulent particle motion in which the settling velocity is expressed by the Newton formula. Because it depends on density and size of particle which are random variable of certain distributions, the settling velocity is a random variable. Applying theorems of probability, concerning distributions function of random variables, the authors present general formula of probability density function of settling velocity for the turbulent motion and particularly calculate probability density function for Weibull’s forms of frequency functions of particle size and density. Distribution of settling velocity will calculate numerically and perform in graphical form.

The paper presents the simulation of calculation of settling velocity distribution on the basis of real distributions of density and projective diameter of particles assuming that particles are spherical.

Abraham F.F., 1970. Functional dependence of drag coefficient of a sphere on Reynolds number. Phys. Fluids, 13, 2194-2195.

Akkerman J.E., 1966. Free settling velocity of mineral particles in liquids. Preparation of ores, 6, 22-25, (in Russian).

Bedran N.G., Denisenko A.I, Pilov P.I., 1976. Calculation of free settling velocity of mineral particles in liquid medium. Journal of Mining, 9, 141-144, (in Russian).

Briens C.L., 1991. Correlation for the direct calculation of the terminal velocity of spherical particles in newtonian and pseudoplastic (power-law) fluids. Powder Technology, 67, 87-91.

Brożek M., 1995. The distribution of selected physical properties in the crushed material. Arch. Min. Sci., Vol. 40, p. 83-100.

Brożek M., Surowiak A., 2004. Distribution of settling velocity of particles in samples of mineral raw materials. Mineral Resources Management, 20, 67-84.

Brożek M., Surowiak A., 2005a. The distribution of settling velocity of non-spherical mineral particles. Acta Montanistica Slovaca, 10, 27-32.

Brożek M., Surowiak A., 2005b. The dependence of distribution of settling velocity of spherical particles on the distribution of particle sizes and densities. Physicochemical Problems of Mineral Processing, 39,199-210.

Brożek M., Surowiak A., 2010. Argument of separation at upgrading in the jig. Arch. Min. Sci., Vol. 55, p. 21-40.

Chrisiansen E.B., Barker D.E., 1965. The effect of shape and density on the free settling of particles at high Reynolds numbers. AIChE Journal, 11, 145-151.

Concha F., Almendra E.R., 1979. Settling velocities of particulate systems, 1, Settling velocities of individual spherical particles. Int. J. Mineral Processing, 5, 349-367.

Finkey J., 1924. Die wissenschaftlichen Grundlagen der nassen Erzaufbereitung. Verlag Springer, Berlin, (in Germany).

Gerstenkorn T., Śródka T., 1972. Kombinatoryka i rachunek prawdopodobieństwa. PWN, Warszawa.

Heider A., Levenspiel O., 1989. Drag coefficient and terminal velocity of spherical and non-spherical particles. Powder Technology, 58, 63-70.

Heiss J.F., Coull J., 1952. On the settling velocity of non-isometric particles in a viscous medium. Chemical Engineering Progress, 48, 133-140.

Kuprin A.I., Klesznin A.A., Fedorenko, G.I., 1983, Influence of bed porosity on jigging efficiency. Journal of Mining, 4, 129-132, (in Russian).

Lashtchenko P.V., 1940. Gravity concentration method. Gostoptechizdat, Moskva, (in Russian).

Madhav G.V., Chhabra R.P., 1994. Settling velocities of non-spherical particles in non-Newtonian polymer solutions. Powder Technology, 78, 77-83.

Madhav G.V., Chhabra R.P., 1995. Drag on non-spherical particles in viscous fluids. Int. J. Mineral Processing, 43, 15-29.

Mayer F.W., 1964. Fundamentals of a potential theory of the jigging process. Proc. VII IMPC, New York, 75-86.

Merinov N.F., 2001. Theoretical aspects of gravity separation. Journal of Mining, no 4-5, 33-46, (in Russian).

Nguyen-van A., Schulze H.J, Kmet S., 1994. A simple algorithm for the calculation of the terminal velocity of a single solid sphere in water. Int. J. Mineral Processing, 41, 305-310.

Nguyen-van A., Stechemasser H., Zobel G., Schulze H.J., 1997. An improved formula for terminal velocity of rigid spheres. Int. J. Mineral Processing, 50, 53-61.

Olajossy A., 1995. Nature and meaning of forces occurring in the problems of gravitational enrichment. Arch. Min. Sci., Vol. 40, p. 247-265.

Olevskij V.A., 1953. On free settling velocity of particles in liquid medium. Papers of Mechanobr Institute, 88-96, (in Russian).

Ponomariev K.K., 1973. Group of differential equations. Press by Minsk High School, Minsk, (in Russian).

Saha G., Purohit N.K., Mitra A.K., 1992. Spherical particle terminal settling velocity and drag in Bingham liquids. Int. J. Mineral Processing, 36, 273-281.

Samylin N.A., Zolotko A.A., Poczinok V.V., 1976. Jigging. Izd. Nedra, Moscov, (in Russian).

Surowiak A., 2014. Influence of particle density distributions of their settling velocity for narrow size fractions. Mineral Resources Management, 30 (in press), (in Polish).

Sztaba K., 1992. Problems of taking into account shapes of mineral grains in flow classficacation. Proc. I Int. Conf. Modern Process Mineralogy and Mineral Processing, Beijing, China, 322-328.

Sztaba K., 2004. Influence of grain size upon falling velocity. Physicochemical Problems of Mineral Processing, 38, 207-220.

Tsakalakis K.G., Stamboltzis G.A., 2001. Prediction of the settling velocity of irregularly shaped particles. Minerals Engineering, 14, 349-357.

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