## ON A MATHEMATICAL MODEL DESCRIBING OPTIMAL PROCESSING MECHANISM OF DISPERSED GRANULAR MATERIALS IN GRAVITATIONAL FLOW WITH HORIZONTAL OR INCLINED VIBRATING SIEVE CLASSIFYING SCREENS

##manager.scheduler.building##: Atbrivosanas aleja 115, k-4 (Faculty of Engineering)

##manager.scheduler.room##: Room 013

Last modified: 01.06.2017

#### Abstract

The investigation of motion and gravitational processing of disperse granular materials is very important for solution of a wide spectrum of technological processes, including the chemical technology of treatment (with or without the decoration-compression procedure) of granular mineral fertilizers and their drying and sorting/separation by means of vibrating sieve classifying screens, in particular. In this work, we have used the apparatus of the theory of continuous media for the mathematical modelling of dynamics of disperse granular materials, and by this we assume that a property of these materials is the distribution of a solid granular component inside of them. The elaborated mathematical model is based on the volume conservation law for granular components, on the momentum conservation law, as well as on the equations for stress tensor in the granular mineral fertilizers and equations for description of the Coulomb granular mineral fertilizers.

#### Keywords

#### References

[1] I. I. Blekhman, *Vibration Mechanics*. Moscow, Russian Federation: Science, 1994, 374 p.

[2] P. V. Klassen, I. G. Grishaev, and I. P. Shomin, *Granulation*. Moscow, USSR: Chemistry, 1991, 240 p.

[3] V. M. Dmitriyev, E. A. Sergeyeva, L. S. Tarova, and S. P. Rudobashta, "The Mathematical Modelling of Mass Transfer in Polydisperse Granular Materials Used in Environment Protection", Herald of the TSU, vol. 9, No. 4, pp. 456-460, 2004.

[4] S. Savage, "Gravity Flow of Cohesionless Granular Materials in Chutes and Channels", Journal of Fluid Mechanics, vol. 92, No. 1, pp. 53-96, 1979.

[5] P. Evesque, "A Simple Incremental Modelling of Granular-Media Mechanics", Poudres & Grains, vol. 9, pp.1-12, 1999.

[6] A. L. Svistkov and B. Lauke, "Differential Constitutive Equations of Incompressible Medium at Finite Strains", Applied Mechanics and Theoretical Physics, vol. 50, No. 3, pp. 158-170, 2009.

[7] F. G. Akhmadiev and R. F. Gizzjatov, "Mathematical modelling and optimization of separation processes of disperse materials multistoreyed sith classifier", Proceedings of the Kazan State University of Architecture and Engineering, vol. 18, No. 4, pp. 330-340, 2011.

[8] A. Lyav, *Mathematical Theory of Elasticity*. Moscow, USSR: ONTI, 1935, 647 p.

[9] H. Deresiewicz, "Mechanics of Granular Matter", Advances in Applied Mechanics, vol. 5, pp. 233-306, 1958.

[10] M. Faraday, "On a Peculiar Class of Acoustical Figures; and on Certain Forms Assumed by Groups of Particles upon Vibrating Elastic Surfaces", Philosophical Trans. Royal Soc. London, vol. 52, pp. 299-340, 1831.

[11] O. Reynolds, "On the Dilatancy of Media Composed of Rigid Particles in Contact", The London, Edinburgh and Dublin Philosophical Magazine and Journal Science, vol. 20, No. 127, pp. 469-483, 1885.

[12] H. M. Jaeger and S. R. Nagel, "Physics of the Granular State", Science, vol. 255, No. 3, pp. 1523-1531, 1995.

[13] P. K. Haff, "Grain Flow as a Fluid-Mechanical Phenomenon", Journal of Fluid Mechanics, vol. 134, pp. 401-430, 1992.

[14] P. W. Rowe, The Stress Dilatancy Relation for Static Equilibrium of an Assembly of Particles in Contact", Proceedings of the Royal Society of London, A269, pp. 500-527, 1962.

[15] J. C. Dutertre and H. F. Winterkorn, "Shear Phenomena in Natural Granular Materials", Princeton Soil Engineering Resources, Series 6, Princeton University Press, Princeton, USA, Contract No AFCRRL-66-771, 1966.