REC «Mekhanobr-tekhnika» (Russia); Institute of Problems of Mechanical Engineering, Russian Academy of
Sciences (Russia):

Blekhman I. I., Doctor of Physical and Mathematical Sciences, Professor, Head of Laboratory, iliya.i.blekhman@gmail.com

Blekhman L. I., Ph. D. in Engineering Sciences, Leading Researcher, liblekhman@yandex.ru

Vasilkov V. B., Doctor of Engineering Sciences, Leading Researcher, vlvasilkov@yandex.ru

Yakimova K. S., Ph. D. in Engineering Sciences, Leading Researcher, yakimova_ks@npkmt.spb.ru

The results of the theoretical studies on loose material mixture vibratory gradient segregation condition, discovered by the authors, are reported. A mathematical model of separation devices, based on application of this effect, is presented. The model is a diffusion equation that takes into account a deterministic factor’s effect, e.g., force of gravity. The equation is solved subject to the appropriate initial conditions and boundary conditions. The established relationships correspond to the known empirical dependence (damped exponential curve) of fine size fraction average concentration upon screen longitudinal coordinate. With that, dependence of quantity in exponent upon main parameters was revealed. Earlier this index had been determined through experimental data. The established formulae reflect the main factor providing for development of new high-capacity vibratory screens, distinguished by intensive sieving process through screening media (sieves) installed on side walls and employing more intensive vibration (with acceleration amplitude of about 10 g and over). These formulae also permit to estimate effects of geometric parameters and, to some extent, vibration parameters, upon process rate in the separation devices in question.
The authors are indebted to L. А. Vaisberg for effectual assistance and significant comments in implementation of this work.
The work was performed with the financial aid from the Ministry of Education and Science of the Russian Federation (the Project No. 14.576.21.0015; unique identifier RFMEFI57614X0015).

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