Features of mathematical modeling of electromagnetic processing of bulk materials

Yuri Zaporozhets, Nina Batechko, Sergey Shostak, Natalia Shkoda, Emilia Dibrivna


The article notes the features of applying the general equations of mathematical physics of an elliptic type in problems of modeling specific phenomena of the interaction of electromagnetic fields with elements and particles of an inhomogeneous dispersed medium. Such phenomena take place in installations for the separation of organic and mineral raw materials or the electromagnetic treatment of grain, seeds, etc. This is relevant, because the usual approach to the formulation of mathematical models in these problems, which is mainly based on differential equations of field theory in a simplified form, does not always adequately reflect the physical essence of the mentioned phenomena. Therefore, it limits the possibilities of an in-depth study of the influence of many factors determining the final results of separation and electromagnetic processing (EMP) processes. In the present work, an alternative approach is proposed based on the use of integral equations of field theory, which is based on the concept of primary and secondary field sources and can significantly reduce the order of the system of equations for the numerical implementation of algorithms for solving EMP problems, and the total amount of necessary computing resources. With this approach, local parameters of the field in interaction with individual particles and their influence on one another become available for calculation. This aspect is essential for determining the technological characteristics of EMP production installations. The presented mathematical model, in contrast to the common simplified approaches to determining the field parameters and ponderomotive forces acting on the particles of matter in the field, adequately reflects the physical laws of the distribution of potentials and electric field strength of real charges and induced sources. Due to this, it clearly reproduces the mechanism of the formation of the main components of mechanical forces acting on the polarized body from the side of the electric field as a whole, through the densities of elementary forces with which the field acts on surface charges induced in dielectric bodies in the field of action of the fields. Such a mathematical model is a universal and compact tool for analysis, design, and optimization of various installations and devices that use an electric field and its electromechanical interaction with the medium and individual bodies


electromagnetic treatment; dispersed materials; mathematical modeling; electric field; particles; substance; force

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