Il'chenko A.V. Magnetic properties of multicomponent heterogeneous media with a doubly periodic structure

Abstract

Heterogeneous media have a wide range of practical applications. Media with a doubly periodic structure (matrices of high-gradient magnetic separators, etc.) occupy an important place. Their study is usually based on experimental and approximate methods and is limited to simple two-phase systems. The development of universal and accurate methods of mathematical modelling of electrophysical processes in such environments is an urgent task The aim of the paper is to develop a method for calculating local and effective parameters of a magnetostatic field with minimal restrictions on the number of phases, their geometry, concentration, and magnetic properties. Based on the theory of elliptic functions and secondary sources, an integral equation is formulated with respect to the magnetization vector of the elements of the main parallelogram of the periods. The calculated expressions for the complex potential, field strength, and components of the effective magnetic permeability tensor are obtained The results of a series of computational experiments confirming the universality and effectiveness of the method are presented As an example of a practical application, a detailed study of the field of the magnetic forces of the matrix is carried out: the lines of magnetic isocline and potential extraction areas for a complex version of the matrix are constructed Within the framework of the developed method, the calculation of local and effective field characteristics is carried out by solving the field problem in the field of an arbitrary parallelogram of periods without specifying boundary conditions on its sides with a comprehensive consideration of significant interdependent factors. The practical value of the method is to create new opportunities for improving the technical characteristics of electrophysical devices for which the universality and accuracy of calculating local and effective field characteristics is decisive. An algorithm for optimizing the characteristics of the separator is proposed.