Calculation of Interaction Forces Between Two Nonlinearly Magnetizable Particles

Purpose. Calculation of the magnetic interaction forces of a pair of nonlinearly magnetized particles arbitrarily located in a uniform external magnetic field. Description of differences in the calculation of interparticle forces using other models.

Methods. The magnetostatic problem for two spherical nonlinearly magnetized particles placed in a uniform magnetic field was transformed by iterative algorithm to a sequence of linear magnetostatic problems, which, in turn, were solved by the finite element method. The computer code that implements the specified algorithm is written in python using the esys.escript library. The obtained energy data were interpolated by splines. Numerical differentiation was used to calculate the forces.

Results. In results data of energy and forces arising between particles were obtained in a wide range of parameters characterizing the problem: the distance between the centers of the particles, the external field intensity, and the angle of the pair relative to the field. The conclusion about attraction between particles as the predominant type of interaction in MRE is confirmed. Compared to previous works, the contribution of the tangential component of the magnetic interaction forces has been significantly refined. The inability of the model of nonlinear interacting dipoles to give a correct estimate of the interaction forces in the considered range of fields for pair of particles located at an angle to the external magnetic field is revealed.

Conclusion. The concept of the magnitude and direction of forces acting between particles located at an angle to the applied magnetic field has been expanded. The necessity of an analytical formula that would describe the dependence of the energy of particles on all three parameters is substantiated: the distance between their centers, the external field, and the angle of rotation relative to this field.

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