Finite Elements and Integro-Differential Methods Are Equivalent for Description of Rotational Dynamics of Spherical Particle During Its Magnetic Alignment

Rotational dynamics of spherical micro-particle in a strong external magnetic field and water as a liquid medium during the particle’s alignment was numerically modeled using two different descriptive approaches. The first is the solution of the Navier-Stokes equations using the finite element method (FEM). And the second is the solution of an integro-differential equation (IDE) for torques experienced on particle, particularly governing magnetic torque and quasi-steady viscous torque and its history non-local addition due to unsteadiness of particle rotation, inertia, viscosity and friction with the non-Basset kernel, described recently [A. Krafcik et al. Appl. Sci. 11(20) (2021) 9651]. As we have shown, both approaches are in good agreement and fully equivalent for the studied model.