A numerical perspective on the relation between particle rotational inertia and the equilibrium magnetization of a ferrofluid

Abstract This work explores, from a numerical perspective, the role of particle rotational inertia on the magnetization dynamics of ferrofluids. A robust numerical method is used for this purpose. The numerical research code is based on the use of a convergent long range dipolar interactions technique. These interactions are computed through a sophisticated Ewald summation procedure. The balance of linear and angular momentum is solved for N ensembles containing N particles each. Long range dipolar magnetic torques are solved in a periodic system of Lattices, spread in physical and reciprocal spaces to assure the convergence on the calculation of the suspension transport properties. A small effect of particle rotational inertia is considered. The system of equations of N particles distributed randomly in space is solved simultaneously for different parallel realizations in order to achieve a meaningful statistics of our many-body system. The results are focused on the behavior of the suspension magnetization for different particle concentrations and intensities of rotational inertia. The physical parameter used to express this effect is the particle rotational Stokes number. The simulations indicate that, from a numerical perspective, rotational inertia may induce a relevant, but often neglected, effect on the magnetization equilibrium of a ferrofluid. This finding is relevant for the community of numericists interested in using Langevin Dynamics applied to dipolar suspensions. We propose an expression with a correction on the effect of the particle rotational inertia to compute the magnetization of a magnetic fluid. The results obtained in this work are compatible with some insights previously pointed out in former scientifical works.