Diffusion-jump model for the combined Brownian and Néel relaxation dynamics of ferrofluids in the presence of external fields and flow

Abstract

ArticleAccepted Version Ilg, P. (2019) Diffusionjump model for the combined Brownian and Neel relaxation dynamics of ferrofluids in the presence of external fields and flow. Physical Review E, 100 (2). 022608.Relaxation of suspended magnetic nanoparticles occurs via Brownian rotational diffusion of the particle as well as internal magnetization dynamics. The latter is often modeled by the stochastic Landau-Lifshitz equation, but its numerical treatment becomes prohibitively expensive in many practical applications due to a time-scale separation between fast, Larmor-type precession and slow, barrier-crossing dynamics. Here, a diffusion-jump model is proposed to take advantage of the timescale separation and to approximate barrier-crossings as thermally activated jump processes that occur alongside rotational diffusion. The predictions of our diffusion-jump model are compared to reference results obtained by solving the stochastic Landau-Lifshitz equation coupled to rotational Brownian motion. Good agreement is found in the regime of high energy barriers where Néel relaxation can be considered a thermally activated rare event. While many works in the field have neglected Néel relaxation altogether, our approach opens the possibility to efficiently include Néel relaxation also into interacting many-particle models.

Dynamics of interacting magnetic nanoparticles: effective behavior from competition between Brownian and Néel relaxation

“…21 Recently, a diffusion-jump model was proposed to efficiently model internal Néel relaxation as a thermally activated jump process alongside the Brownian rotational diffusion of the MNPs. 22 For non-interacting MNPs, good agreement with the underlying model of Shliomis and Stepanov was found over a reasonable range of model parameters.…”

“…We here follow ref. 22 and assume sufficiently large magnetic anisotropy energies k that the magnetic moments are well-aligned with the particle's easy axis, u i = AEn i , so that the transition rates w vanish unless u i 0 = Àu i .…”

“…To answer these questions, we build on the model proposed in ref. 22 and perform extensive Brownian dynamics simulations of the translational and rotational dynamics of interacting dipolar particles coupled to thermally activated Néel relaxation processes for a broad range of concentrations and dipolar interaction strengths.…”

Effects of interactions on magnetization relaxation dynamics in ferrofluids

“…The latter is strongly influenced by the viscosity of the carrier liquid and the interactions between the particles. The dynamics of magnetic relaxation have been the subject of several experimental [28][29][30][31][32][33][34][35][36][37] and simulation [38][39][40][41][42][43][44][45][46] studies. Theoretically, the influence of the interactions on the so-called dynamic (or frequency-dependent) initial magnetic susceptibility has been evaluated within various approaches [41,42,[47][48][49][50][51][52][53][54].…”

“…Second, simulating Brownian and Néel relaxation simultaneously in a bulk system is computationally laborious due to the presence of very different characteristic timescales. Efforts have been made to simulate efficiently both types of relaxation in single particles and clusters of particles [45]. Brownian-dynamics simulations are therefore used here as idealized "experiments," in which the nonmagnetic interactions between particles are prescribed, and complicating factors arising from polydispersity and Néel relaxation are eliminated.…”