Oscillatory shear response of dilute ferrofluids: Predictions from rotational Brownian dynamics simulations and ferrohydrodynamics modeling

Abstract

Ferrofluids are colloidal suspensions of magnetic nanoparticles that exhibit normal liquid behavior in the absence of magnetic fields but respond to imposed magnetic fields by changing their viscosity without loss of fluidity. The response of ferrofluids to constant shear and magnetic fields has received a lot of attention, but the response of ferrofluids to oscillatory shear remains largely unexplored. In the present work we used rotational Brownian dynamics to study the dynamic properties of ferrofluids with thermally blocked nanoparticles under oscillatory shear and constant magnetic fields. Comparisons between simulations and modeling using the ferrohydrodynamics equations were also made. Simulation results show that, for small rotational Péclet number, the in-phase and out-of-phase components of the complex viscosity depend on the magnitude of the magnetic field and frequency of the shear, following a Maxwell-like model with field-dependent viscosity and characteristic time equal to the field-dependent transverse magnetic relaxation time of the nanoparticles. Comparison between simulations and the numerical solution of the ferrohydrodynamic equations shows that the oscillatory rotational magnetoviscosity for an oscillating shear field obtained using the kinetic magnetization relaxation equation quantitatively agrees with simulations for a wide range of Péclet number and Langevin parameter but has quantitative deviations from the simulations at high values of the Langevin parameter. These predictions indicate an apparent elastic character to the rheology of these suspensions, even though we are considering the infinitely dilute limit in which there are negligible particle-particle interactions and, as such, chains do not form. Additionally, an asymptotic analytical solution of the ferrohydrodynamics equations, valid for Pe<<2, was used to demonstrate that the Cox-Merz rule applies for dilute ferrofluids under conditions of small shear rates. At higher shear rates the Cox-Merz rule ceases to apply.

Theoretical predictions for spatially-focused heating of magnetic nanoparticles guided by magnetic particle imaging field gradients

“…To obtain the time dependent magnetization for the calculation of the energy dissipation rate, we solve the phenomenological magnetization equation derived by Martsenyuk, Raikher, and Shliomis (hereafter referred to as the MRSh equation)[27]. This equation takes into account the effect of field strength on the relaxation time and is valid at moderate to high field amplitudes and frequencies [31, 32], that is, conditions where the magnetic response of the nanoparticles is no longer linear with the applied magnetic field and for particles relaxing by the Brownian mechanism. In our earlier work [33], we have used the MRSh equation to model the properties of magnetic nanoparticles in a magnetic particle spectrometer and have obtained good agreement with experiments.…”

Ferrohydrodynamic modeling of magnetic nanoparticle harmonic spectra for magnetic particle imaging

“…However, this equation has been shown to be inaccurate in predicting the magnetoviscous response of ferrofluids at moderate field magnitude and frequency. 19,20 For fields comparable to those employed in the MPS, another magnetization equation (the MRSh equation) was derived microscopically from the Fokker-Planck equation by Martsenyuk et al 12 They employed an effective-field method, which resulted in closure of the first moment of magnetization, resulting in…”

Multiparticle Collision Dynamics for Ferrofluids

“…In particular, we employ the classical model of ferrofluid dynamics of rigid dipoles proposed in Ref. 4 and widely studied since 8,27,28 . In the freedraining limit and neglecting inter-particle interactions, the torque balance of viscous, magnetic, and Brownian torques reads…”