Based on numerical results of dynamic susceptibility, a simple theory of the dynamic response of a ferrofluid to an ac magnetic field is obtained that includes both the effects of interparticle dipole-dipole interactions and the dependence on field amplitude. Interparticle interactions are incorporated in the theory using the so-called modified mean-field approach. The new theory has the following important characteristics: in the noninteracting regime at a weak ac field, it gives the correct single-particle Debye theory results; it expands the applicability of known theories valid for high concentrations [Ivanov, Zverev, and Kantorovich, Soft Matter 12, 3507 (2016)] or large values of ac field amplitudes [Yoshida and Enpuku, Jpn. J. Appl. Phys. 48, 127002 (2009)], in accordance with their applicability. The susceptibility spectra are analyzed in detail. It is demonstrated that interparticle dipole-dipole interactions and an increase in field amplitude have an opposite effect on the dynamic response of ferrofluids, so that at certain field amplitudes, relaxation processes in the system of interacting particles are determined by the characteristic relaxation times for an ideal paramagnetic gas. The new theory correctly predicts the dynamic susceptibility and characteristic relaxation times of a ferrofluid at high ac field amplitudes as long as the Langevin susceptibility ${\chi }_L\lesssim 1$, which is a complex characteristic of ferrofluid density and the intensity of interparticle dipole-dipole interactions.

• Received 14 July 2021
• Accepted 20 September 2021

DOI:https://doi.org/10.1103/PhysRevE.104.044604