First-principles magnetization relaxation equation of interacting ferrofluids with applications to magnetoviscous effects

Abstract

Magnetization relaxation equation (MRE) plays a primary role in numerous phenomena and applications involving ferrofluid dynamics. However, as yet there exist no MREs derived from first principles and applicable to concentrated and strongly interacting ferrofluids. In this paper, we derive a novel MRE based on the projection operator technique. It sufficiently accounts for interparticle correlations beyond the scope of previous models. The MREs by Martsenyuk, Raikher, and Shliomis and by Zubarev and Yushkov (ZY), respectively, for ideal and weakly nonideal (WNI) ferrofluids, are recovered as low-order approximations. We also investigate the magnetoviscous effects. For the first time, we unveil qualitatively the different roles played by short- and long-range interparticle correlations. The long-range correlation effect dominates in a WNI ferrofluid, and both our MRE and the ZY model are in quantitative agreement with simulations on field-dependent rotational viscosity. However, for strongly nonideal ferrofluids, short-range correlations can become substantial and compete with long-range correlations to reduce rotational viscosities. Our MRE is the first dynamic model faithfully capturing both short- and long-range correlations, thereby applicable to ferrofluids characterized by a broad range of concentrations and interacting strengths. It is expected to be a cornerstone for quantitative modeling of the dynamic response of ferrofluids to external fields or flow deformations. Because most commercial ferrofluids are designed to be strongly nonideal to enhance magnetic response, our theory may provide fresh insights for applications of realistic ferrofluids in industry and biomedicine.