This study investigates magnetization relaxation effects in ferrofluids using a coupled molecular dynamics and Lattice Boltzmann simulation framework. The model incorporates dipole-dipole and short-range (Lennard-Jones) interactions between particles, couples hydrodynamic interactions, and employs a bidisperse model for particle distribution. The magnetization component along the magnetic field direction, Mx*, increases and saturates with the Langevin parameter αL. However, larger shear rates γ* or pressure differences P* (beyond a threshold) slow this saturation due to the greater difficulty larger particles face in aligning with the magnetic field. The off-field magnetization component My*, arising from relaxation, exhibits a non-monotonic dependence on αL, first increasing and then decreasing under shear and pressure difference. This behavior is attributed to the evolving chain-like microstructures within the ferrofluid at different field intensities. Higher particle concentrations φm or dipole coupling parameters λ lead to larger maximum values of My*. The competition between the magnetic field and shear flow, along with shear-rate-dependent chain size distributions, leads to a larger γ* requires a stronger magnetic field for My* to peak, and the peak value itself increases with γ*. The pressure difference P* influences magnetization by modifying the local shear rate distribution, with its hydrodynamic effects becoming significant only after P* exceeds a critical value.
Yang et al. (Sun,) studied this question.