Effects of magnetization relaxation in ferrofluid film flows under a uniform magnetic field

Abstract

We analyze the magnetization relaxation effects of a ferrofluid film flow governed by the ferrohydrodynamics encompassing the Fokker–Planck magnetization equation in a Couette–Poiseuille configuration subject to an applied uniform stationary magnetic field perpendicular to the boundaries. A solver based on OpenFOAM is programmed to find solutions numerically for the velocity, spin velocity, and magnetization in ferrofluid films under the combined pressure gradient, boundary flow, and magnetic field forcing. The solver is validated by comparison with the classical Couette–Poiseuille flows and the analytic solutions of the magnetization relaxation problem when the product of flow vorticity and relaxation time is much smaller than unit, ΩτB≪1. We compare the effects of magnetization relaxation obtained from the phenomenological magnetization equation with those from the equation derived microscopically. The results obtained from the former equation are not suitable for the description of ferrofluid film flows. Due to the magnetization relaxation effects, a misalignment between the local magnetization and the local magnetic field is observed. The net effects are that the flow is hampered by magnetic fields and it manifests as diminished slopes of vorticity profiles and reduced volumetric flow rates. The magnetization relaxation effects also slow down the spin velocity of particles or change their direction, which leads to an enhanced effective viscosity. The total tangential stress exerted on the moving boundary is higher than that of the classical Couette–Poiseuille flow owing to the addition of a magnetic stress. The magnetization relaxation effect is more significant in cases of ferrofluids with higher relaxation times.