Concentration profiles of ferrofluids in magnetic fields

Abstract

Ferrofluids are dispersion of magnetic nanoparticles which are often used in magnetic field gradients during applications. When the magnetic field gradient is sufficiently strong it can pull magnetic nanoparticles out of solution, an unwanted side effect often described through theory based on ideal point dipoles. In this thesis, a closed form equation for the concentration profile of point dipoles in arbitrary fields is derived. It is found that for magnets much smaller than the fluid column, the concentration of nanoparticles near the magnet exceeds the densest packing fraction. For a better description, concentration profiles accounting for the excluded volume of particles are described with thermodynamic theory. Furthermore, an original theory describing the timescale of the sedimentation towards an equilibrium concentration profile is derived. This theory does not try to solve the full concentration profile as function of time, but rather it describes the flux through a point that starts at the equilibrium concentration. The advantage of this theory is that it can describe the sedimentation of particles with interactions in arbitrary fields. These new theories were used to describe new, original measurements of concentration profiles in magnetized ferrofluids in an analytical centrifuge. The equilibrium theory accounting for excluded volume fits the measured profiles much better than the theory assuming point dipoles. The time-dependent theory matches the experiments reasonably well, both in timescale and average concentration change, with an improvement of two orders of magnitude over a previously reported method [Taketome, Jap.J.Appl.Phys., 1980].