Floating of dia-, para-, and superparamagnetic bodies in magnetic fluids: Analysis of wall effects in the framework of inductive approach

Abstract

Laboratory experiments and numerical simulations were carried out to investigate physical patterns and main characteristics of the magnetic ponderomotive buoyancy force acting on solid dia-, para-, and superparamagnetic bodies immersed in cylindrical containers filled with magnetic fluids and magnetized by a uniform magnetic field. The experimental measurements of the magnetic buoyancy force validated with numerical simulations are reliable enough for use in the benchmark testing of various applications (ferrofluid sensors, measuring devices, separators, etc.). It is shown that the superparamagnetic bodies have one (stable) equilibrium position in the center of the container in virtue of the fact that the ponderomotive force is monotonous. The non-magnetic bodies have an unstable equilibrium position in the center of the container and the force is non-monotonous with two extrema due to the competition between two mechanisms: the inhomogeneous demagnetizing field inside the cylindrical container, and the interaction of the non-magnetic body dipole with its own mirror image. Due to this competition, the force can change its direction depending on the geometry of the container, the applied magnetic field, and the nonlinear ferrofluid magnetization law. The results demonstrate that the non-magnetic bodies may be in stable equilibrium near the container walls only if two independent conditions are met: the gradient demagnetizing field is weak (the container is wide or quasi-ellipsoidal), and the applied field is weak (the ferrofluid magnetization curve is quasi-linear). If any of these conditions is abandoned, then the non-magnetic body is unable to levitate and falls on the container wall.