Electromagnetic interaction between a rising spherical particle in a conducting liquid and a localized magnetic field

Lorentz force velocimetry (LFV) is a non-contact electromagnetic flow measurement technique for electrically conductive liquids. It is based on measuring the flow-induced force acting on an external permanent magnet. Motivated by extending LFV to liquid metal two-phase flow measurement, in a first test we consider the free rising of a non-conductive spherical particle in a thin tube of liquid metal (GaInSn) initially at rest. Here the measured force is due to the displacement flow induced by the rising particle. In this paper, numerical results are presented for three different analytical solutions of flows around a moving sphere under a localized magnetic field. This simplification is made since the hydrodynamic flow is difficult to measure or to compute. The Lorentz forces are compared to experiments. The aim of the present work is to check if our simple numerical model can provide Lorentz forces comparable to the experiments. The results show that the peak values of the Lorentz force from the analytical velocity fields provide us an upper limit to the measurement results. In the case of viscous flow around a moving sphere we recover the typical time-scale of Lorentz force signals. (paper)