Modeling of the Particle Build-Up Evolution on a Single-Wire Magnetic Capture from Axial Stream Flow

Abstract

The kinetic equation of the accumulation of magnetic particles from axial flow on a magnetized ferromagnetic wire in an external homogeneous magnetic field has been developed in this study. A new differential equation of the evolution of the accumulation radius over time, which considers both the capture and the detachment of the particles in the accumulation profile on the wire, has been formulated. The evolution of the radius of the accumulation profile over time was obtained from both the differential kinetic equation based on population theory and from the stochastic Fokker–Planck equation. In the limit approach (t→∞), it was observed that the expressions of the saturation radius of the accumulation radius on the magnetized wire of the particles obtained from both models were the same. It is emphasized that the obtained results are valid for both the initial and steady-state build-up of the particle capture process. These results were compared with the experimental results from the literature, and it was observed that the theoretical and experimental results were in good agreement. The effects of both capture and detachment events on the accumulation of particles on the magnetized wire were evaluated.