High gradient magnetic separation with involved Basset history force: Configuration with single axial wire

Abstract High gradient magnetic separation (HGMS) is an efficient and useful technique for the recovery of weakly magnetized microparticles. Usually the process of magnetic particle capture is considered to be governed by competition between the magnetic attraction of the particles to the magnetized wires, the Stokes viscous drag, and gravitational force on the particle. For the complete description of the motion of magnetic microparticles we have used the Maxey-Riley integro-differential equation containing also additional forces. We have therefore analysed the importance of these forces, especially the Basset history force and the added mass force, using an axial single wire HGMS filter with a bounded flow field. As has been found, magnitude of the Basset history force is largest in the close proximity to ferromagnetic wire, when the acceleration of microparticles is highest due to the large value of magnetic force. Including the Basset history force term into the description of the movement of a spherical magnetic particle in the moving fluid under the influence of the external magnetic force causes an expected deceleration of its movement. For example, relative capturing delay reaches values up to 10% (in absolute values few hundreds of microseconds). The obtained results clearly demonstrate the importance of these, usually neglected forces for the correct description of capture dynamics.