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This work reports numerical investigation of lateral migration of a paramagnetic microparticle of an elliptic shape in a plane Poiseuille flow of a Newtonian fluid under a uniform magnetic field by direct numerical simulation (DNS). A finite element method (FEM) based on the arbitrary Lagrangian–Eulerian (ALE) approach is used to study the effects of strength and direction of the magnetic field, particle–wall separation distance and particle shape on the lateral migration. The particle is shown to exhibit negligible lateral migration in the absence of a magnetic field. When the magnetic field is applied, the particle migrates laterally. The migration direction depends on the direction of the external magnetic field, which controls the symmetry property of the particle rotational velocity. The magnitude of net lateral migration velocity over a π cycle is increased with the magnetic field strength when the particle is able to execute complete rotations, expect for α = 45° and 135°. By investigating a wide range of parameters, our direct numerical simulations yield a comprehensive understanding of the particle migration mechanism. Based on the numerical data, an empirical scaling relationship is proposed to relate the lateral migration distance to the asymmetry of the rotational velocity and lateral oscillation amplitude. The scaling relationship provides useful guidelines on design of devices to manipulate nonspherical micro-particles, which have important applications in lab-on-a-chip technology, biology and biomedical engineering.

Numerical Study of Lateral Migration of Elliptical Magnetic Microparticles in Microchannels in Uniform Magnetic Fields