Abstract
We numerically investigated the dynamics of a paramagnetic elliptical particle immersed in a low Reynolds number Poiseuille flow in a curved channel and under a uniform magnetic field by direct numerical simulation. A finite element method, based on an arbitrary Lagrangian-Eulerian approach, analyzed how the channel geometry, the strength and direction of the magnetic field, and the particle shape affected the rotation and radial migration of the particle. The net radial migration of the particle was analyzed after executing a rotation and at the exit of the curved channel with and without a magnetic field. In the absence of a magnetic field, the rotation is symmetric, but the particle-wall distance remains the same. When a magnetic field is applied, the rotation of symmetry is broken, and the particle-wall distance increases as the magnetic field strength increases. The causation of the radial migration is due to the magnetic angular velocity caused by the magnetic torque that constantly changes directions during particle transportation. This research provides a method of magnetically manipulating non-spherical particles on lab-on-a-chip devices for industrial and biological applications.
Highlights
Applying magnetic fields to separate magnetic micro- and nanoparticles by shape immersed in a fluid is a long searched for achievement in biomedical and industrial applications, such as cell separation [1,2], drug deliverance [3,4], mining ores [5], and waste management [6]
We focus on a two-dimensional study for an elliptical particle in low Reynolds number, Poiseuille flows in a curved channel, and under a uniform magnetic field
We have compared some of our results to an elliptical particle in the absence of a magnetic field observed in Appendix C
Summary
Applying magnetic fields to separate magnetic micro- and nanoparticles by shape immersed in a fluid is a long searched for achievement in biomedical and industrial applications, such as cell separation [1,2], drug deliverance [3,4], mining ores [5], and waste management [6]. The method of magnetic separation in these industries stems from the use of magnetophoresis, i.e., magnetic forces. Passive methods to separate particles by shape and size have been studied through inertial effects in curved channels by the primary flow (influenced by the Reynolds number) and secondary flow (influenced by the Deans number). The separation of particles by shape and size are caused by vortices due to the cross-sectional shape of the channel including trapezoidal [13,15,16,18], or rectangular [8,9,10,11,12,14,17,19,20], and caused by the magnitude of the Deans number, Reynolds number, and the hydraulic diameter. Additional strategies include a more active approach on particle separation or particle movement in curved channels, such as dielectrophorsis [21,22] and magnetophoresis [23]
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