## Abstract

We present an Euler–Lagrange approach for simulating magneto-Archimedes separation of almost neutrally buoyant spherical particles in the ﬂow of a paramagnetic liquid, which is of direct relevance for separating different types of plastic by magnetic density separation.

A four-way coupled point-particle method is employed where all relevant interactions between an external magnetic ﬁeld, a magnetic ﬂuid and discrete immersed particles are taken into account. Particle–particle interaction is modelled by a hard-sphere collision model which takes the interstitial ﬂuid effects into account. First, the motion of rigid spherical particles in a paramagnetic liquid is studied in single- and two-particle systems.

We ﬁnd good agreements between our numerical results and experiments performed in a paramagnetic liquid exposed to a non-homogeneous magnetic ﬁeld, also in the case of two colliding particles. Next, we investigate the magneto-Archimedes separation of particles with different mass densities in many-particle systems interacting with the ﬂuid.

Our results reveal that history effects and interparticle interactions signiﬁcantly inﬂuence the levitation dynamics of particles and have a detrimental impact on the separation performance. We also investigate the effect of particle size and initial distribution on the separation performance. Results show that a reduction in the particle size from 4 to 2 mm leads to a 40 % increase in the separation time. Moreover, preseparation of particles into two groups of light and heavy particles decreases the separation time by 33 %. The presented method is shown to be a robust and efﬁcient computational framework for the investigation of particle-laden ﬂows of magnetically responsive ﬂuids.

A four-way coupled point-particle method is employed where all relevant interactions between an external magnetic ﬁeld, a magnetic ﬂuid and discrete immersed particles are taken into account. Particle–particle interaction is modelled by a hard-sphere collision model which takes the interstitial ﬂuid effects into account. First, the motion of rigid spherical particles in a paramagnetic liquid is studied in single- and two-particle systems.

We ﬁnd good agreements between our numerical results and experiments performed in a paramagnetic liquid exposed to a non-homogeneous magnetic ﬁeld, also in the case of two colliding particles. Next, we investigate the magneto-Archimedes separation of particles with different mass densities in many-particle systems interacting with the ﬂuid.

Our results reveal that history effects and interparticle interactions signiﬁcantly inﬂuence the levitation dynamics of particles and have a detrimental impact on the separation performance. We also investigate the effect of particle size and initial distribution on the separation performance. Results show that a reduction in the particle size from 4 to 2 mm leads to a 40 % increase in the separation time. Moreover, preseparation of particles into two groups of light and heavy particles decreases the separation time by 33 %. The presented method is shown to be a robust and efﬁcient computational framework for the investigation of particle-laden ﬂows of magnetically responsive ﬂuids.

Original language | English |
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Article number | A52 |

Number of pages | 35 |

Journal | Journal of Fluid Mechanics |

Volume | 910 |

DOIs | |

Publication status | Published - 22 Jan 2021 |

## Keywords

- Particle separation
- Magnetic density separation
- Particlle-laden flows
- Magneto-Archimedes levitation
- History force
- Direct numerical simulation
- computational methods
- particle/fluid flow
- magnetic fluids