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Dynamics of Paramagnetic and Ferromagnetic Ellipsoidal Particles in Shear Flow under a Uniform Magnetic Field
Physical Review Fluids
  • Christopher A. Sobecki
  • Jie Zhang
  • Yanzhi Zhang, Missouri University of Science and Technology
  • Cheng Wang, Missouri University of Science and Technology

We investigate the two-dimensional dynamic motion of magnetic particles of ellipsoidal shapes in shear flow under the influence of a uniform magnetic field. In the first part, we present a theoretical analysis of the rotational dynamics of the particles in simple shear flow. By considering paramagnetic and ferromagnetic particles, we study the effects of the direction and strength of the magnetic field on the particle rotation. The critical magnetic-field strength, at which particle rotation is impeded, is determined. In a weak-field regime (i.e., below the critical strength) where the particles execute complete rotations, the symmetry property of the rotational velocity is shown to depend on the direction of the magnetic field. In a strong-field regime (i.e., above the critical strength), the particles are impeded at steady angles and the stability of these angles is examined. Under a uniform field, paramagnetic and ferromagnetic particles behave differently, in terms of the critical strength, symmetry property of the rotational velocity, and steady angles. In the second part, we use two-dimensional numerical simulations to study the implications of rotational dynamics for lateral migration of the particles in wall-bound shear flows. In the weak-field regime, the paramagnetic prolate particles migrate away when the field is applied perpendicular to the flow and towards the bounded wall when the field is applied parallel to the flow. Ferromagnetic particles exhibit negligible migration under fields that are parallel or perpendicular to the flow. The different lateral migration behaviors are due to the difference in the symmetry property of particle rotational velocity. In the strong-field regime, the particles are impeded at different stable steady angles, which result in different lateral migration behaviors as well. The fundamental insights from our work demonstrate various feasible strategies for manipulating paramagnetic and ferromagnetic particles.

Mathematics and Statistics
Second Department
Mechanical and Aerospace Engineering
Keywords and Phrases
  • Ferromagnetic materials,
  • Ferromagnetism,
  • Magnetic bubbles,
  • Magnetic field effects,
  • Paramagnetism,
  • Rotation, Critical magnetic field,
  • Ellipsoidal particles,
  • Ferromagnetic particles,
  • Rotational dynamics,
  • Rotational velocity,
  • Symmetry properties,
  • Two-dimensional numerical simulation,
  • Uniform magnetic fields, Shear flow
Document Type
Article - Journal
Document Version
Final Version
File Type
© 2018 American Physical Society, All rights reserved.
Publication Date
Citation Information
Christopher A. Sobecki, Jie Zhang, Yanzhi Zhang and Cheng Wang. "Dynamics of Paramagnetic and Ferromagnetic Ellipsoidal Particles in Shear Flow under a Uniform Magnetic Field" Physical Review Fluids Vol. 3 Iss. 8 (2018) ISSN: 2469-990X
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