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Hydrodynamic flows induced by localized torques (rotlets) in wedge-shaped geometries

Abdallah Daddi-Moussa-Ider1,*, Jakob Mihatsch2, Michael J. Mitchell1, Elsen Tjhung1, and Andreas M. Menzel2,†

  • *Contact author: abdallah.daddi-moussa-ider@open.ac.uk
  • †Contact author: a.menzel@ovgu.de
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Phys. Rev. Fluids 11, 034101 – Published 2 March, 2026

DOI: https://doi.org/10.1103/44n5-2jyb

Abstract

Wedge-shaped geometries in low-Reynolds-number flows are of increasing importance, for instance, in the design of microfluidic devices. The corresponding Green's functions describing the induced flow in response to a locally applied force were derived some time ago. To achieve a complete characterization of particle motion at low Reynolds numbers, we derive the flow response to locally applied torques. This is accomplished through a direct calculation based on the Fourier-Kontorovich-Lebedev transform using the Papkovich-Neuber representation of the hydrodynamic fields. We then illustrate the resulting flow fields, highlighting their structure, key features, and dependence on the geometry and orientation of the applied torque. Based on these solutions, we compute the corresponding hydrodynamic mobility tensor that couples torque and motion. Owing to the broken spatial symmetry imposed by the wedge-shaped confinement, a particle subjected to a torque will experience not only rotational motion, but also translational motion. These results provide analytical tools relevant for predicting and controlling particle behavior in confined microfluidic environments.

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Outline

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Phys. Rev. Fluids 11, 034101– Published 2 March, 2026
  • Received 18 November 2025
  • Accepted 10 February 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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