Anisotropic particle in viscous shear flow: Navier slip, reciprocal symmetry, and Jeffery orbit

Jiaolong Zhang, Xinpeng Xu, Tiezheng Qian*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

14 Scopus citations

Abstract

The hydrodynamic reciprocal theorem for Stokes flows is generalized to incorporate the Navier slip boundary condition, which can be derived from Onsager's variational principle of least energy dissipation. The hydrodynamic reciprocal relations and the Jeffery orbit, both of which arise from the motion of a slippery anisotropic particle in a simple viscous shear flow, are investigated theoretically and numerically using the fluid particle dynamics method [Phys. Rev. Lett. 85, 1338 (2000)PRLTAO0031-900710.1103/PhysRevLett.85.1338]. For a slippery elliptical particle in a linear shear flow, the hydrodynamic reciprocal relations between the rotational torque and the shear stress are studied and related to the Jeffery orbit, showing that the boundary slip can effectively enhance the anisotropy of the particle. Physically, by replacing the no-slip boundary condition with the Navier slip condition at the particle surface, the cross coupling between the rotational torque and the shear stress is enhanced, as manifested through a dimensionless parameter in both of the hydrodynamic reciprocal relations and the Jeffery orbit. In addition, simulations for a circular particle patterned with portions of no-slip and Navier slip are carried out, showing that the particle possesses an effective anisotropy and follows the Jeffery orbit as well. This effective anisotropy can be tuned by changing the ratio of no-slip portion to slip potion. The connection of the present work to nematic liquid crystals' constitutive relations is discussed.

Original languageEnglish
Article number033016
JournalPhysical Review E
Volume91
Issue number3
DOIs
StatePublished - 26 Mar 2015
Externally publishedYes

Fingerprint

Dive into the research topics of 'Anisotropic particle in viscous shear flow: Navier slip, reciprocal symmetry, and Jeffery orbit'. Together they form a unique fingerprint.

Cite this