Effect of weak fluid inertia upon Jeffery orbits

Area of Science:

• Fluid dynamics
• Particle dynamics
• Rheology

Background:

• Neutrally buoyant axisymmetric particles exhibit Jeffery orbits in viscous shear flow when inertia is negligible.
• The behavior of these particles under inertial effects is not fully understood, leading to simulation interpretation puzzles.

Purpose of the Study:

• To investigate how inertial effects perturb Jeffery orbits.
• To derive an equation of motion for spheroidal particles at low shear Reynolds numbers.
• To analyze the stability of the log-rolling orbit and its dependence on particle shape.

Main Methods:

• Perturbative solution of coupled particle-flow equations.
• Analysis of equations of motion at small shear Reynolds numbers.
• Linear stability analysis of specific particle orbits.

Main Results:

• Inertial effects lift the degeneracy of Jeffery orbits.
• An equation of motion is derived for spheroidal particles with arbitrary aspect ratios at small shear Reynolds numbers.
• The log-rolling orbit is found to be unstable for prolate spheroids.

Conclusions:

• Inertia significantly alters particle rotation dynamics, destabilizing Jeffery orbits for certain shapes.
• The findings resolve discrepancies in direct numerical simulations.
• Unsteady and nonlinear terms in Navier-Stokes equations are critical for accurate modeling.