An anisotropic particle in a simple shear flow: an instance of chaotic scattering

TL;DR

This paper investigates how the flow topology around anisotropic particles like spheroids differs from spheres in shear flows, revealing complex pathline structures that impact transport and suspension rheology.

Contribution

It demonstrates that the flow topology around a neutrally buoyant spheroid is fundamentally different from that around a sphere, affecting transport and rheological properties.

Findings

Flow topology around spheroids differs significantly from spheres.

The topology influences scalar transport in shear flows.

Implications for rheology of suspensions of anisotropic particles.

Abstract

In the Stokesian limit, the streamline topology around a single neutrally buoyant sphere is identical to the topology of pair-sphere pathlines, both in an ambient simple shear flow. In both cases there are fore-aft symmetric open and closed trajectories spatially demarcated by an axisymmetric separatrix surface. This topology has crucial implications for both scalar transport from a single sphere, and for the rheology of a dilute suspension of spheres. We show that the topology of the fluid pathlines around a neutrally buoyant freely rotating spheroid, in simple shear flow, is profoundly different, and will have a crucial bearing on transport from such particles in shearing flows. To the extent that fluid pathlines in the single-spheroid problem and pair-trajectories in the two-spheroid problem, are expected to bear a qualitative resemblance to each other, the non-trivial trajectory topology identified here will also have significant consequences for the rheology of dilute suspensions of anisotropic particles.