# Preferential sampling enabled by particle finite size and anisotropic shape

## TL;DR

This study demonstrates that finite size and anisotropic shape of particles can cause preferential sampling in flow fields, independent of inertia, with simulation evidence showing length-dependent sampling patterns and flow nonlinearity effects.

## Contribution

The paper provides analytical and simulation evidence that finite size and shape alone induce preferential sampling, highlighting the role of flow nonlinearity and particle length.

## Key findings

- Preferential sampling occurs due to finite size and shape, not inertia.
- Rod length increases the tendency to sample specific flow regions.
- Chaotic trajectories emerge as rod length increases, linked to flow nonlinearity.

## Abstract

Anisotropic, finite-sized particles, common in environmental and industrial flows, exhibit complex dynamics distinct from those of small, spherical particles. Their shape introduces orientation-dependent forces, and their finite size affects how they experience the flow field. While the effects of particle inertia are known to cause preferential sampling, in this study we consider whether preferential sampling can arise due to finite size and shape alone by considering inertialess rods using slender-body theory. First, we show analytically that preferential sampling can only occur in this limit given the presence of three ingredients: finite particle size, anisotropic particle shape, and a nonlinear flow field. Next, to demonstrate this effect, we simulate rods in a steady 2D cellular flow: the Taylor-Green vortex flow. By analyzing the rod trajectories, we find that rods do indeed preferentially sample areas of both high and low vorticity, corresponding to the fixed points of the flow: the high vorticity cell centers and the low vorticity saddle points in the corners of each cell. This preferential sampling increases with increasing rod length. We also analyze the same data with respect to the flow's nonlinearity (i.e. curvature) to find that the rods preferentially sample the linear regions of the flow and undersample the nonlinear regions. Finally, we analyze the nonlinear dynamics of this system, showing that chaotic trajectories appear as the rod length increases, and that these chaotic regions in the flow also tend to overlap with higher flow nonlinearity. Overall, we show how finite size and anisotropic shape alone can cause particles to preferentially sample a flow field, and that this preferential sampling is highly linked to the flow's nonlinearity.