Taylor dispersion of elongated rods

TL;DR

This paper investigates how elongated particles, such as nanorods, disperse in fluid flows, revealing that their shape and flow conditions significantly enhance their longitudinal spreading compared to spherical particles.

Contribution

The study provides a combined numerical and theoretical analysis of elongated particle dispersion, extending Taylor's classical dispersion theory to account for particle shape and flow-induced orientation effects.

Findings

Elongated particles exhibit increased longitudinal dispersion in shear flows.

Alignment with flow in high shear enhances dispersion due to anisotropic diffusivities.

A simple correction factor extends Taylor's dispersion prediction to elongated particles.

Abstract

Particles transported in fluid flows, such as cells, polymers, or nanorods, are rarely spherical. In this study, we numerically and theoretically investigate the dispersion of an initially localized patch of passive elongated Brownian particles constrained to one degree of rotational freedom in a two-dimensional Poiseuille flow, demonstrating that elongated particles exhibit an enhanced longitudinal dispersion. In a shear flow, the rods translate due to advection and diffusion and rotate due to rotational diffusion and their classical Jeffery's orbit. The magnitude of the enhanced dispersion depends on the particle's aspect ratio and the relative importance of its shear-induced rotational advection and rotational diffusivity. When rotational diffusion dominates, we recover the classical Taylor dispersion result for the longitudinal spreading rate using an orientationally averaged translational diffusivity for the rods. However, in the high-shear limit, the rods tend to align with the flow and ultimately disperse more due to their anisotropic diffusivities. Results from our Monte Carlo simulations of the particle dispersion are captured remarkably well by a simple theory inspired by Taylor's original work. For long times and large Peclet numbers, an effective one-dimensional transport equation is derived with integral expressions for the particles' longitudinal transport speed and dispersion coefficient. The enhanced dispersion coefficient can be collapsed along a single curve for particles of high aspect ratio, representing a simple correction factor that extends Taylor's original prediction to elongated particles.