Long-time anomalous swimmer diffusion in smectic liquid crystals

TL;DR

This paper investigates how active particles move in smectic liquid crystals, revealing a unique long-time diffusion behavior characterized by a logarithmic tail in the mean-square displacement, influenced by director fluctuations.

Contribution

It introduces a hydrodynamic theory and simulation results showing the distinct long-time anomalous diffusion of swimmers in smectic liquid crystals, different from isotropic or nematic fluids.

Findings

MSD transverse to the director shows a logarithmic tail at long times.

Diffusion behavior differs significantly from isotropic or nematic fluids.

Director fluctuations play a crucial role in long-time swimmer dynamics.

Abstract

The dynamics of self-locomotion of active particles in aligned or liquid crystalline fluids strongly deviates from that in simple isotropic media. We explore the long-time dynamics of a swimmer moving in a three-dimensional smectic liquid crystal and find that the mean-square displacement (MSD) transverse to the director exhibits a distinct logarithmic tail at long times. The scaling is distinctly different from that in an isotropic or nematic fluid and hints at the subtle but important role of the director fluctuation spectrum in governing the long-time motility of active particles. Our findings are based on a generic hydrodynamic theory and Brownian dynamics computer simulation of a three-dimensional soft mesogen model.