Friction Drag on a Particle Moving in a Nematic Liquid Crystal

TL;DR

This study computationally investigates the anisotropic drag force on a sphere in a nematic liquid crystal, aligning well with experimental results and exploring effects of anchoring and phase transitions.

Contribution

It provides a detailed computational analysis of drag anisotropy in nematic liquid crystals, including effects of anchoring and phase transitions, which was not extensively studied before.

Findings

Drag force anisotropy ratio ~1.5 matches experiments

Weak anchoring effects are minimal for most applications

Behavior near nematic-isotropic transition is characterized

Abstract

The flow of a liquid crystal around a particle does not only depend on its shape and the viscosity coefficients but also on the direction of the molecules. We studied the resulting drag force on a sphere moving in a nematic liquid crystal (MBBA) in a low Reynold's number approach for a fixed director field (low Ericksen number regime) using the computational artificial compressibility method. Taking the necessary disclination loop around the sphere into account, the value of the drag force anisotropy (F_\perp/F_\parallel=1.50) for an exactly computed field is in good agreement with experiments (~1.5) done by conductivity diffusion measurements. We also present data for weak anchoring of the molecules on the particle surface and of trial fields, which show to be sufficiently good for most applications. Furthermore, the behaviour of the friction close to the transition point nematic <-> isotropic and for a rod-like and a disc-like liquid crystal will be given.