Long-ranged order and flow alignment in sheared $p-$atic liquid crystals

TL;DR

This paper develops a hydrodynamic theory for p-atic liquid crystals, revealing long-range order and flow alignment phenomena in sheared two-dimensional anisotropic fluids with discrete rotational symmetry.

Contribution

It introduces an order parameter tensor tailored for p-atic phases, enabling analysis of flow-induced order and alignment not captured by previous O(2)-based theories.

Findings

Long-range orientational order can occur under shear flow.

Flow alignment is possible at high shear rates.

The theory extends understanding of 2D anisotropic fluid behavior.

Abstract

We formulate a hydrodynamic theory of $p-$atic liquid crystals, namely two-dimensional anisotropic fluids endowed with generic $p-$fold rotational symmetry. Our approach, based on an order parameter tensor that directly embodies the discrete rotational symmetry of $p-$atic phases, allows us to unveil several unknown aspects of flowing $p-$atics, that previous theories, characterized by ${\rm O(2)}$ rotational symmetry, could not account for. This includes the onset of long-ranged orientational order in the presence of a simple shear flow of arbitrary shear rate, as opposed to the standard quasi-long-ranged order of two-dimensional liquid crystals, and the possibility of flow alignment at large shear rates.