Geometrical control of active turbulence in curved topographies

TL;DR

This paper explores how the Gaussian curvature of a curved surface influences the chaotic flow of active nematic liquid crystals, revealing linear relationships between curvature and key fluid properties, supported by simulations and experiments.

Contribution

It demonstrates that substrate curvature acts as a control parameter for active turbulence, linking geometry to fluid dynamics in active nematics.

Findings

Topological charge density is linearly related to Gaussian curvature.

Defect creation and annihilation rates depend linearly on curvature.

Experimental results on microtubule-kinesin suspensions agree with theoretical predictions.

Abstract

We investigate the turbulent dynamics of a two-dimensional active nematic liquid crystal con- strained on a curved surface. Using a combination of hydrodynamic and particle-based simulations, we demonstrate that the fundamental structural features of the fluid, such as the topological charge density, the defect number density, the nematic order parameter and defect creation and annihilation rates, are simple linear functions of the substrate Gaussian curvature, which then acts as a control parameter for the chaotic flow. Our theoretical predictions are then compared with experiments on microtubule-kinesin suspensions confined on toroidal active droplets, finding excellent qualitative agreement.