Active Liquid Crystals in Confinement

Abstract

Living systems flow. What appears obvious from our daily observation of people, birds or insects remains surprisingly true at the smallest scale of life. Even at the earliest stages of embryonic development, the most elementary units of living systems, cell tissues, exhibit sustained currents. This perpetual movement is a signature of one of the fundamental properties of living systems - their ability to consume energy and transform it into directed motion. Living systems also cooperate. In the same way as fish swimming collectively form large scale structures to fool their predators, cells self-organize in tissues of increasingly complex shapes. Pattern formation in biology involves many processes from chemical signalling to hydrodynamics. Yet, the striking similarity between the flows and shapes adopted by collective systems at all scales of life motivated the development of a unifying theory, containing the minimal physical processes involved. This framework is called active soft matter. It refers to any system composed of self-driven units that consume and convert energy into directed motion. In some cases, the particles are so densely packed that they can be described as a continuous phase with long-range orientational order. This particular class has been termed active liquid crystals, of which cell tissues are the flagship illustration. These systems are characterized by a peculiar interplay between order and flows. The constant energy consumption drives them out of thermodynamic equilibrium. As a consequence, they are constantly deforming by sustained - and typically chaotic - flows. Reciprocally, the flow pattern directly depends on the local ordering of the particles.

Beyond the apparent chaos, this interplay between activity and order also confers to active liquid crystals a fascinating ability to adapt to the environments where they reside. In this work, we investigate the interplay between the geometry, the order and the flows of an active liquid crystal. Using novel micro-printing techniques, we develop versatile experimental setups that allow us to study how geometrical confinement tames the active flows and defect properties. We specifically investigate the effect of lateral confinement, topology, boundary roughness and Gaussian curvature.

We report dramatic transformations of the spatio-temporal dynamics of an in vitro microtuble-based active nematic system. The so-called active turbulence reorganizes into vortex lattices, directed, or defect-free unidirectional flows. Topological defects, which determine the active flow behavior, are created and annihilated on the boundaries rather than in the bulk, and acquire a strong orientational order in narrow channels. Their nucleation is governed by an instability whose wavelength is effectively screened by the lateral confinement. Their density, spatial distribution, orientation, and velocities evade most of the laws derived for unconfined active nematics. The careful description of the co-evolving order and flow patterns away from active turbulence enables us, to some extent, to disentangle the way they interact. In addition, we relate the transition to ordered regimes to generic descriptions of spatio- temporal chaos in out-of-equilibrium fluids, in an effort to understand the physics of these complex systems through universal laws.

Dramatic transitions also occur in the case of closed interfaces i.e surfaces with no boundaries. In the last part of the manuscript, we report an original example of spinning active nematic droplets. We condense an active nematic layer on the outer surface of oil droplets with an ellipsoidal shape. In this configuration, topology and Gaussian curvature contribute to the emergence of a chiral symmetry breaking in the active deformations. This chirality is transferred to the solid-body dynamics of the ellipsoids, which rotate with a surprisingly constant pulsation. These results demonstrate how the non- equilibrium dynamics of active materials could be converted into macroscopic engines. Our result not only improve the theoretical understanding of active liquid crystals. We also demonstrate promising strategies to control the spatial organization and the active flows through geometrical confinement, which could contribute to the design of autonomous microfluidic systems performing complex tasks without any external input.

Els sistemes vius flueixen. El que sembla evident a partir de la nostra observació diària de persones, aus o insectes segueix sent sorprenentment cert a la menor escala de la vida. Aquest moviment perpetu és una signatura d’una de les propietats fonamentals dels sistemes vius: la seva capacitat de consumir energia i transformar-la en moviment dirigit. Els sistemes de vida també cooperen. La cridanera similitud entre els fluxos i les formes adoptades pels sistemes col·lectius a totes les escales de la vida va motivar el desenvolupament d’una teoria unificadora, que contenia els processos físics mínims implicats. Aquest marc s’anomena matèria tova activa. Es refereix a qualsevol sistema compost per unitats impulsades per si mateixes que consumeixen i converteixen l’energia en moviment dirigit. En aquest treball s’investiga la interacció entre la geometria, l’ordre i els fluxos d’un cristall líquid actiu. Amb noves tècniques de microimpressió, desenvolupem configuracions experimentals versàtils que ens permeten estudiar com la confinament geomètrica doma els fluxos actius i les propietats dels defectes. Investiguem específicament l'efecte del confinament lateral, la topologia, la rugositat del límit i la curvatura gaussiana. Es reporten transformacions dramàtiques de la dinàmica espaciotemporal d’un sistema nemàtic actiu basat en microtubs. Una acurada descripció de l'ordre i dels patrons de flux que evolucionen lluny de les turbulències actives ens permet, fins a cert punt, desvincular la forma en què interactuen. A més, relacionem la transició a règims ordenats a descripcions genèriques del caos espaciotemporal en fluids fora d'equilibri, en un esforç per comprendre la física d'aquests sistemes complexos mitjançant lleis universals. A la darrera part del manuscrit, es presenta un exemple original de gota de gotes nemàtiques actives. Aquests resultats demostren com la dinàmica de no equilibri dels materials actius es podia convertir en motors macroscòpics. El nostre resultat no només millora la comprensió teòrica dels cristalls líquids actius. També demostrem estratègies prometedores per controlar l’organització espacial i els fluxos actius mitjançant confinament geomètric, que podrien contribuir al disseny de sistemes microfluídics autònoms que realitzen tasques complexes sense cap entrada externa.