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Active Liquid Crystals in Confinement

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Active Liquid Crystals in Confinement Active Liquid Crystals in Confinement Jérôme Hardoüin Aquesta tesi doctoral està subjecta a la llicència Reconeixement 4.0. Espanya de Creative Commons. Esta tesis doctoral está sujeta a la licencia Reconocimiento 4.0. España de Creative Commons. This doctoral thesis is licensed under the Creative Commons Attribution 4.0. Spain License. Active Liquid Crystals in Confinement Programa de doctorat en Nanociències Autor/a: Jérôme Hardoüin Director/a: Francesc Sagués Tutor/a: Jordi Ignés Active Liquid Crystals in Confinement Jérôme Hardoüin October 28, 2019 Contents Introduction1 Preface 7 1 Flow and Order: the physics of Active Liquid Crystals9 1.1 Active Matter.................................. 9 1.1.1 Zoology of Active Matter........................ 9 1.1.2 Emergent Properties of far from equilibrium systems . 10 1.1.3 From the microscopic to the macroscopic: modelling active systems 11 1.2 Liquid Crystals ................................. 17 1.2.1 Mesophases ............................... 17 1.2.2 Phase transitions............................ 18 1.2.3 Liquids with elasticity ......................... 18 1.2.4 Director field and order parameter .................. 18 1.2.5 Elastic energy.............................. 19 1.2.6 Topological defects........................... 19 1.2.7 Liquid crystals in confinement: defects and topology . 23 1.3 Flow and Order: the physics of Active Nematics............... 27 1.3.1 An out-of-equilibrium liquid crystal.................. 28 1.4 Scientific Objectives............................... 34 1.4.1 Influence of lateral confinement .................... 35 1.4.2 Influence of topology.......................... 36 1.4.3 Active nematics at a wall........................ 37 1.4.4 Active nematics at curved interfaces.................. 38 2 Materials and Methods 41 2.1 Active Nematics Synthesis........................... 41 2.1.1 Active Gel Preparation......................... 41 2.1.2 Basic sample design........................... 44 2.2 Imaging and Analysis.............................. 46 2.2.1 Optical setups.............................. 46 2.2.2 Image processing ............................ 48 2.2.3 Determining director and defects in active nematics......... 50 2.2.4 Characterization of the flow field ................... 52 2.3 Numerical methods (chapter3) ........................ 55 2.4 Experimental techniques............................ 57 2.4.1 Surface Microfluidics (Chapter3,4 and5).............. 57 i CONTENTS 2.4.2 Active emulsions: droplets, shells and ellipsoids ........... 60 3 Active nematics under lateral Confinement 69 3.1 State of the art ................................. 69 3.2 Experimental setup: surface microfluidics................... 69 3.3 Computational Setup.............................. 70 3.4 Results and Discussion............................. 70 3.4.1 A defect-free state: shear flow disrupted by instabilities . 72 3.4.2 The dancing state: a one-dimensional line of flow vortices . 74 3.5 Summary .................................... 76 4 Effect of Topology 83 4.1 Experimental Setup............................... 83 4.2 Results...................................... 84 4.2.1 Transport and polarization in isolated annuli............. 84 4.2.2 Cross-talks between flows and order in connected annuli . 87 4.2.3 Frustated topology with a genus 3 topology ............. 91 4.3 Discussion.................................... 92 5 Active Nematics at a Wall: Description and Control 99 5.1 Motivation: perturbations from the boundaries................ 99 5.2 Properties of an isolated negative defect at a wall . 100 5.2.1 Nucleation, Structure and Motility ..................101 5.2.2 Forces ..................................105 5.2.3 Hydrodynamics of active nematics using BioFlow . 109 5.2.4 Conclusion................................117 5.3 Collective dynamics of negative defects at a wall . 118 5.3.1 On the road to spatio-temporal chaos . 118 5.3.2 Describing Chaos: the Kuramoto-Sivashinski equation . 120 5.3.3 KSE and 1D active nematics......................122 5.3.4 Statistical properties of localized structures . 124 5.3.5 Energy spectrum in Active Nematics . 130 5.3.6 Conclusion................................139 5.4 Controlling Wall Defects............................140 5.4.1 Effect of an indentation ........................140 5.4.2 Effect of a ratchet pattern.......................142 5.4.3 Effect of wall curvature.........................148 5.4.4 Conclusion................................149 6 Active Nematics and Curvature 155 6.1 Introduction...................................155 6.1.1 Geometrical frustration and topological charge . 155 6.1.2 Defects and local curvature ......................159 6.1.3 Experimental active nematics on curved interfaces . 160 6.1.4 Motivation................................160 6.2 Synthesis of smectic ellipsoids .........................163 6.3 Active nematic emulsions............................165 ii CONTENTS 6.4 Results......................................167 6.4.1 Solid body dynamics..........................168 6.4.2 Active nematic deformations......................170 6.5 Summary ....................................174 6.6 Simulation Results ...............................176 6.7 Role the the viscous anisotropy ........................176 6.8 Conclusion and perspectives..........................177 Closing remarks 183 Conclusion 191 Acknowledgments 195 Bibliography 197 iii List of videos 3.1 Shear flow of active nematics confined in a 50 µm channel. The images were acquired with a laser scanning confocal microscope (see Methods sec- tion 2.2.1). frame rate: 0.15 fps. scale:0.73 µm/px.............. 80 3.2 Shear state from the simulations. Defects are highlighted by the green circle (+1/2) and the blue triangle (-1/2). Channel width is 32 lattice sites. 80 3.3 Defect tracking in the shear state. Active nematics confined in a 80 µm channel. The images were acquired with a laser scanning confocal micro- scope (see Methods section 2.2.1). frame rate: 1 fps. scale:0.69 µm/px. scale bar 50µm................................. 80 3.4 Dancing disclination state in a 120 µm channel. Positive (+1/2) defects are overlaid with green disks. The images were acquired with a laser scan- ning confocal microscope (see Methods section 2.2.1). frame rate: 0.6 fps. scale:0.56 µm/px................................ 80 3.5 Dancing state from the simulations. Channel width is 60 lattice sites. 81 3.6 Switching state in active nematics confined in a 90 µm channel. The im- ages were acquired with a laser scanning confocal microscope (see Methods section 2.2.1). frame rate: 0.3 fps. scale:0.79 µm/px............. 81 3.7 Switching state from the simulations. Defects are highlighted by the green circle (+1/2) and the blue triangle (-1/2). Channel width is 40 lattice sites....................................... 81 3.8 Self-collapsing state from the simulations. The bend instabilities grow and then collapse in on themselves. Channel width is 30 lattice sites. 81 4.1 Symmetry Breaking Confocal fluorescence video of active nematics con- fined in a 60 µm wide annulus. scale bar: 100 µm.............. 96 4.2 Switching state Confocal fluorescence video of active nematics confined in a 110 µm wide annulus. scale bar: 100 µm................. 96 4.3 Turbulent state Confocal fluorescence video of active nematics confined in a 200 µm wide annulus. scale bar: 100 µm................. 97 4.4 Synchronisation in a Genus 2 Confocal fluorescence video of active nematics confined in a genus 2 handle-body, with an overlapping distance of D/2R0 = 0.94. The width of each annulus is w = 80 µm. scale bar: 100 µm...................................... 97 v LIST OF VIDEOS 4.5 Frustration in a Genus 3 Confocal fluorescence video of active nematics confined in a genus 3 handle-body. The width of each annulus is w = 80 µm and the overlapping distance is D/2R0 = 0.83. scale bar: 100 µm...... 98 5.1 Steady regime of an isolated wall-defect in a disk. Fluorescence micro- graph of active nematics confined in a disk of 170 µm radius. Frame rate: 5 fps. Scale bar: 100 µm. This video corresponds to the flow regime de- scribed in Fig. 5.2 (c).............................. 152 5.2 Nucleation and merging regime of an isolated wall-defect in a disk. Fluorescence micrograph of active nematics confined in a disk of 170 µm radius. Frame rate: 5 fps. Scale bar: 100 µm. This video corresponds to the flow regime described in Fig. 5.2 (d)................... 152 5.3 Drifting regime of an isolated wall-defect in a disk. Fluorescence mi- crograph of active nematics confined in a disk of 170 µm radius. Frame rate: 5 fps. Scale bar: 100 µm. This video corresponds to the flow regime described in Fig. 5.2 (e)............................ 152 5.4 Collective dynamics at a wall. Fluorescent micrograph of active ne- matics in the vicinity of a flat wall. The wall is located at the bottom of the image. Frame rate: 2 fps. Scale bar: 100 µm. This video corresponds to the analysis proposed in Fig. 5.24..................... 153 5.5 Periodic dynamics in a small disk Time-lapse of the periodic oscillation of active nematics confined in a 130 µm corrugated disk. The indentation is located to the left side of the disk. Frame rate: 5 fps. Scale bar: 100 µm. This video corresponds to the analysis performed in Fig. 5.29........ 153 5.6 Effect of a ratchet pattern Fluorescence micrograph of active nematics facing a wall patterned with ratchets. The wavelength of the pattern, λ =200 µm is fixed for all the experiments. In this example, the height is h =100 µm. Frame rate: 2 fps. Scale
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