Modeling and simulations of dynamics and motility in active fluids Giuseppe Negro Dottorato in Fisica XXXII ciclo Supervisor Università degli studi di Bari "A. Moro" Prof. Giuseppe Gonnella Dr. Antonio Lamura Modeling and simulations o dynamics and motility in active fluids Dottorato in Fisica XXXII Ciclo Università degli studi di Bari "A. Moro'1 by Giuseppe Negro to obtain the degree of PhD Project duration: November 1,2016 - November 1,2019 Supervisor Prof. G. Gonnella Dipartimento di Fisica "M. Merlin" Bari Dr. A. Lamura CNR, Bari CONTENTS 1 Active Matter 1 1.1 Order and collective m otion......................................................................................... ...2 1.2 Active matter confined in droplets................................................................................7 1.3 Rheology 8 1.4 Outline of the Thesis 8 2 Dynamical models for multiphase and active fluids 11 2.1 Order parameters 12 2.2 Free energy 13 2.2.1 Chiral liquid cry stals......................................................................................... ...15 2.2.2 Anchoring ............................................................................................................ ...15 2.2.3 Topological d efects................................................................................................17 2.3 Active Forces 20 2.3.1 Fluid mixtures with an active com ponent ...................................................22 2.4 Hydrodynamic equations 25 2.5 Spontaneous flow 27 3 Lattice Boltzmann Methods 33 3.1 General features of lattice Boltzmann method 35 3.1.1 The keystone ofLB method: Gauss-Hermite quadrature................... ...38 3.1.2 Lattice Boltzmann for a simple fluid................................................................40 3.2 Chapman-Enskog expansion 42 3.2.1 Recover Continuity Equation......................................................................... ...43 3.2.2 Recover Navier-Stokes Equations ...................................................................44 3.3 LBM beyond simple fluids 45 3.3.1 Stress tensor in the second m om ent................................................................45 3.3.2 Forcing scheme ......................................................................................................47 3.4 Coupling with advection-diffusion equation 48 3.4.1 Full LBM ap p roach................................................................................................48 3.4.2 Hybrid LBM ap p ro ach ...................................................................................... ...49 3.5 LBM for Active Fluids 50 3.6 Boundary conditions 52 3.7 Error analysis and comparison with finite difference Lattice Boltzmann: when collision-streaming is enou gh 53 3.8 Stability, efficiency and parallelization 63 4 SelfPropelled Droplets 67 4.1 Spontaneous symmetry breaking and self-propulsion 68 4.2 Nematic droplet with active force dipole and tangential anchoring: spon- taneous rotation 71 4.3 Rotation and propulsion in 3d active chiral d rop lets............................................. 73 4.3.1 Cholesteric droplet with active force dipoles: screwlike propulsion . 74 4.3.2 Cholesteric droplets with active torque dipoles: rotation and discli- nation dance ... 76 4.3.3 Overview and the role of h a n d n e s s ................................................................ 78 4.4 Hydrodynamics of contraction-based motility in a compressible active flu id ... 80 4.4.1 Hydrodynamic m o d e l...................................................................................... ... 80 4.4.2 Contraction induced clustering and m o tility ............................................. 82 5 Morphological and rheological properties of active emulsions 87 5.1 Morphological characterization of an active polar emulsion: activity en- hanced hexatic order ...................................................................................................... 88 5.1.1 Asymmetric e m u lsio n ...................................................................................... 90 5.1.2 Overview and 3D m orp hologies................................................................... 93 5.2 Rheology of active polar em ulsions......................................................................... 94 5.2.1 Linear flow and symmetry breaking transition ...................................... 96 5.2.2 Linear velocity profiles and lamellar phase................................................ 97 5.2.3 Unidirectional m otion........................................................................................ 98 5.2.4 Symmetric shear thinning profiles................................................................. 99 5.2.5 Activity quench.....................................................................................................100 5.2.6 Intermittent flo w ................................................................................................100 5.2.7 Overview and phase diagram ...................................................................... 106 5.2.8 Rheology of contractile em ulsions................................................................107 6 Conclusions 111 Bibliography 125 A Liquid-Vapor Phase separation 145 A.1 Kinetics and m orp h o logy.............................................................................................147 B Mapping with physical units 151 C Adimensional numbers 153 D Movies description 157 D.1 Self propelled chiral droplet......................................................................................... 157 D.2 Movies sheared active em ulsions................................................................................158 A bstract This thesis deals with the description, at a continuum level, of active fluids. Examples of active fluids are suspensions of biological filaments, such as actomayosin microtubules bundles, activated with motor proteins and bacterial cultures. The constituents of these systems have the natural tendency to assemble and align, thus developing structures with typical polar or nematic order. Combination of this property with self-motility capacity is at the origin of a wealth of interesting phenomena, including spontaneous flow and unusual rheological properties. Some experimental evidence will be presented in Chapter 1. In the last two decades much effort has been posed in understanding these proper­ ties with the declared aim to reproduce, control and exploit them. Here we mainly focus on self-propulsion and the rheology of active emulsions. To describe these phenom­ ena we rely on a continuous description that makes use of vectorial or tensorial order parameters borrowed form liquid-crystal theory. The dynamical models used will be presented in Chapter 2. The dynamical equations are numerically solved using a well known Navier-Stokes solver, the Lattice Boltzmann Method, coupled with finite differ- ence method. This numerical scheme and its MPI implementation will be described in Chapter 3. In Chapter 4 and 5 we will present our numerical results. In particular in Chapter 4 we will focus on self-propulsion. First results concerning a scalar active model, to spot out the role of compressibility in cell propulsion, will be presented. Then in the second part of Chapter 4 we will present some mesmerizing results regarding the self- propulsions of an active cholesteric droplet. In Chapter 5 the morphology and rheology of an emulsion composed of an active and a passive phase will be analysed. Within our model it is possible to reproduce some rheological experiments regarding bacterial suspensions, and to explain the origin of the different flow regimes observed. A cknowledgments First and foremost, I would like to thankProf. Giuseppe Gonnella, my supervisor, for his invaluable guidance, infinite patience, and constant dedication to his job. I would also like to thank Dr. Antonio Lamura. Thanks to his helpful conversations and teachings, I’ve acquired much of the knowledge and the skills I needed to put this work together. I thank Prof. D. Marenduzzo for sharing his endless inspiring views and for his car- ing guidance during the two periods I spent in Edinburgh. I am also very grateful to Dr. Adriano Tiribocchi, who started this work years ago, and never stopped providing support and new ideas to our group. I am grateful to my colleague Livio Carenza, for making amazing this journey. Shar­ ing working hours with him will be hardly forgettable, making this Ph.D. infinitely more valuable. I am grateful to Alessia, who gave me shelter and offered me support, love and joy, through the good and the bad. I am grateful to my family: my father Jimmy, my mother Tina, my brother Sabino, and my "sister" Francesca, for supporting me in pursuing my studies. I am also deeply grateful to my grandmother Janna who always motivated me. For the third time in a thesis, I have to be grateful to Lino and Daniela. To me you have been, and still are, my extended family. 1 Activ e M a tter Any physical isolated system evolves towards equilibrium. No matter which is its na­ ture - a gas in a box, a system of electric charges or the whole universe - it will evolve to minimize some thermodynamic potential or free energy to end up in a state where no flow of any kind occurs, where all forces sum up to zero and temperature is uniform in space and constant in time. This is the HeatDeath ofthe Universe. Despite thermo- dynamics predicts this as the inevitable end of any system, there is a huge number of situations