Mesoscale particle-based modelling of active nematic liquid crystals

Abstract

Active matter --- materials with energy injection at local scales --- has developed rapidly in the past few decades, with applications ranging from the macroscopic scale of crowds and animal flocks, down to the mesoscale of bacteria colonies and active gels, and finally to the microscopic scale of sub-cellular fluids. Active fluids exhibit feedback loops that can drive or mitigate activity. For example, in the quintessential experimental active-nematic system of microtubule bundles interlinked with kinesin molecular motors activity has a sigmoidal dependence on the density of ATP fuel. Likewise, bundles of contractile nematic actin-myosin systems can form into dense jammed asters, locking in myosin molecular motors and jamming the actin, and bacteria have been shown to perform quorum sensing by inhibiting their motion upon receipt of a chemical secreted by other bacteria. Despite the rapid development of active matter theory and experiment, there are still significant gaps in our understanding: Notably, there are limited simulation methods suitable for studies at the mesoscale. For instance, despite many numerical studies investigating the behaviour of colloidal particles in athermal baths, there has been little work investigating how oriented active flows, such as active-nematics, affect the dynamics of colloids. To address these gaps, this thesis presents a particle-based mesoscale simulation method known as Multi-Particle Collision Dynamics (MPCD) for simulating active fluctuating nematohydrodynamics. It extends an existing algorithm for nematic fluids in MPCD to produce an active-nematic MCPD method (AN-MPCD) through the introduction of a local force dipole. Despite its simplicity, AN-MPCD reproduces key quantities of active-nematic turbulence, such as spontaneous flows and the continuous creation/annihilation of topological defects. This simple model exhibits pronounced density fluctuations, typical of active particle models. By de-coupling the magnitude of activity from the local density, or applying a sigmoidal modulation function with respect to the local density, we show that density fluctuations are strongly mitigated while key scalings of active-nematic turbulence persist. Analysis of the density-induced pressure gradients reveal that activity modulation suppresses the effect of density fluctuations on solutes in active fluids, at the expense of fluctuations in the active force. Finally, we employ the modulated AN-MPCD method to study anchored passive colloids in active nematics. Homeotropic colloids possess non-monotonic effective diffusion, giving rise to a critical activity for enhanced diffusivity. When the colloidal radius is comparable to the active nematic length scale, active turbulence causes a colloidal companion defect to unbind from the colloid, leading to a non-zero topological charge on the colloid-companion complex. This non-zero charge encourages oppositely charged defects to approach the complex, indirectly propelling the complex through the fluid and enhancing the effective diffusion. The development of the AN-MPCD method opens up a wide range of possibilities for the study of solutes immersed in active solvents, including passive colloids, polymers, and porous media, but can be extended further to novel systems of passive clusters in active fluids. It also opens the door to future studies of how the formulation of activity and spatial modulation can affect bulk active turbulence