The concept of ‘active matter’ refers to a system that is far away from equilibrium. It comprises internal self-driven units that consume a local fuel (e.g., chemical fuel) from surroundings and transforms it into mechanical work. It is ubiquitous not only in the macroworld such as flocking of fish, birds or animal herds, but also pervasive in the microworld. Examples include biological swimmers such as bacteria and microalgae, synthetic colloidal surfers actuated by chemical reactions, as well as purified biopolymers (e.g., microtubules (MTs)) mixed with molecular motors. In contrast to the previously well-studied passive systems where the instability mainly comes from the thermodynamic fluctuations, the inherent spontaneity of the active matter endows itself with a complex and ever-changing dynamics and structure, the study of which is still nascent.In this thesis, we focus primarily on a specific type of active system in the microscale that is featured by comprising self-driven particles with elongated shape, i.e., the rod-like particles. Such system is described as ‘active nematics’ due to its resemblance to nematic liquid crystals. The out-of-equilibrium pattern formation of active nematics is caused by the inextricable interplay between the short-range steric interaction and the long-range hydrodynamics. As a result, the dynamics and structure of active nematics display hallmarks of collective motion of particles, chaotic flow structure and the concomitantly long-ranged nematic order and motile topological defect. To gain a physical insight to such complex while intriguing phenomena, we develop a coarse-grained Q-tensor continuum theory coupled with low-Reynold fluid dynamics. With the assistance of computational framework for simulating suspensions of rigid particles in Newtonian Stokes flow, we are able to conduct large-scale particle simulations to mimic many-particle couplings.The thesis is organized as follows: In chapter 1, we study the complex dynamics of a two-dimensional suspension comprising non-motile active particles confined in an annulus. A coarse-grained liquid crystal model is employed to describe the nematic structure evolution, and hydrodynamically couples with the Stokes equation to solve for the induced active flows in the annulus. In chapter 2, We study fluid and mass transport in a dilute apolar active suspension confined in a rectangular channel. By using a Galerkin mixed finite element method, we are able to reveal various patterns of spontaneous coherent flows that can be unidirectional, traveling-wave, and chaotic. In chapter 3, we study the long-time rotational Brownian diffusivity in a crowded bath of hard rods with finite aspect ratios, where the topological constraint dominate over hydrodynamics. In chapter 4, we study the nonlinear dynamics of an undulatory microswimmer in a quasi-2D liquid-crystal polymer solution.
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