Computational rheology of liquid crystalline composite and active materials
Liquid crystals are a type of soft matter that exists as a mesophase between the solid and liquid phase. As a result, they are observed to exhibit some properties which are characteristic of each of these phases. For example, a liquid crystalline material can flow and be poured as can a liquid, and display long-range orientational, but not positional, order as observed in a solid. Examples of liquid crystals can be found in many technological devices, in particular they are used in electronic displays. Additionally, the molecules in a wide variety of soaps and detergents can form liquid crystalline phases. The simplest type of liquid crystal molecule can be modelled as a thin, long rod. Active matter refers to a system of particles which can take in energy, either from an external or an internal fuel source and dissipate this energy. This can lead to, for example, self-motility, growth or replication of the particles. Examples of active matter include suspensions of swimming bacteria and collections of cytoskeletal filaments, such as actin or microtubules, and molecular motors, such as myosin or kinesin. We model active materials as liquid crystal rods which exert a force dipole along their primary axis, either outwards or inwards. These are known as extensile and contractile materials respectively. In this thesis we present computational simulation results investigating the rheological properties of active and liquid crystalline composite materials. Starting with the rheology of active nematic fluids under Poiseuille flow in a channel, we show that there exists a regime in which contractile materials exhibit a plug like flow and permeation-like behaviour as observed in cholesterics. Additionally, specific to extensile materials, we have carried out simulations seeking to answer the questions posed by the existence of a near-zero, or negative shear viscosity, measured in experiments. Presented in this thesis, we show that for a fully three-dimensional extensile material, the viscosity is not a state function, and is related to the microstate of the system. Furthermore, we have investigated two different models for liquid crystal composite emulsions, consisting of isotropic droplets dispersed within a continuous nematic solvent. In these simulations the two dimensional emulsions were subjected to a Poiseuille flow and the viscosity was measured. Interestingly, we observe a yield stress response and discontinuous shear thinning of the fluid not seen in the case of a typical, isotropic emulsion.