Mathematical modelling of active nematic liquid crystals in confined regions

Student thesis: Doctoral Thesis

Abstract

This thesis focusses on the application of continuum theories and modelling techniques of liquid crystalline fluids to the area of anisotropy and self-organisation derived from active agents. The research involves a continuum description of anisotropic active fluids, using adapted forms of continuum hydrodynamic theories of liquid crystals.We first consider the director structures of inactive nematic liquid crystals confined in rectangular regions. We use a mixture of analytical and numerical calculations to examine the energies of non-trivial nematic equilibria which exchange stabilities with constant equilibria at critical anchoring strengths. For the remainder of the thesis, we consider active nematic liquid crystals in confined regions.We first use an adapted Ericksen-Leslie theory to investigate spontaneous flow transitions of active nematics, with the liquid crystal confined in a one-dimensional shallow channel. We examine how internally generated flows induced by activity are affected by externally induced flows due to, pressure gradients and external orienting fields. We then investigate a shallow channel of active nematic in terms of an adapted Q-tensor theory for uniaxial nematic liquid crystals.Such a model allows for an investigation into the effects of variable ordering caused by changes in the temperature. Finally, we investigate active nematics confined in two-dimensional regions. We first consider wedge geometries containing an active nematic with a singularity at the wedge corner, deriving analytic solutions of a simplified version of the Ericksen-Leslie equations. We then employ numerical calculations to find steady solutions of the full non-linear Ericksen-Leslie equations for active nematics confined in rectangular regions.
Date of Award20 Feb 2020
Original languageEnglish
Awarding Institution
  • University Of Strathclyde
SponsorsEPSRC (Engineering and Physical Sciences Research Council)
SupervisorNigel Mottram (Supervisor) & Geoffrey McKay (Supervisor)

Cite this