Mathematical modelling of active nematic liquid crystals in confined regions

  • Joshua Walton

Student thesis: Doctoral Thesis


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)

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