Numerical simulation of liquid crystalline flows

UoM administered thesis: Phd

Abstract

The term complex fluids refers to a group of materials whose behaviour is intermediate between solids and liquids. They have found applications in numerous areas and are used to manufacture foods, cosmetics and medicines. With the rise of computer power over the last few decades and in the spirit of the Fourth Industrial Revolution (Industry 4.0), there is an increased tendency for in-silico product development. Physical experiments are reduced to the minimum and substituted with computer simulation in order to decrease the roll-out time of new formulations. Numerical calculations can provide an insight into the microstructure behaviour, however computations are only as good as the physics embedded in the constitutive equation. This project aims to assess the suitability of some of the existing governing equations of liquid crystals to model soap behaviour. In the thesis, we aim to examine the impact of the non-Newtonian microstructure on the material behaviour in complex geometries. The flow of liquid crystals through a curved pipe in the limit of infinite Ericksen number is analysed. The governing equations are solved analytically and reveal that the secondary flow arises at zero Reynolds number due to the misalignment between the microstructure orientation (director) and flow. Different mechanisms driving the secondary flow are distinguished: 1) the combination of normal stresses and geometry curvature and; 2) non-axisymmetric stress distribution caused by the flow curvature. Depending on material properties, those effects may act in the opposite direction, so the rotation of the secondary flow can vary. Additionally, the geometry curvature shifts the velocity field towards the bend axis, which results in the re-orientation of the internal microstructure. Analytical estimations are complemented with numerical simulations to give an insight into the flow behaviour at finite Ericksen numbers. The direction and intensity of the secondary motion depend on the director orientation on boundaries and the Ericksen number that quantifies the strength of viscous to elastic effects; for liquid crystals with specific material properties, a flow reversal is possible. Numerical simulations show that the pipe curvature manifests its presence outside the elbow. There is a spike in the velocity field as the fluid enters/leaves the elbow, while the director development length downstream of the bend is affected by the Ericksen number and material properties. In the last part of the thesis, a planar contraction geometry is used to compare director and Q-tensor frameworks of simulating liquid crystals. The vectorial approach cannot model the head-tail symmetry and predicts different flow fields for boundary conditions with the same physical meaning; a drawback that is particularly evident at low Ericksen number flows with homeotropic anchoring. There is less ambiguity with wall-parallel anchoring, where vectorial and tensorial frameworks produce similar results, provided that the correct set of boundary conditions is chosen.

Details

Original languageEnglish
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Award date1 Aug 2022