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Numerical modelling of liquid crystal flows in confined domains Bhatia, Somesh


Liquid crystals are anisotropic, viscoelastic materials with properties intermediate of solids and liquids. They are useful structural and functional materials and due to their ability to form ordered layers close to the bounding surfaces they are used as lubricants. Under the application of a hydrodynamic field, based on the type of velocity profile, values of non-dimensional numbers and anchoring angles, different orientation profiles are observed. Leslie-Ericksen and Landau-de Gennes theories are used to understand the evolution of the microstructure. Leslie-Ericksen theory, due to its simplicity can be used to obtain the behavior of flow aligning nematic liquid crystals. Landau-de Gennes theory is a mesoscopic model and apart from its ability to capture singular solutions can be employed in a study of lubrication using liquid crystals. This research work contains studies of liquid crystals in different flow conditions, such as the Couette flow and the Channel flow. In the study of Couette flow of Graphene oxide suspensions in water, the Leslie-Ericksen theory was used to obtain the orientation and viscosity profiles at different shear rates, up until flow alignment was observed. In the numerical study of pressure-driven channel flows, a Marker and Cell based solution methodology was implemented to solve the Leslie-Ericksen hydrodynamic theory. The expected flow alignment of liquid crystals was obtained which validated the solver. A preliminary study combining the moving wall and pressure driven flow showed that the orientation profile obtained depends on the local direction of shear and the direction of shear gradient. The scaling analysis was applied to Landau-de Gennes theory to derive the simplified equations of a planar lubrication theory. The theory was then validated by comparison with the solution obtained from numerically solving the full set of equations using the Couette flow profile. The parametric studies conducted showed that the solution was in the Elasticity-driven steady state. A discussion of the physical conditions showed its applicability for films of thickness lesser than 1 mm for a 1 m long domain.

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