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This project addresses using experimental and numerical techniques what happens when a liquid crystal is brought into contact with a flowing liquid, i.e., a situation with dynamic anchoring of the mesogenic molecules at the surface. Specifically we are studying the geometry of “driven cavity flow” with a nematic liquid crystal confined to a square well with a conventional (i.e., non-liquid crystalline) fluid flowing above. This geometry is of technological relevance, e.g., in the development of biosensors, where liquid crystals are brought into contact with a layer of phospholipid molecules or bound biomolecules such as proteins or viruses. Liquid crystal biosensors rely on optically monitoring the local nematic director changes due to the interaction of the liquid crystal molecules with the biological target. This local reorientation of the director is then amplified by the presence of long range orientational order in the nematic, and the perturbed director field is optically observed. 

 If the walls of the confining well are treated with a homeotropic surface alignment layer the nematic director field will necessarily exhibit a defect structure which is readily observed both experimentally and numerically. As the fluid flows we expect that the defect will be dragged by the fluid and the structure distorted.  The distortion will be sensitive to both the fluid velocity and the presence of any surfactants in the fluid.

To model our problem and obtain results relevant to the time and length scales of the experimental system we are using the Lattice Boltzmann (LB) technique as applied to liquid crystals. The LB technique is a mesoscopic simulation method bridging the gap between molecular dynamics at the microscopic scale and continuum modeling approaches, and has been used to study cavity flow for single fluids. The LB technique assumes a target set of hydrodynamic equations of motion which govern the spatial and temporal variations of the nematic order parameter. There are a number of choices for the hydrodynamic equations (nematodynamics) for nematic liquid crystals. We have chosen to use the equations of Qian and Shen which have been successfully applied to interfacial problems. The nematodynamic equations consist of the momentum evolution equation for the fluid velocity and an evolution equation for the nematic order parameter tensor.

This grant is supporting a Physics graduate student, Pengyu Liu, who is working under Pelcovits' supervision to carry out the numerical simulations. Under Pelcovits' guidance Liu has mastered the rather convoluted literature on nematodynamic equations and derived the Qian-Shen equations. Furthermore, he has developed and debugged his own LB code for the Qian-Shen system of equations. He is currently in the process of validating his code by aiming to reproduce LB results in the literature for nematic viscosities. Last spring Liu enrolled in a computational fluid dynamics course at Brown and as a final project for the class he carried out an analysis of conventional driven cavity flow which has prepared him to model the geometry of relevance to the present project. Liu is now in the process of coding a two-dimensional LB simulation of  driven cavity flow of an isotropic fluid above a confined nematic. While a full three-dimensional simulation would be desirable,  the state-of-the-art in LB studies of two-phase liquid crystal systems is the simulation of two-dimensional systems because of the high computational overhead. The director field produced by the simulations will then be compared with experimental data using computational optical modeling. 

To summarize the progress to date on the numerical simulations: the necessary groundwork has been laid during the first grant year to commence studying the problem of interest during the second grant year.