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Micropolar Theory and its Application to Nematic Liquid Crystal

James Lee (George Washington University), Jiaoyan Li (The George Washington University)

Complex Fluids: Suspensions, Emulsions, and Gels

Wed 10:45 - 12:15

Barus-Holley 160

Micropolar theory, developed by Eringen, is a rigorous extension of the classical continuum mechanics to microscopic space and time scales. It envisions a material body as a continuous collection of finite-size particles; each is capable of moving (macro motion) and rotating (micro motion). The purpose to go beyond the classical continuum mechanics is to take into account the microstructure of the material body in question while still keeping the advantages of continuum theory intact. We first derive a set of constitutive equations for generalized micropolar viscoelastic solids. Nematic liquid crystal is a chemical compound which consists of long chain molecules and has four phases – the fourth phase, liquid crystal phase, is the one between solid and fluid existing in a specific temperature range. In this phase it possesses both characters of solid and fluid. Based on these characters, we give an idealized definition to nematic liquid crystal as: Nematic liquid crystal, a subclass of micropolar viscoelastic solid, is a material body that takes any state leaving density unchanged and gradient of microrotation vanished as reference state. This means the nematic liquid crystal prefers its long chain molecules to remain parallel to each other; other than that, it flows like a fluid. We did construct a constitutive theory which (1) indeed reflects the definition of the nematic liquid crystal, and (2) possesses anisotropic material properties indicating the feature of a solid. We take the well known physical phenomenon, orientation of nematic liquid crystal being parallel to the static magnetic field, as the starting point. We will show that molecules in nematic liquid crystal with random alignments initially can self-align themselves. Then the flow problem that we solved indicates the coupling between velocity field and rotational field, which is the fundamental characteristics of Micropolar theory.