Multiscale Models of Metallic Particles in Nematic Liquid Crystals

In this paper we use the method of homogenization to derive a set of approximate equations which describe a nematic liquid crystal colloid in which the dopants are freely rotating metallic particles. Previously we have studied the approximate behavior of liquid crystals doped with particles under the assumption that these remain stationary [T. P. Bennett, G. D'Alessandro, and K. R. Daly, Phys. Rev. E, 90 (2014), 062505, https://doi.org/10.1103/PhysRevE.90.062505]. This paper builds on our previous work by extending the theory to include rotating particles. We find a set of governing equations for the nematic liquid crystal and for the dopant particles. Effective material parameters are given explicitly in terms of the microscopic particle-liquid crystal interaction parameters by a sequence of cell problems solved on the microscale. We validate our model by direct comparison to large-scale numerical simulation and find excellent agreement for a variety of dopant shapes.