Micropolar Media

There are materials with internal structure (e.g. composites, polymers, liquid crystals, soil, and bone) for which a reasonable model should view the points no longer as purely geometric in character but as rigid-body particles or even deformable continua. Models accounting for rigid-body particles are within the theories of micropolar media; those allowing for the deformation of particles are regarded as micromorphic media.
The deformation of the micropolar continuum is described by ascribing, to each particle of the continuum, the position vector, and three orthonormal vectors (called directors) that describe the translations and the orientation changes of the particles. The balance laws of mass, linear momentum, angular momentum, and energy are derived by allowing for an orientational momentum, a body couple density, and a surface couple density. Next some constitutive models are developed, in particular some thermoviscous micropolar media. As a relevant topic, the micropolar model is applied to the description of liquid crystals, mainly the nematics. Mixtures of micropolar constituents are considered; the second law and the growth terms show interesting modelling subjects. As an application of the mixture theory, the model for nanofluids is established where a (solute) constituent has a natural micropolar character.