Micropolar mixtures and balance of orientational momentum

Abstract

The paper is mainly devoted to the balance equations for anisotropic fluids such as, for instance, liquid crystals and cell populations in extracellular liquids. The body is modelled as a mixture of reacting micropolar constituents, the micropolar structure being associated with an orientational momentum in terms of a inertia tensor. Next thermodynamic restrictions are derived for constitutive equations involving the temperatures, the mass densities, their gradients and the stretching tensors of the constituents. The whole set of evolution equations is then established. While current models in the literature involve a (first-order or a second-order) evolution equation for the director, the present approach leads to an evolution equation for the intrinsic angular velocity as it happens for rigid bodies. The relation to the main models appeared in the literature is provided and the reason for the different form of evolution equations is outlined.