An Eulerian formulation of a size-dependent anisotropic non-Newtonian viscous Cosserat fluid

Abstract

An Eulerian formulation of a size-dependent three-dimensional Cosserat continuum is developed for purely mechanical response of an anisotropic non-Newtonian viscous Cosserat fluid. The constitutive equations are Eulerian in the sense that they depend only on quantities that can be determined in the current state of the fluid. The Cosserat theory admits a triad of linearly independent deformable directors vectors at each material point, which are determined by higher-order balances of director momentum. It is shown that the balance of angular momentum of the Cosserat fluid imposes a non-trivial restriction on coupling between kinetic and kinematic variables that is satisfied by the proposed constitutive equations. An analytical solution of anisotropic Newtonian viscous fluid flow in a channel demonstrates size-dependence of the pressure driving the flow that is not present in the standard solution of a simple viscous fluid.