Viscous drag and rod orientation kinematics in an orthotropic fluid

Abstract

A model is proposed, where the evolution of the orientation of each fiber is coupled to the orientations of the surrounding fibers in the flow of a fiber-filled fluid and includes the effects of the fiber volume fraction and aspect ratio. This is performed by accounting for the effective behavior of the fiber-filled fluid, which is anisotropic although the fibers are embedded in an isotropic Newtonian fluid. The rotation of a fiber in these conditions is predicted by a dumbbell model, which allows an extension of Jeffery's equation to anisotropic cases. This involves the numerical evaluation of the drag force applied on a sphere in an orthotropic incompressible fluid, which is evaluated by finite element simulations. A simple fit is proposed for the practical use of the coupled model, which is applied finally to the orientation kinematics of a population of fibers in a simple shear flow, and the results are compared with the ones given by the standard uncoupled approach.