Viscous drag and rod orientation kinematics in an orthotropic fluid

Abstract

a b s t r a c tA 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.

On the Kelvin–Voigt model in anisotropic viscoelasticity

“…In such a way, we have a clear control of the most general transverse incompressible isotropic viscoelastic model of differential type linear in the second-order tensor D. The restriction on the hyperelastic part of the stress tensor that we assume for the sake of the simplicity has no impact on our results. Of course, this study can be extended to more complicated symmetries, as those in Gilormini and Chinesta [13], and for measurements of the arising constitutive parameters, as, e.g., those discuss in Grillo et al [14].…”

“…The restriction on the hyperelastic part of the stress tensor that we assume for the sake of the simplicity has no impact on our results. Of course, this study can be extended to more complicated symmetries, as those in Gilormini and Chinesta [13], and for measurements of the arising constitutive parameters, as, e.g., those discuss in Grillo et al [14].…”