Validation of a New Closure Model for Flow-Induced Alignment of Fibers

Abstract

A closure model for flow-induced orientation of short fibers is presented and discussed. The model retains all the six-fold symmetry and contraction properties of the fourth order tensor. A derivation of the model is presented and the conditions required for the model to be realizable are discussed. The model is validated against analytical and numerical solutions of the exact distribution function for the fiber orientation state for different flow fields. Variations of this model and its limitations are also discussed.