SUMMARY

Transport of fibrous matter is encountered in modern industrial applications such as papermaking, concrete reinforcement, and injection molding. The end-product quality in these applications is strongly dependent on flow properties and fiber orientation. The bulk deformation of the suspensions is generally modeled by non-Newtonian constitutive relations, and fiber orientation modeling is based on the Fokker-Planck equation. Using these ideas, this work presents a numerical analysis of fiber orientation kinetics for suspensions up to the semiconcentrated regime, where the effects of the flow and suspension on fiber orientation are represented on by a rotational diffusion coefficient. To this end, probabilistic measures for the fiber orientation, namely the fiber orientation probability density function (FOPD) and orientation tensors, are employed. The rheology of the suspension is modeled as a shear-thinning Herschel-Bulkley (HB) fluid. Flows of HB fluids are studied for laminar and turbulent flows in canonical geometries. An extensive statistical analysis with new data is presented to demonstrate the effects of yield stress and shear thinning on the flow characteristics and fiber orientation. Fiber orientation is obtained at a single point for simple flows and in contracting channels. For the former, a new solver is developed to obtain the FOPD. The results show significant improvements over existing results, and new ideas for the rotational diffusion coefficient for semiconcentrated suspensions are developed. For contracting channels, the governing equations for second-order orientation tensor are solved in order to obtain fiber orientation in practically relevant applications. A systematic analysis is presented to show the effect of the rheological properties and the rotational diffusion coefficient in these applications. It is demonstrated that the fiber orientation changes non-linearly in response to changes in the rheology and rotational diffusion coefficient.