Numerical analysis of complex flow of fibre suspensions in a viscoelastic fluid

Research efforts made so far to simulate fibre suspension flows are limited to fibre suspensions in Newtonian fluids. Though short fibre composites are mostly made of polymers, lack of suitable constitutive equations for fibre suspensions in viscoelastic fluids frustrates attempts to simulate flows of these suspensions. A preliminary work done by the author led to a constitutive equation for semiconcentrated fibre suspensions in the Oldroyd-B fluid. This paper describes the mathematical formulation of the flow problems for such a suspension and the numerical procedure to solve them. Some numerical results of flow past a sphere in a tube are also presented. This paper is supported by the University of Melbourne, the National Natural Science Foundation of China and Zhejiang Province.