Multi-scale mathematic modeling of non-isothermal polymeric flow of fiber suspensions

Multi-scale numerical analysis of non-isothermal polymeric flow of fiber suspensions is presented by numerical simulation using a multi-scale modeling. And the multi-scale modeling is established by the coupling of three scales, the macroscopic flow field, the mesoscopic fiber orientation and the microscopic macromolecular information. The constitutive equation which incorporates specific features of polymeric melt of fiber suspensions and its constituents is represented by linear sum of the stress contributions from the three scales. Using the multi-scale modeling, numerical simulations of the polymeric flow of fiber suspensions through a planar contraction cavity and the predicted stress distribution of different scales and fiber orientation are presented. A parametric study based on the fiber aspect ratio, volume fraction and interaction coefficient is used to explore the effects of fiber on system performance. The effects of different inlet temperatures on the stress are also discussed. The present results may elucidate the relationship of the three scales, and exhibit the possibility for developing a meaningful rheological modeling of the polymeric flow of fiber suspensions at the multi-level for industrial application.