Analytical solutions for fiber orientation in 2‐D flows of dilute suspensions

Abstract Analytical solutions for fiber orientation in dilute solutions are presented for both 2‐D planar and axisymmetric flow. The viscosity is assumed to be independent of position along the flow direction, but varies through the thickness of the mold cavity. For the particular case of a laminate of two fluids, an analytical solution is derived. Based upon the assumption that the fluid adjacent to the mold wall exhibits reduced viscosity due to non‐isothermal considerations, the fluid kinematics simplify, and an analytical solution to Jeffery's orientation equation is derived. Since the fiber orientation analysis is based on Jeffery's equation, it is valid only for dilute suspensions, i.e. for fiber volume fraction < 1/(fiber aspect ratio) ² . Qualitatively, the analytical results obtained provide superior correlation with experimental results, indicating that non‐isothermal fluid flow may play an important role in the development of the fiber orientation distribution in the molded component.