A Rheological Equation of State for Semiconcentrated Fiber Suspensions

A rheological equation of state is developed for a semiconcentrated suspension of stiff fibers in a Newtonian solvent with volume fraction φ in the range (D/L)2<φ<(D/L), where L/D is the length‐to‐diameter ratio of the fibers. The constitutive equation gives the stress in terms of an integral over a function of the Cauchy strain tensor and the orientation vector for a fiber. An expression is also obtained for the evolution of the fiber orientation. The development is restricted to homogeneous flows. It is found that in start‐up of steady shear or elongational flow the orientation of the fibers and the measurable rheological properties both depend only on the total applied strain. For a fiber number density of n the contribution of the fibers to the stress is roughly nL3 times that of the solvent when the fibers are randomly oriented, as for example at the beginning of a flow. In the model presented here the viscosity (at steady state) is identical to that of the Newtonian solvent, because of the alignment...