Rheological properties of dilute suspensions of rigid and flexible fibers

• Quantitative prediction of the rheological properties of dilute, flexible fiber suspensions.
• Evidence of a buckling transition accessible through standard rheology measurements.
• Fiber curvature increases viscosity, while shape fluctuations due to buckling decrease viscosity.

Particle-level simulations are used to study the rheology of monodispersed suspensions of rigid and flexible fibers in a creeping, simple shear flow of a Newtonian fluid. We also investigate the influence of different equilibrium shapes (straight and curved) of the fibers on the behavior of the suspension. A parametric study of the impacts of fiber flexural rigidity and morphology on rheology quantifies the effects of these realistic fiber features on the experimentally accessible rheological properties. A fiber is modeled as a chain of rigid cylindrical segments, interacting through a two-way coupling with the fluid described by the incompressible three-dimensional Navier–Stokes equations. The initial fiber configuration is in the flow–gradient plane. We show that, when the shear rate is increased, straight flexible fibers undergo a buckling transition, leading to the development of finite first and second normal stress differences and a reduction of the viscosity. These effects, triggered by shape fluctuations, are dissimilar to the effects induced by the curvature of stiff, curved fibers, for which the viscosity increases with the curvature of the fiber. An analysis of the orbital drift of fibers initially oriented at an angle to the flow–gradient plane provides an estimate for the time-scale within which the prediction of the rheological behavior is valid. The information obtained in this work can be used in the experimental characterization of fiber morphology and mechanics through rheology.