Stochastic model for predicting the shape of flexible fibers in suspensions

We describe the shape of moderately flexible fibers settling under inertial conditions in dilute and semidilute suspension and examine the hydrodynamic forces on the fibers that create different fiber shapes. The analysis is based on numerical simulations, using an immersed boundary method, to couple the motion of the fibers to the fluid dynamics. The direct numerical simulation results show that while fiber curvature can have a nonmonotonic dependence on fiber concentration, fiber torsion monotonically increases with increasing the concentration of fibers. Based on the concept of splitting the total forces into a mean and a stochastic part, we propose a reduced-order, stochastic model that can, with a reasonable accuracy, model the three-dimensional fiber shapes at different fiber concentrations, flexibility, and inertia. This model also helps us understand how random hydrodynamic fluctuations and fluid-mediated forces due to the presence of neighboring fibers contribute to the total forces on the fibers and fiber shapes.