Shape evolution of long flexible fibers in viscous flows

The present work studies numerically the dynamics and shape evolution of long flexible fibers suspended in a Newtonian viscous cellular flow using a particle-level fiber simulation technique. The fiber is modeled as a chain of massless rigid cylindrical segments connected by ball and socket joints; one-way coupling between the fibers and the flow is considered while Brownian motion is neglected. The effect of stiffness, equilibrium shape, and aspect ratio of the fibers on the shape evolution of the fibers are analyzed. Moreover, the influence of fiber stiffness and their initial positions and orientations on fiber transport is investigated. For the conditions considered, the results show that the fiber curvature field resembles that of the flow streamline. It is found that the stiffer fibers experience not only a quicker relaxation phase, in which they transient from their initial shape to their "steady-state shape," but they also regain their equilibrium shape to a larger extent. The findings also demonstrate that even a small deviation of fiber shape from perfectly straight impacts significantly the early-stage evolution of the fiber shape and their bending behavior. Increasing the fiber aspect ratio, when other parameters are kept fixed, leads the fiber to behave more flexible, and it consequently deforms to a larger extent to adjust to the shape of the flow streamlines. In agreement with the available experimental results, the fiber transport studies show that either the fiber becomes trapped within the vortices of the cellular array or it moves across the vortical arrays while exhibiting various complex shapes