Collisions and caustics frequencies of long flexible fibers in two-dimensional flow fields

Abstract

The present work analyzes numerical simulations of long flexible fibers in two-dimensional flows. The focus is on the frequency at which caustics occur and the characterization of the collisions among fibers. The continuous flexible fibers are modeled as a set of connected rigid cylinders, where forces are applied to the center of mass of each cylinder determining their motion and fiber deformation. A domestic numerical code, which implements a fourth-order Runge–Kutta method to solve the system of ordinary differential equations, was validated against experimental data in a previous study. The two-dimensional steady analytical velocity fields correspond to the Arnold–Beltrami–Childress flows. Simulations are performed for a wide range of Stokes numbers ranging from 0.05 to 10.87. In a previous study, the frequency of caustics formation was shown to correlate strongly with fiber clustering. Now, a dimensionless caustics frequency is related to the Stokes number. The number of collisions correlates negatively with the Stokes number and positively with the clustering and the frequency of caustics formation. At low Stokes numbers, collisions are preferentially perpendicular, decreasing the angle of collision as the Stokes number increases. Most of the collisions occur at low relative velocities between the two colliding fibers. The angle of collision is strongly determined by vorticity and inertia, while the relative velocities of the fibers colliding seem to be determined by the characteristic velocity field.