Entanglement of Elastic Fibers in low Reynolds Fluid Flow

We report a discrete differential geometry based simulation for entanglement of elastic rods that couples the structural elasticity, hydrodynamic loading, and rod-rod contact. In nature, such entanglement can play a beneficial role, e.g. bundling in bacterial flagella; however, can also be a nuisance, e.g. trichobezoar (hairball) in human stomach. We consider a model system where elastic rods are injected, at a controlled velocity, one after another into a spherical tank full of viscous fluid. The simulation tool for this process is a combination of the following four components: the Discrete Elastic Rods algorithm for the elasticity of the rods, the modified mass method to impose the boundary condition, a penalty force-based collision detection and handling algorithm, and the Resistive Force Theory for hydrodynamic loading. We conduct experiments with a collaborative robot that injects the rods at a prescribed velocity and video records the process. In both experiments and simulations, we find that entanglement process is governed by the ratio of the elastic bending forces to the viscous forces. By exploring parameter space, we construct phase boundaries delineating the regions of entanglement.