Tumbling and Vorticity Drift of Flexible Helicoidal Polymers in Shear Flow

Helicoidal structures are frequent among organisms and macromolecules with biological relevance, whose motion and rheological properties are significantly influenced by the chiral symmetry. The role of filament flexibility and hydrodynamic interactions in the behavior of helix-like polymers in shear flow is investigated here with simulation and analytical approaches. Stability regimes can be identified in dependence of polymer flexibilities and shear rates that result in configurations without helical symmetry. In the stable regime, elongated helices tumble following Jeffery-type orbits, with frequencies corresponding to an effective aspect ratio, which depends on geometry, flexibility, and shear rate. Drift in the vorticity direction can be quantified in the simulations with a velocity that depends both on the helix intrinsic geometrical parameters and on its flexibility. Using resistive force theory, we obtain an expression for the vorticity drift velocity directly as a function of the helix geometry and shear rate that quantitatively describes the simulation results. These results are expected to be useful in the development and optimization of separation techniques of racemic mixtures.