Q-tensor model for undulatory swimming in lyotropic liquid-crystalline polymers*

Microorganisms may exhibit rich swimming behaviors in anisotropic fluids, such as liquid crystals, that have direction-dependent physical and rheological properties. Here we construct a two-dimensional computation model to study the undulatory swimming mechanisms of microswimmers in a solution of rigid, rodlike liquid-crystalline polymers. We describe the fluid phase using Doi's Q-tensor model, and treat the swimmer as a finite-length flexible fiber with imposed propagating traveling waves on the body curvature. The fluid-structure interactions are resolved via an Immersed Boundary method. Compared to the swimming dynamics in Newtonian fluids, we observe non-Newtonian behaviors that feature both enhanced and retarded swimming motions in lyotropic liquid-crystalline polymers. We reveal the propulsion mechanism by analyzing the near-body flow fields and polymeric force distributions, together with asymptotic analysis for an idealized model of Taylor's swimming sheet.