Undulatory swimming in lyotropic liquid crystal polymers at finite Reynolds numbers

Microorganisms swimming are typically explored in low-Reynolds-number environments where fluid inertia is negligible. However, in complex fluids such as lyotropic liquid crystal polymers (LCPs), the interplay between fluid inertia and anisotropy may lead to distinctive dynamical features. This study combines asymptotic analysis and direct numerical simulations to investigate the role of fluid inertia in undulatory locomotion through a lyotropic LCP using a classical model of Taylor’s swimming sheet. In isotropic LCPs, we suggest that the behaviours of swimmers are similar to those observed in Oldroyd-B viscoelastic fluids. Fluid inertia enhances the swimming speed and mechanical efficiency at finite Reynolds numbers. By contrast, in nematic LCPs, we reveal that the swimming speed and efficiency monotonically decrease with Reynolds numbers for parallel and perpendicular swimming, showing Newtonian-like behaviours. We demonstrate that the phase transition of the LCPs significantly alters their mechanical responses.