Swimming at Low Reynolds Number: How Symmetrically Pulsating Bubbles in Anisotropic Fluids Achieve Directional Motion

Microorganisms reside in low Reynolds environments, where viscous forces dominate over inertial forces. In this regime, the Navier-Stokes equation becomes time-independent. Therefore, microbes must break time-reversal symmetry to achieve net motion, which is vital for their survival. Employing thermotropic nematic liquid crystals (LCs) as a continuous phase, we demonstrate that a pulsating air bubble accompanying a topological defect can swim in the anisotropic fluid at a low Reynolds number despite the bubble's symmetric shape and motion. The deformed nematic director field around the bubble provides the centrosymmetry breaking, and the surrounding LC's nematodynamic response to the bubble's pulsation breaks the time-reversal symmetry. Our dumbbell model explains experimentally observed scaling relations and addresses how to optimize a pulsation profile to enhance swimming speed. Proposing a new mechanism that symmetry breaking solely in a fluid can realize symmetric and reciprocal swimmers, this study deepens our understanding of microswimmers in complex fluids.