Reciprocal microswimming in fluctuating and confined environments

From bacteria and sperm cells to artificial microrobots, self-propelled microscopic objects at low Reynolds numbers often perceive fluctuating mechanical and chemical stimuli and contact exterior wall boundaries both in nature and the laboratory. In this paper, we theoretically investigate the fundamental features of microswimmers by focusing on their reciprocal deformation. Although the scallop theorem prohibits the net locomotion of reciprocal microswimmers, by analyzing a two-sphere swimmer model, we show that in a fluctuating and geometrically confined environment, reciprocal deformations can afford a statistically average displacement. After designing the shape gait, a reciprocal swimmer can migrate in any direction, even in the statistical sense, while the statistical average of passive rigid particles statistically diffuses in a particular direction in the presence of external boundaries. To elucidate this symmetry breakdown, by introducing an impulse response function, we derive a general formula for predicting the nonzero net displacement of a reciprocal swimmer. Using this theory, we determine the relation between the shape gait and net locomotion as well as the net diffusion constant increase and decrease, owing to a reciprocal deformation. Based on these findings and a theoretical formulation, we provide a fundamental basis for environment-coupled statistical locomotion. Thus, this paper is valuable for understanding biophysical phenomena in fluctuating environments, designing artificial microrobots, and conducting laboratory experiments.