A mathematical model for micro-and nano-swimmers

In order to explore the kinetic characteristics of planktonic microorganisms and nanometer biological motors, a mathematical model is developed to estimate the hydrodynamic force in the migration of micro-and nano-swimmers by using the Laplace transformation and linear superposition. Based on the model, it is found that a micro-and nano-swimmer will enjoy a positive propulsive force by improving frequencies or generating traveling waves along its body if it is not time reversible. The results obtained in this study provide a physical insight into the behaviors of the micro-and nano-swimmer at low Reynolds numbers, and the corresponding quantitative basis can also be potentially used in the design of nanorobot and nanosized biomaterials.