Presentation of the Microswimming project

The study of microswimmers was initiated by the observations of G. Taylor in 1950 and E. Purcell in 1977. The first one proposed a self-propulsion model in which the swimmer advanced by means of sinusoidal motion of its tail, while the second one noticed the peculiarity of swimming in fluids characterized by low Reynolds numbers. At the microscale viscous forces overcome inertial ones, and non-reciprocal swimming strategies must be adopted in order to produce a net advancement. As a result, microswimmers whose stroke technique is similar to the scallop’s are not able to move forward when relying on their self-propulsion alone. This remark is due to the fact that Navier-Stokes equations can be approximated by Stokes equations at such small scale, and the resulting time invariance plays a key role when selecting the admissible swimming strategies.

This approximation has been exploited in mathematical literature about microswimming to obtain controllability results about different kinds of swimmers: by using Resistive Force Theory, fluid dynamics is encoded in some coefficients that allow to describe the microswimmer through rigid body equations alone.

Due to their small dimensions, microswimmers can travel in narrow channels. A possible application of microswimming studies is the field of medical microrobots. There are two possible types of employ: the first one is targeted drug delivery, the second one is microsurgery or non-invasive medical examinations. In these cases an accurate control of the robot is of great importance, especially close to obstacles or walls. Another important point is the design of the robot, which should favour control ease and efficiency.