Optimization of a Purcell micro-swimmer using the Bocop solver
Pierre Martinon



At the microscopic scale, the situation is the one of low Reynolds numbers, with inertial forces neglected with respect to viscosity.

Therefore the hydrodynamics of the system are governed by the Stokes equation, and the dynamics of the swimmer follow the Newton laws without inertia.

Resistive Force Theory (RFT) provides a local drag approximation, assuming that the force exerted on the swimmer by the fluid is linear with respect to velocity. In this framework, the dynamics of the N-link swimmer in a plane can be expressed as an ODE, which allows to find the optimal swimming strategy for different objective functions such as maximal displacement or efficiency.

It can be proven and checked in the simulations that optimal solutions are typically sequences of periodic strokes.