Fluid transport at low Reynolds number with magnetically actuated artificial cilia

By numerical modeling we investigate fluid transport in low-Reynolds-number flow achieved with a special elastic filament or artifical cilium attached to a planar surface. The filament is made of superparamagnetic particles linked together by DNA double strands. An external magnetic field induces dipolar interactions between the beads of the filament which provides a convenient way of actuating the cilium in a well-controlled manner. The filament has recently been used to successfully construct the first artificial micro-swimmer [R. Dreyfus at al., Nature 437, 862 (2005)]. In our numerical study we introduce a measure, which we call pumping performance, to quantify the fluid transport induced by the magnetically actuated cilium and identify an optimum stroke pattern of the filament. It consists of a slow transport stroke and a fast recovery stroke. Our detailed parameter study also reveals that for sufficiently large magnetic fields the artificial cilium is mainly governed by the Mason number that compares frictional to magnetic forces. Initial studies on multi-cilia systems show that the pumping performance is very sensitive to the imposed phase lag between neighboring cilia, i.e., to the details of the initiated metachronal wave.