a1 Physique et Mécanique des Milieux Hétérogenes, UMR 7636 CNRS/ESPCI ParisTech, Université Pierre et Marie Curie, Universite Paris Diderot, 10, rue Vauquelin, 75005 Paris, France
a2 Department of Mathematics and Lawrence Berkeley National Laboratory, University of California, Berkeley, CA 94720, USA
a3 Mathematics Institute, University of Warwick, Coventry CV4 7AL, UK
Flexible superparamagnetic filaments (‘fleximags’) are very slender elastic filaments, which can be driven by distributed magnetic torques to mimic closely the behaviour of biological flagella. Previously, fleximags have been used as a basis for artificial micro-swimmers capable of transporting small cargos Dreyfus et al. (Nature, vol. 437, 2005, p. 862). Here, we demonstrate how these filaments can be anchored to a wall to make carpets of artificial micro-magnetic cilia with tunable densities. We analyse the dynamics of an artificial cilium under both planar and three-dimensional beating patterns. We show that the dynamics are controlled by a single characteristic length scale varying with the inverse square root of the driving frequency, providing a mechanism to break the fore and aft symmetry and to generate net fluxes and forces. However, we show that an effective geometrical reciprocity in the filament dynamics creates intrinsic limitations upon the ability of the artificial flagellum to pump fluid when driven in two dimensions.
(Received October 27 2010)
(Revised October 27 2010)
(Accepted December 23 2010)
(Online publication March 15 2011)