Eur. Phys. J. E (2004) 13: 379-390
https://doi.org/10.1140/epje/i2003-10083-9

Membranes with rotating motors: Microvortex assemblies

¹ Institut Curie, UMR 168, 26 rue d’Ulm, F-75248, Paris Cédex 05, France
² Fachbereich Physik, Philipps-Universität Marburg, D-35032, Marburg, Germany
³ Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Straße 38, D-01187, Dresden, Germany
⁴ Ecole supérieure de physique et chimie industrielles, 10 rue Vauquelin, F-75231, Paris Cédex 05, France

^* e-mail: peter.lenz@physik.uni-marburg.de

Abstract

We study collections of rotatory motors confined to 2-dimensional manifolds. The rotational motion induces a repulsive hydrodynamic interaction between motors leading to a non-trivial collective behavior. For high rotation speed, motors should arrange on a triangular lattice exhibiting crystalline order. At low speed, they form a disordered phase where diffusion is enhanced by velocity fluctuations. In confining geometries and under suitable boundary conditions, motor-generated flow might enhance left-right symmetry-breaking transport. All these effects should be experimentally observable for motors driven by external fields and for dipolar biological motors embedded into lipid membranes in a viscoelastic solvent.