Selfpropelled Brownian spinning top: Dynamics of a biaxial swimmer at low Reynolds numbers
Abstract
Recently the Brownian dynamics of selfpropelled (active) rodlike particles was explored to model the motion of colloidal microswimmers, catalytically driven nanorods, and bacteria. Here we generalize this description to biaxial particles with arbitrary shape and derive the corresponding Langevin equation for a selfpropelled Brownian spinning top. The biaxial swimmer is exposed to a hydrodynamic Stokes friction force at low Reynolds numbers, to fluctuating random forces and torques as well as to an external and an internal (effective) force and torque. The latter quantities control its selfpropulsion. Due to biaxiality and hydrodynamic translationalrotational coupling, the Langevin equation can only be solved numerically. In the special case of an orthotropic particle in the absence of external forces and torques, the noisefree (zerotemperature) trajectory is analytically found to be a circular helix. This trajectory is confirmed numerically to be more complex in the general case of an arbitrarily shaped particle under the influence of arbitrary forces and torques involving a transient irregular motion before ending up in a simple periodic motion. By contrast, if the external force vanishes, no transient regime is found, and the particle moves on a superhelical trajectory. For orthotropic particles, the noiseaveraged trajectory is a generalized conchospiral. We furthermore study the reduction of the model to two spatial dimensions and classify the noisefree trajectories completely finding circles, straight lines with and without transients, as well as cycloids and arbitrary periodic trajectories.
 Publication:

Physical Review E
 Pub Date:
 February 2012
 DOI:
 10.1103/PhysRevE.85.021406
 arXiv:
 arXiv:1110.2030
 Bibcode:
 2012PhRvE..85b1406W
 Keywords:

 82.70.Dd;
 05.40.Jc;
 Colloids;
 Brownian motion;
 Condensed Matter  Soft Condensed Matter;
 Physics  Biological Physics;
 Physics  Classical Physics
 EPrint:
 13 pages, 4 figures, 2 tables