Eur. Phys. J. E (2012) 35: 67
https://doi.org/10.1140/epje/i2012-12067-0

Regular Article

Random motion with interfacial contact: Driven diffusion vis-à-vis mechanical activation

Department of Chemical Engineering, Lehigh University, 18015, Bethlehem, PA, USA

^* e-mail: mkc4@lehigh.edu

Received: 13 March 2012
Revised: 28 May 2012
Accepted: 3 July 2012
Published online: 6 August 2012

Abstract

Rolling of a small sphere on a patterned support of an elastomer is governed by a non-linear friction. No motion occurs when the external field is weaker than the frictional resistance. However, with the intervention of an external noise, a viscous friction like behavior emerges; thus the sphere rolls with a uniform drift velocity that is proportional to the applied field. At a very low noise strength, the sphere exhibits a stick-slip behavior with motion occurring always along the bias. With the increase in the noise strength, the sphere exhibits a diffusive drift accompanied with forward and backward displacements. During this stage of driven diffusive motion, the ratio of the integrated probabilities of the negative-to-positive work fluctuations decreases monotonically with the time of observation, from which a temperature like intensive parameter can be estimated. This parameter conforms to Einstein’s ratio of diffusivity and mobility that increases almost linearly, even though the diffusivity increases super-linearly, with the strength of the noise. A new barrier crossing experiment is introduced that can be performed either with a hard (e.g. a steel ball) or with a soft (e.g. a water drop) sphere in contact with a periodically undulated substrate. The frequency of barrier crossing follows a transition state equation allowing a direct estimation of the effective temperature. These experiments as well as certain numerical simulations suggest that the effective temperature of a system controlled by a non-linear friction may not have a unique value.