Nonlinear response and emerging nonequilibrium microstructures for biased diffusion in confined crowded environments

O. Bénichou, P. Illien, G. Oshanin, A. Sarracino, and R. Voituriez
Phys. Rev. E 93, 032128 – Published 15 March 2016

Abstract

We study analytically the dynamics and the microstructural changes of a host medium caused by a driven tracer particle moving in a confined, quiescent molecular crowding environment. Imitating typical settings of active microrheology experiments, we consider here a minimal model comprising a geometrically confined lattice system (a two-dimensional striplike or a three-dimensional capillary-like system) populated by two types of hard-core particles with stochastic dynamics (a tracer particle driven by a constant external force and bath particles moving completely at random). Resorting to a decoupling scheme, which permits us to go beyond the linear-response approximation (Stokes regime) for arbitrary densities of the lattice gas particles, we determine the force-velocity relation for the tracer particle and the stationary density profiles of the host medium particles around it. These results are validated a posteriori by extensive numerical simulations for a wide range of parameters. Our theoretical analysis reveals two striking features: (a) We show that, under certain conditions, the terminal velocity of the driven tracer particle is a nonmonotonic function of the force, so in some parameter range the differential mobility becomes negative, and (b) the biased particle drives the whole system into a nonequilibrium steady state with a stationary particle density profile past the tracer, which decays exponentially, in sharp contrast with the behavior observed for unbounded lattices, where an algebraic decay is known to take place.

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  • Received 27 October 2015

DOI:https://doi.org/10.1103/PhysRevE.93.032128

©2016 American Physical Society

Physics Subject Headings (PhySH)

  1. Research Areas
  1. Techniques
Statistical Physics & Thermodynamics

Authors & Affiliations

O. Bénichou1, P. Illien1,2,3, G. Oshanin1, A. Sarracino1,4, and R. Voituriez1

  • 1Laboratoire de Physique Théorique de la Matière Condensée, UPMC, CNRS UMR 7600, Sorbonne Universités, 4 Place Jussieu, 75252 Paris Cedex 05, France
  • 2Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford OX1 3NP, United Kingdom
  • 3Department of Chemistry, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
  • 4CNR-ISC and Dipartimento di Fisica, Sapienza Università di Roma, p.le A. Moro 2, 00185 Roma, Italy

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Vol. 93, Iss. 3 — March 2016

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