Nonlinear response and emerging nonequilibrium micro-structures for biased diffusion in confined crowding environments

TL;DR

This paper develops an analytical model for a driven tracer particle in confined crowded environments, revealing nonlinear responses and nonequilibrium micro-structures, validated by simulations, with implications for micro-rheology.

Contribution

It introduces a decoupling scheme to analyze nonlinear force-velocity relations and density profiles in confined lattice systems, extending beyond linear response theories.

Findings

Terminal velocity can be nonmonotonic with force.

Differential mobility can become negative.

Density profiles decay exponentially in confined geometries.

Abstract

We study analytically the dynamics and the micro-structural changes of a host medium caused by a driven tracer particle moving in a confined, quiescent molecular crowding environment. Imitating typical settings of active micro-rheology experiments, we consider here a minimal model comprising a geometrically confined lattice system -- a two-dimensional strip-like or a three-dimensional capillary-like -- 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 that 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.