On the Hydrodynamic Equilibrium of a Rod in a Lattice Fluid

TL;DR

This paper models the equilibrium and dynamics of a large rod in a lattice fluid of smaller particles, revealing how shaking induces a reversible random walk around a height proportional to log N.

Contribution

It introduces a stochastic lattice model capturing the hydrodynamic behavior of a rod in a fluid of monomers, highlighting the effect of shaking on rod dynamics.

Findings

Rod exhibits a reversible random walk around a height proportional to log N.

Shaking causes decoupling of rod motion from monomers, leading to new dynamic behavior.

Model provides insights into hydrodynamic equilibrium in lattice fluid systems.

Abstract

We model the behavior of a big (Brazil) nut in a medium of smaller nuts with a stochastic asymmetric simple exclusion dynamics of a polymer-monomer lattice system. The polymer or `rod' can move up or down in an external negative field, occupying N horizontal lattice sites where the monomers cannot enter. The monomers (at most one per site) or `fluid particles' are moving symmetrically in the horizontal plane and asymmetrically in the vertical direction, also with a negative field. For a fixed position of the rod, this lattice fluid is in equilibrium with a vertical height profile reversible for the monomers' motion. Upon `shaking' (speeding up the monomers) the motion of the `rod' dynamically decouples from that of the monomers resulting in a reversible random walk for the rod around an average height proportional to log N.