A lattice Boltzmann model with random dynamical constraints

TL;DR

This paper presents a modified lattice Boltzmann model that simulates a one-dimensional fluid interacting with randomly moving obstacles, capturing dynamic heterogeneities and complex relaxation behaviors.

Contribution

The introduced model incorporates finite-lifetime obstacles into the lattice Boltzmann framework, enabling simulation of dynamic heterogeneities in fluid systems.

Findings

Heterogeneous patterns in fluid density emerge from the model.

Non-exponential relaxation observed in two-time autocorrelation functions.

Dynamic obstacles induce complex, non-linear fluid behaviors.

Abstract

In this paper we introduce a modified lattice Boltzmann model (LBM) with the capability of mimicking a fluid system with dynamic heterogeneities. The physical system is modeled as a one-dimensional fluid, interacting with finite-lifetime moving obstacles. Fluid motion is described by a lattice Boltzmann equation and obstacles are randomly distributed semi-permeable barriers which constrain the motion of the fluid particles. After a lifetime delay, obstacles move to new random positions. It is found that the non-linearly coupled dynamics of the fluid and obstacles produces heterogeneous patterns in fluid density and non-exponential relaxation of two-time autocorrelation function.