Lattice Boltzmann model with hierarchical interactions

TL;DR

This paper introduces a lattice Boltzmann model with hierarchical interactions to simulate non-ideal fluid dynamics, revealing complex disordered patterns and potential for modeling glassy states.

Contribution

It develops a novel lattice Boltzmann approach incorporating hierarchical pseudo-potentials to study frustrated fluid behaviors and disordered states.

Findings

Disordered fluid patterns emerge above a critical interaction strength.

Contrasts with typical phase-separation in binary fluids.

Potential for modeling glassy dynamics with effective Boltzmann equations.

Abstract

We present a numerical study of the dynamics of a non-ideal fluid subject to a density-dependent pseudo-potential characterized by a hierarchy of nested attractive and repulsive interactions. It is shown that above a critical threshold of the interaction strength, the competition between stable and unstable regions results in a short-ranged disordered fluid pattern with sharp density contrasts. These disordered configurations contrast with phase-separation scenarios typically observed in binary fluids. The present results indicate that frustration can be modelled within the framework of a suitable one-body effective Boltzmann equation. The lattice implementation of such an effective Boltzmann equation may be seen as a preliminary step towards the development of complementary/alternative approaches to truly atomistic methods for the computational study of glassy dynamics.