Metastable and Unstable Dynamics in multi-phase lattice Boltzmann

TL;DR

This paper provides a detailed quantitative analysis of metastability and phase separation in a multi-phase lattice Boltzmann model, confirming theoretical predictions with high-precision numerical verification and demonstrating reproducibility through an open-source framework.

Contribution

It introduces a comprehensive characterization of metastability in multi-phase lattice Boltzmann models, including theoretical derivation and numerical validation of structure factors and critical exponents.

Findings

Structure factor diverges near critical point and spinodal line.

Critical exponents match theoretical predictions.

Phase separation patterns align with molecular dynamics simulations.

Abstract

We quantitatively characterize the metastability in a multi-phase lattice Boltzmann model. The structure factor of density fluctuations is theoretically obtained and numerically verified to a high precision, for all simulated wave-vectors and reduced temperatures. The static structure factor is found to consistently diverge as the temperature approaches the critical-point or the density approaches the spinodal line at a sub-critical temperature. Theoretically predicted critical exponents are observed in both cases. Finally, the phase separation in the unstable branch follows the same pattern, i.e. the generation of interfaces with different topology, as observed in molecular dynamics simulations. All results can be independently reproduced through the ``idea.deploy" framework https://github.com/lullimat/idea.deploy