Lattice Boltzmann Simulations of Non-Equilibrium Fluctuations in a Non-Ideal Binary Mixture

TL;DR

This paper extends lattice Boltzmann simulations to study non-equilibrium fluctuations in a non-ideal binary mixture, revealing long-range correlations and pressure effects, and aligning well with fluctuating hydrodynamics predictions.

Contribution

It presents the first fluctuating LB simulation of NE fluctuations in a binary mixture with confinement and non-ideal equation of state, highlighting long-range correlations and pressure modifications.

Findings

Long-range ($oldsymbol{q}|^{-4}$) correlations in NE fluctuations.

Quantitative agreement with fluctuating hydrodynamics.

Observation of NE pressure effects due to long-range fluctuations.

Abstract

In the recent years the lattice Boltzmann (LB) methodology has been fruitfully extended to include the effects of thermal fluctuations. So far, all studied cases pertain equilibrium fluctuations, i.e. fluctuations with respect to an equilibrium background state. In this paper we take a step further and present results of fluctuating LB simulations of a binary mixture confined between two parallel walls in presence of a constant concentration gradient in the wall-to-wall direction. This is a paradigmatic set-up for the study of non-equilibrium (NE) fluctuations, i.e. fluctuations with respect to a non- equilibrium state. We analyze the dependence of the structure factors for the hydrodynamical fields on the wave vector $\boldsymbol{q}$ in both the directions parallel and perpendicular to the walls, as well as the finite-size effects induced by confinement, highlighting the long-range ($\sim |\boldsymbol{q}|^{-4}$) nature of correlations in the NE framework. Results quantitatively agree with the predictions of fluctuating hydrodynamics. Moreover, in presence of a non-ideal (NI) equation of state of the mixture, we also observe that the (spatially homogeneous) average pressure changes, due to a genuinely new contribution triggered by the long-range nature of NE fluctuations. These NE pressure effects are studied at changing the system size and the concentration gradient. Taken all together, we argue that these findings are instrumental to boost the applicability of the fluctuating LB methodology in the framework of NE fluctuations, possibly in conjunction with experiments.