Weighted density Lattice Boltzmann approach to fluids under confinement

TL;DR

This paper enhances a kinetic approach for inhomogeneous fluids by incorporating weighted density approximations, improving transport coefficient predictions, and applying a Lattice Boltzmann method to study confined fluid flows.

Contribution

It introduces a weighted density approximation into the Enskog-like kinetic approach, enabling more accurate transport coefficient calculations and numerical solutions for confined fluids.

Findings

Improved prediction of transport coefficients with weighted density approximation.

Numerical solution of phase space distribution in confined geometries.

Analysis of Poiseuille flow in confined hard-sphere fluids.

Abstract

The Enskog-like kinetic approach, recently introduced by us to study strongly inhomogeneous flu- ids, is reconsidered in order to improve the description of the transport coefficients. The approach is based on a separation of the interaction between hydrodynamic and non-hydrodynamic parts. The latter is treated within a simple relaxation approximation. We show that, by considering the non-hydrodynamic part via a weighted density approximation, we obtain a better prediction of the transport coefficients. By virtue of the simplicity of the kinetic equation we are able to solve numer- ically the phase space distribution in the presence of inhomogeneities, such as confining surfaces, via a Lattice Boltzmann method. Analytical estimates of the importance of these corrections to the transport coefficients in bulk conditions is provided. Poiseuille flow of the hard-sphere fluid confined between two parallel smooth walls is studied and their pore-averaged properties are determined.