## What is it about?

The so-called velocity autocorrelation function, or VACF, is a statistical function whose information characterizes the molecular-structural and dynamical signatures that give a particular fluid its identity. We develop a theory, based on the perspective of continuum hydrodynamics, that naturally accounts for the discrete, non-continuum nature of a fluid when viewed at the scale of individual atoms, molecules or particles. Unlike previous efforts, the presented theory appears to be applicable at all densities. The methodology is applied to various model fluids, including dense fluids such as liquid noble gases, alkali metals, and supercritical argon, as well as dilute gases. The resulting VACF calculations show remarkable agreement with direct VACF calculations from simulations of particles.

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## Why is it important?

The methodology developed in this study shows that the intuitive language of fluid mechanics can be applied right down to the scale of the individual atoms, molecules or particles that make up a real fluid. The equations of fluid motion proposed in this work, though remarkably simple, appear to be surprisingly general, since they provide a satisfactory molecular-scale description of a simple fluid of any density. In the approach we develop, we identify a heretofore unexamined mathematical distribution that we believe captures elements of the motion of discrete particles (kinetics) and the smooth description of fluids (continuum hydrodynamics). This mathematical distribution appears to serve as a physical "bridge" between the discrete-particle and continuum perspectives, the two primary ways in which scientists and engineers model the collective behavior of a system comprising very large numbers of identical or similar particles.

## Read the Original

This page is a summary of: Molecular hydrodynamic theory of the velocity autocorrelation function, The Journal of Chemical Physics, August 2023, American Institute of Physics,

DOI: 10.1063/5.0153649.

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