Molecular hydrodynamics from memory kernels

TL;DR

This paper derives the hydrodynamic Basset-Boussinesq force from molecular dynamics simulations, revealing a long-time tail in the memory kernel and discussing the transition from molecular to hydrodynamic behavior.

Contribution

It demonstrates how the hydrodynamic force emerges from molecular memory kernels and introduces a generalized concept of hydrodynamic added mass, including cases with negative mass.

Findings

Memory kernel decays as t^{-3/2}

Hydrodynamic force emerges from molecular memory effects

Transition from molecular to hydrodynamic regimes analyzed

Abstract

The memory kernel for a tagged particle in a fluid, computed from molecular dynamics simulations, decays algebraically as $t^{-3/2}$. We show how the hydrodynamic Basset-Boussinesq force naturally emerges from this long-time tail and generalize the concept of hydrodynamic added mass. This mass term is negative in the present case of a molecular solute, at odds with incompressible hydrodynamics predictions. We finally discuss the various contributions to the friction, the associated time scales and the cross-over between the molecular and hydrodynamic regimes upon increasing the solute radius.