Pair diffusion, hydrodynamic interactions, and available volume in dense fluids

TL;DR

This study calculates the distance-dependent pair diffusion coefficient in dense fluids, revealing hydrodynamic interactions and their relation to fluid structure and available volume, with implications for colloid and polymer dynamics.

Contribution

It introduces a simulation-based method to determine D(r) in dense suspensions, connecting microscopic fluid structure to hydrodynamic interactions.

Findings

D(r) agrees with hydrodynamic theory beyond 3 diameters

Memory effects influence pair diffusion at short times

Deviations at short distances relate to local available volume

Abstract

We calculate the pair diffusion coefficient D(r) as a function of the distance r between two hard-sphere particles in a dense monodisperse suspension. The distance-dependent pair diffusion coefficient describes the hydrodynamic interactions between particles in a fluid that are central to theories of polymer and colloid dynamics. We determine D(r) from the propagators (Green's functions) of particle pairs obtained from discontinuous molecular dynamics simulations. At distances exceeding 3 molecular diameters, the calculated pair diffusion coefficients are in excellent agreement with predictions from exact macroscopic hydrodynamic theory for large Brownian particles suspended in a solvent bath, as well as the Oseen approximation. However, the asymptotic 1/r distance dependence of D(r) associated with hydrodynamic effects emerges only after the pair distance dynamics has been followed for relatively long times, indicating non-negligible memory effects in the pair diffusion at short times. Deviations of the calculated D(r) from the hydrodynamic models at short distances r reflect the underlying many-body fluid structure, and are found to be correlated to differences in the local available volume. The procedure used here to determine the pair diffusion coefficients can also be used for single-particle diffusion in confinement with spherical symmetry.