Tracer diffusivity in a time or space dependent temperature field

TL;DR

This paper revisits the calculation of tracer diffusivity in heterogeneous temperature fields, revealing hydrodynamic fluctuations' universal, anisotropic, and memory-effect contributions to the self-diffusion tensor.

Contribution

It demonstrates that hydrodynamic fluctuations universally influence tracer diffusion, leading to anisotropic and retarded effects in temperature-heterogeneous environments.

Findings

Hydrodynamic fluctuations contribute universally to self-diffusion.

Temperature heterogeneity induces anisotropic diffusion tensors.

Memory effects arise from hydrodynamic interactions during diffusion.

Abstract

The conventional assumption that the self-diffusion coefficient of a small tracer can be obtained by a local and instantaneous application of Einstein's relation in a temperature field with spatial and temporal heterogeneity is revisited. It is shown that hydrodynamic fluctuations contribute to the self-diffusion tensor in a universal way, i.e. independent of the size and shape of the tracer. The hydrodynamic contribution is anisotropic--it reflects knowledge of the global anisotropy in the temperature profile, leading to anisotropic self-diffusion tensor for a spherical tracer. It is also retarded--it creates memory effects during the diffusion process due to hydrodynamic interactions.