The conventional assumption, that the self-diffusion coefficient of a small tracer could be obtained by a local and instantaneous application of Einstein’s relationship in a temperature field with spatial and temporal heterogeneity, was questioned. It was shown that hydrodynamic fluctuations contributed to the self-diffusion tensor; regardless of the size and shape of the tracer. The hydrodynamic contribution was anisotropic, in that it reflected a knowledge of the global anisotropy in the temperature profile, leading to an anisotropic self-diffusion tensor for a spherical tracer. It was also retarded, and created memory effects during diffusion; due to hydrodynamic interactions.

Tracer Diffusivity in a Time- or Space-Dependent Temperature Field. R.Golestanian, A.Ajdari: Europhysics Letters, 2002, 59[6], 800-6