Bulk dynamics of Brownian hard disks: Dynamical density functional theory versus experiments on two-dimensional colloidal hard spheres

TL;DR

This study compares dynamical density functional theory predictions with experiments on two-dimensional colloidal hard spheres, showing good agreement at moderate densities but deviations at higher packing fractions due to hydrodynamic effects.

Contribution

The paper extends a DDFT approach to two dimensions and compares its predictions with experimental data for colloidal hard disks, highlighting its accuracy and limitations.

Findings

DDFT matches experiments well up to packing fraction ~0.60

Hydrodynamic effects significantly influence short-time diffusion in experiments

DDFT neglecting hydrodynamics shows no density dependence in diffusion

Abstract

Using dynamical density functional theory (DDFT), we theoretically study Brownian self-diffusion and structural relaxation of hard disks and compare to experimental results on quasi two-dimensional colloidal hard spheres. To this end, we calculate the self and distinct van Hove correlation functions by extending a recently proposed DDFT-approach for three-dimensional systems to two dimensions. We find that the theoretical results for both self- and distinct part of the van Hove function are in very good quantitative agreement with the experiments up to relatively high fluid packing fractions of roughly 0.60. However, at even higher densities, deviations between experiment and the theoretical approach become clearly visible. Upon increasing packing fraction, in experiments the short-time self diffusive behavior is strongly affected by hydrodynamic effects and leads to a significant decrease in the respective mean-squared displacement. In contrast, and in accordance with previous simulation studies, the present DDFT which neglects hydrodynamic effects, shows no dependence on the particle density for this quantity.