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

Area of Science:

• Fluid dynamics
• Colloid science
• Statistical mechanics

Background:

• Hydrodynamic interactions are crucial for understanding polymer and colloid dynamics.
• The pair diffusion coefficient D(r) quantifies these interactions between particles.
• Accurate calculation of D(r) is essential for theoretical models.

Purpose of the Study:

• To calculate the pair diffusion coefficient D(r) for hard spheres in a dense fluid.
• To compare simulation results with macroscopic hydrodynamic theories and approximations.
• To investigate the influence of fluid structure and memory effects on D(r).

Main Methods:

• Molecular dynamics simulations were used to obtain particle pair propagators (Green's functions).
• The pair diffusion coefficient D(r) was determined from these simulation data.
• Comparison with exact macroscopic hydrodynamic theory and the Oseen approximation was performed.

Main Results:

• D(r) agrees well with hydrodynamic theories for distances greater than ~3 molecular diameters.
• The asymptotic 1/r dependence of D(r) appears only after long simulation times, indicating short-time memory effects.
• Deviations from hydrodynamic models at short distances correlate with local available volume and many-body fluid structure.

Conclusions:

• Macroscopic hydrodynamic theories accurately describe pair diffusion at larger scales.
• Short-time dynamics are influenced by memory effects and local fluid structure, deviating from simple hydrodynamic predictions.
• The methodology is applicable to single-particle diffusion in confined systems.