Close packing density of polydisperse hard spheres

Area of Science:

• Physics
• Materials Science
• Chemical Engineering

Background:

• The random close packed state is crucial for modeling granular materials, but real materials have polydisperse particle sizes.
• Existing models often assume monodisperse spheres, limiting their applicability to real-world scenarios.

Purpose of the Study:

• To develop a simple yet accurate approximation for the random close packing density of hard spheres with any size distribution.
• To validate the proposed theory through extensive simulations.

Main Methods:

• Mapping a three-dimensional sphere packing problem onto a one-dimensional equivalent.
• Performing extensive simulations of elastic sphere mixtures with hydrodynamic friction.

Main Results:

• The developed theory accurately predicts random close packing density for bidisperse, tridisperse, and log-normal distributions.
• Simulations confirmed a weak dependence on fluid viscosity and particle size, which can be eliminated by specific mass-size relations.
• The theory correctly reproduces known limits for large size ratios.

Conclusions:

• The proposed theory provides a robust method for determining the random close packing density of polydisperse hard spheres.
• This work offers a more realistic approach to modeling granular materials in physics and engineering applications.