Toward Bernal Random Loose Packing through freeze-thaw cycling

TL;DR

This study investigates how freeze-thaw cycles influence the packing density of spheres in water, revealing a convergence to a Bernal-like random loose packing state through experimental and numerical analysis.

Contribution

It demonstrates that freeze-thaw cycling can reliably produce a Bernal random loose packing state in granular materials, supported by both experiments and simulations.

Findings

Packing fraction converges to 0.595 after multiple cycles.

Packs remain fully random during the process.

Freeze-thaw cycling is an effective homogeneous driving method.

Abstract

We study the effect of freeze-thaw cycling on the packing fraction of equal spheres immersed in water. The water located between the grains experiences a dilatation during freezing and a contraction during melting. After several cycles, the packing fraction converges to a particular value $\eta_{\infty} = 0.595$ independently of its initial value $\eta_0$. This behavior is well reproduced by numerical simulations. Moreover, the numerical results allow to analyze the packing structural configuration. With a Vorono\"i partition analysis, we show that the piles are fully random during the whole process and are characterized by two parameters: the average Vorono\"i volume $\mu_v$ (related to the packing fraction $\eta$) and the standard deviation $\sigma_v$ of Vorono\"i volumes. The freeze-thaw driving modify the volume standard deviation $\sigma_v$ to converge to a particular disordered state with a packing fraction corresponding to the Random Loose Packing fraction $\eta_{BRLP}$ obtained by Bernal during his pioneering experimental work. Therefore, freeze-thaw cycling is found to be a soft and spatially homogeneous driving method for disordered granular materials.