Toward Bernal Random Loose Packing through freeze-thaw cycling

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.