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Robust threshold for Degree Ranked Percolation of granular packings

By: Vasco Braz
From: CFTC, Faculdade de Ciências, Universidade de Lisboa
At: Building C8, room 8.2.06
[2025-02-18]

Amorphous molecular powders are prevalent in daily life, from common food products like flour, sugar, coffee, and cocoa to powders used in pharmaceuticals and construction. When exposed to high humidity or elevated temperatures, particle viscosity increases due to plasticization, promoting the formation of sinter bridges. Over time, particles agglomerate, eventually forming lumps that span the entire powder bed, leading to caking and affecting mechanical properties and quality perception.

Recently, it has been demonstrated that the caking of amorphous powders can be mapped as a percolation problem, where site occupation follows a well-defined order depending on the physical causes leading to caking. When caking is induced by a humidity shock, the process follows an ordered percolation based on increasing particle size. Conversely, if caking is triggered by a sudden increase in temperature, site occupation tends to follow the inverse order.

Studying the ordered percolation threshold in granular packs is particularly relevant for systems composed of particles with varying sizes and shapes or different geometric and dimensional constraints. In this work, we investigate the effect of size dispersion in granular beds on the percolation threshold when contact network nodes are occupied in an ordered manner, from the least connected nodes (typically smaller grains) to the more connected ones (typically larger grains). We demonstrate that, across a wide range of size distributions, the ranked percolation threshold changes substantially, while the average number of connections per particle remains approximately constant. Using numerical simulations and an analytical approach, we show that the existence of a characteristic critical fraction of connections per particle results from the peaked nature of degree distributions arising due to strong spatial constraints.