Ranked percolation model for the caking time of amorphous molecular powders

When amorphous molecular powders are exposed to high humidity levels or temperatures, the particle viscosity increases due to plasticization, promoting the formation of sinter bridges between pairs of particles in contact. Over time, these bridges facilitate particle agglomeration, eventually leading to the formation of a macroscopic cake that alters the mechanical properties and affects product quality. In this work, we model the caking process of amorphous powders subjected to a temperature shock as a bond percolation problem and investigate how particle bed heterogeneities influence the percolation threshold and, consequently, the expected caking times. Our findings indicate that a slight dispersion in particle size lowers the percolation threshold compared to a monodisperse bed or random percolation in polydisperse systems. Furthermore, we show that the expected caking time exhibits a non-monotonic behavior with the size dispersion, initially decreasing for low dispersion values and increasing for higher values. These results provide insights into the role of the particle size distribution on the caking dynamics of amorphous molecular powders