Power-law and exponential segregation in two-dimensional silos of granular mixtures

When a binary mixture of granular materials, differing in shape or size, is poured into a quasi-two-dimensional silo, segregation of the mixture is observed. Depending on the size ratio d2/d1 of the species, the mixture segregates completely or partially into the pure species. To study the partial-segregation effect we propose a theoretical model based on the work of Boutreux and de Gennes [J. Phys. I 6, 1295 (1996)] but we introduce more realistic collision functions. To compare the partial- and complete-segregation effects, we also discuss calculations for the complete-segregation model proposed by Makse [Phys. Rev. E 56, 7008 (1997)]. Our experiments confirm the analytical solutions for both types of segregation. We find that the transition from complete segregation to partial segregation appears as the size ratio of the species is decreased below a critical value, which is found to be d2/d1 approximately 1.4 for our system. Our experimental and analytical studies predict the regime for applicability of both partial- and complete-segregation models in terms of the size ratio of the species and the respective model parameters.