Granular Species Segregation under Vertical Tapping: Effects of Size, Density, Friction, and Shaking Amplitude Massimo Pica Ciamarra, * Maria Domenica De Vizia, Annalisa Fierro, Marco Tarzia, Antonio Coniglio, and Mario Nicodemi Dipartimento di Scienze Fisiche, Universita ´ di Napoli ‘‘Federico II’’, Coherentia-CNR, INFN, CRdC AMRA, Napoli, Italy (Received 29 July 2005; published 8 February 2006) We present extensive molecular dynamics simulations on species segregation in a granular mixture subject to vertical taps. We discuss how grain properties, e.g., size, density, friction, as well as shaking properties, e.g., amplitude and frequency, affect such a phenomenon. Both the Brazil nut effect (larger particles on the top, BN) and the reverse Brazil nut effect (larger particles on the bottom, RBN) are found and we derive the system comprehensive ‘‘segregation diagram’’ and the BN to RBN crossover line. We also discuss the role of friction and show that particles which differ only for their frictional properties segregate in states depending on the tapping acceleration and frequency. DOI: 10.1103/PhysRevLett.96.058001 PACS numbers: 45.70.Mg, 45.70.Qj Granular materials are systems of many particles inter- acting via short ranged repulsive and dissipative forces, both normal and tangential to the surface of contact. They are characterized by an energy scale mgd (of a grain of mass m and linear size d in the gravitational field g) which is many orders of magnitude larger than the thermal energy k B T, and are thus named ‘‘nonthermal’’ systems. These characteristics make difficult the understanding of the large variety of counterintuitive phenomena granular materials exhibit, which are of great interest both for their industrial relevance and for the theoretical challenges posed to phys- icist and engineers. Particularly the phenomenon of size segregation under vertical vibrations [1], which we consider here, has emerged as a real conundrum. Contrary to intuition, an originally disordered mixture when subject to vertical vi- brations tends to order: large particles typically rise to the top, as small particles percolate into their voids during shaking [1–4] or move to the bottom due to convection mechanisms [5–7], giving rise to the so-called ‘‘Brazil nut effect’’ (BN). Differences in particle density also affect size separation [see references in [8] ] and reverse-BN (RBN), with small grains above, can be observed, too [9,10]. The picture where grain sizes and weights are the parameters explaining segregation is found, however, to be too simple [9–20] and a full scenario is still missing. In correspondence with some existing experiments [21– 23], here we consider segregation phenomena in molecular dynamics simulations of tap dynamics: grains confined in a box are shaken and after each shake fully dissipate their kinetic energy before being shaken again. A picture of our model system is given in the left panel of Fig. 1 showing the final BN configuration reached by an initially disor- dered mixture shaken with an amplitude   A! 2 =g  1 (where ! is the shake frequency, A its amplitude, and g gravity acceleration, see below). An example of the role of the external drive on segregation can be appreciated by comparison with the right panel of Fig. 1 showing the final RBN configuration reached by the same mixture when shaken at   3. We show below how grain properties, e.g., size, density, friction, as well as the external forcing, e.g., shaking amplitude and frequency, affect the process and derive for the first time a comprehensive nontrivial ‘‘segregation diagram.’’ The richness of such a diagram is not captured by current theoretical approaches [9,12,19] and calls for new theoretical and experimental investigations. Simulations. —We make soft-core molecular dynamics simulations of a system of N l  240 large grains of di- ameter D l  1 cm and density  l  1:9 g cm 3 , and N s small grains with diameter D s and the density  s . We vary D s and  s and chose the number N s in such a way that the FIG. 1. We show a mixture of N l  240 large particles of diameter D l  1 cm and density  l  1:9 g cm 3 (dark gray particles) and N s  360 small particles of diameter D s  0:8 cm and density  s  1:27 g cm 3 (white particles). It is contained in a box (whose base is made of other immobile grains, light gray particles, see text) and is subject to vertical taps with normalized amplitude . The pictures show two configurations at rest attained at stationarity: interestingly, when shaken with   1 (left) the system goes into a BN configuration and when   3 (right) it goes in a RBN configu- ration. PRL 96, 058001 (2006) PHYSICAL REVIEW LETTERS week ending 10 FEBRUARY 2006 0031-9007= 06=96(5)=058001(4)$23.00 058001-1 © 2006 The American Physical Society