title: Critical flow and clustering in a model of granular transport: the interplay between drift and antidiffusion.
abstract: We study the transport of granular matter through a staircaselike array of K vertically vibrated compartments. Given a constant inflow rate Q<Q{cr}(K) into the top compartment, a continuous particle flow establishes itself along the entire length of the system. However, as soon as Q grows beyond the critical value Q{cr}(K) the particles form a cluster and the flow comes to a halt. Interestingly, this clustering is preceded by a subcritical warning signal: for Q values just below Q{cr}(K) the density profile along the conveyor belt spontaneously develops a pattern in which the compartments are alternatingly densely and sparsely populated. In a previous paper [Kanellopoulos and van der Weele, Int. J. Bifurcation Chaos 21, 2305 (2011)] this pattern was shown to be the result of a period-doubling bifurcation. The present paper aims at unravelling the physical mechanism that lies at the basis of the pattern formation. To this end we study the continuum version of the same system, replacing the compartment number k=1,...,K by a continuous variable x. The dynamics of the system is now described (instead of by K coupled ordinary differential equations) by a single partial differential equation of the Fokker-Planck type, with a drift and a diffusive term that both depend on the density. The drift term turns out to be responsible for the subcritical density oscillations, thereby paving the way for the eventual clustering which sets in when the diffusion coefficient becomes negative. The observed sequence of events in the granular transport system is thus explained as an interplay between drift and (anti)diffusion.
authors.affiliation: Mathematics Department, University of Patras, 26500 Patras, Greece.
authors.forename: Giorgos
authors.initials: G
authors.lastname: Kanellopoulos
authors.forename: Ko
authors.initials: K
authors.lastname: van der Weele
mesh_terms: D003102:Colloids / Q000737:chemistry*; D003198:Computer Simulation; D008956:Models, Chemical; D008958:Models, Molecular; D009038:Motion; D012212:Rheology / Q000379:methods*
chemical_list: D003102:Colloids