Lab Home | Phone | Search
Center for Nonlinear Studies  Center for Nonlinear Studies
 Colloquia Archive 
 Postdoc Seminars Archive 
 Quantum Lunch 
 CMS Colloquia 
 Q-Mat Seminars 
 Q-Mat Seminars Archive 
 Kac Lectures 
 Dist. Quant. Lecture 
 Ulam Scholar 
 Summer Research 
 Student Application 
 Past Visitors 
 PD Travel Request 
 History of CNLS 
 Maps, Directions 
 CNLS Office 
Tuesday, February 12, 2013
11:00 AM - 12:00 PM
CNLS Conference Room (TA-3, Bldg 1690)


Transport phenomena in flows of granular materials

Ivan Christov
Princeton University

Flowing granular materials are an example of a heterogeneous complex system away from equilibrium. As a result, their dynamics are still poorly understood. One canonical example is granular flow in a slowly-rotating container. Under some mild assumptions, the kinematics of the flow can be modeled and scalar mixing studied with the advection-diffusion equation paradigm. The shape of the container can induce chaotic trajectories, while the properties of the individual particles can lead to self-organization (demixing). The balance between these two effects leads to intricate persistent mixing patterns, which we show correspond to eigenmodes of an appropriate operator (Christov, Ottino & Lueptow, Phys. Fluids, 2011). However, granular materials do not perform thermally driven Brownian motion, so diffusion is observed in such systems because agitation (flow) causes inelastic collisions between particles. In a variation of the previous experiment, it has been suggested that axial diffusion of granular matter in a rotating drum might be "anomalous" in the sense that the mean squared displacement of particles follows a power law in time with exponent less than unity. Further numerical and experimental studies have been unable to definitively confirm or disprove whether a fractional diffusion equation describes this process. We can show that such a paradox can be resolved using Barenblatt's theory of self-similar intermediate asymptotics (Christov & Stone, Proc. Natl Acad. Sci. USA, 2012). Specifically, we find an analytical expression for the instantaneous scaling exponent of a macroscopic concentration profile, as a function of the initial distribution. Then, by incorporating concentration-dependent diffusivity into the model, we show the existence of a crossover from an anomalous scaling (consistent with experimental observations) to a normal diffusive scaling at very long times.

Host: Eli Ben-Naim, T-4