Woodruff School of Mechanical Engineering
Faculty Candidate Seminar
Transport Phenomena in Flows of Granular Materials
Dr. Ivan Christov
Monday, March 4, 2013 at 11:00:00 AM
MRDC Building, Room 4211
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.
Dr. Christov received his Ph.D. in Engineering Sciences and Applied Mathematics from Northwestern University in June of 2011, where he was a Walter P. Murphy Fellow. Subsequently, he was awarded an NSF Mathematical Sciences Postdoctoral Research Fellowship and is currently a Visiting Postdoctoral Research Fellow in Prof. Howard A. Stone's Complex Fluids Group at Princeton University. Previously, he has interned at the U.S. Naval Research Laboratory and the ExxonMobil Upstream Research Company. His research interests are primarily in the area of modeling and numerical simulation of nonlinear and complex systems, with an emphasis on transport and wave phenomena. Recently, he has been a short-term visiting researcher at the Oxford Centre for Collaborative Applied Mathematics and at the University of Bristol. He has given over a dozen invited lectures internationally and published over 20 articles in peer-reviewed scientific journals.
Refreshments will be served.