Segregation dynamics in debris flows

Debris flows are massive flows consisting of mixtures of particles of different sizes and interstitial fluids such as water and mud. In sheared mixtures of different-sized (same density) particles, it is well known that larger particles tend to go up (toward the free surface), and the smaller particles, down, commonly referred to as the “Brazil-nut problem” or “kinetic sieving”. When kinetic sieving fluxes are combined with advection in flows, they can give rise to a spectacular range of segregation patterns. These segregation / advection dynamics are recognized as playing a role in the coarsening of a debris flow front (its “snout”) and the coarsening of the self-formed channel sides or levees. Since particle size distribution influences the flow dynamics including entrainment of bed materials, modeling segregation dynamics in debris flows is important for modeling the debris flows themselves.

In sparser systems, the Brazil-nut segregation is well-modeled using kinetic theory applied to dissipative systems, where an underlying assumption involves random, uncorrelated collisions. In denser systems, where kinetic theory breaks down we have recently developed a new mixture model that demonstrates the segregation fluxes are driven by two effects associated with the kinetic stress or granular temperature (the kinetic energy associated with velocity fluctuations): (1) the difference between the partitioning of kinetic and contact stresses among the species in the mixture and (2) a kinetic stress gradient. Both model frameworks involve the temperature gradient as a driving force for segregation, but kinetic theory sends larger particles toward lower temperatures, and our mixture model sends larger particles away from lower temperatures. Which framework works under what conditions appears to depend on correlations in the flow such as those manifested in clusters and force chains. We discuss the application of each theoretical framework to representing segregation dynamics in debris flows and the application to modeling flow and entrainment as they depend on particle size distributions.