James T. Jenkins
- School of Civil and Environmental Engineering, Cornell University, Ithaca, USA -
Title : Fluid-Particle Flow at and near a Particle Bed
We describe continuum models for the interaction of particles at and near a horizontal particle bed, under a turbulent shearing flow of a liquid.. We focus on situations that are steady and uniform in the flow direction. The particles are subject to gravity and the drag of the liquid above bed; they also experience fluid-mitigated collisions with particles of the bed and, perhaps, similar collisions with particles above the bed.
For modest strengths of shearing flow, a dilute cloud of saltating (jumping) particles above the bed exchange momentum with the fluid and collide with and rebound from particles of the bed. Because the cloud is dilute, regions of the bed subject to collisions are able to relax between collisions.
As the strength of the turbulent shearing above the bed increases, the momentum transfer between the fluid and particles above the bed is augmented by collisions between particles, and regions of the bed that experience a collision are not able to relax between collisions.
With further increases in shearing strength, a dense cloud of colliding particles forms beneath a more dilute cloud of saltating and colliding particles over a bed that is agitated, with an agitation that diminishes into its interior.
We will introduce models for the flow and the bed in the limits of pure saltation and pure collision and discuss possible ways that the two extremes can be linked and/or combined to provide the transition from one to the other.
- Institut de Physique du Globe de Paris, France -
Title : Shape, size and stability of alluvial rivers
Alluvial rivers build their bed with the sediment they carry. They obey Lacey's law which states that the width of a river scales with the square root of its discharge. This universal behavior suggests a common physical origin, but there is no consensus yet about what mechanism selects the size and shape of an alluvial river. Here we produce a small river in a laboratory experiment by pouring a viscous fluid on a layer of plastic sediment (Figure). With time, this laminar river reaches a steady-state geometry. In the absence of sediment transport, the combination of gravity and flow-induced stress maintains the bed surface at the threshold of motion.
If we impose a sediment discharge, the river adjusts by widening its channel. Particle tracking then reveals that the grains entrained by the flow behave as a collection of random walkers. Accordingly, they diffuse towards the less active areas of the bed. The shape of the river's cross-section results from the balance between this diffusive flux, which pushes the entrained grains towards the banks, and gravity, which returns them towards the center of the channel.
As the sediment discharge increases, the channel gets wider and shallower. Eventually, it destabilizes into new channels. A linear stability analysis suggests that the diffusion of the sediment causes this instability, which could explain the formation of braided rivers.
- Department of Earth Sciences, Durham University, UK -
- Planetary Science Institute, Tucson, USA -
Title : Particle-Fluid Flows on Earth and Mars
Powder snow avalanches, turbidity currents, debris flows, and pyroclastic flows are all examples of Terrestrial geophysical flows with a strong coupling between particles and a fluid. The particles are suspended by turbulence and the excess weight of the mixture drives the flow down or along a slope. Similar flows have now been directly observed on Mars and there is indirect evidence on other planetary bodies. Observations of dune gullies and recurring slope lineae on Mars are evidence for entirely new classes of flows. There is controversy about the flow mechanisms but they are possible caused by carbon dioxide sublimation and thermo-diffusion, respectively. To understand these observations physics based models that can be correctly scaled to very different temperatures, pressure and gravitational fields are necessary. We describe several such models and how they can be tested and developed using a combination of direct numerical simulation, laboratory experiments and field observations.
- IUSTI/CNRS, Marseille, France -
Title : Complex suspensions
Adding rigid particles in a fluid is known to change its properties, which might be a strategy to control the behavior of complex fluids. However, despite its long research history and its practical relevance both in industrial applications and in geophysical problems, the mechanics of suspensions in the dense regime remains poorly understood. In this talk, we will first discuss results obtained for suspensions of rigid spheres and rigid fibers in a newtonian fluid, with a special attention to the very dense regime close to the jamming transition. The investigation of this extreme regime has been made possible thanks to the development of a « pressure imposed rheometer ». We will then present the case of suspensions in a yield stress fluid, showing how empirical constitutive laws can be proposed from the knowledge of the rheology of newtonian suspensions. Finally, experiments on the rheology of a suspension in cornstarch will be presented, with a special interest on how the discontinuous shear thickening transition is modified by the presence of rigid coarse particles.