Retrogressive failure of a layer of granular material on an inclined plane - Aaron Russell
The flow of granular materials down an inclined plane is closely related to many natural hazards, such as landslides and avalanches, which can cause serious damage to life and property. Avalanches can be triggered by many different factors, such as human activities, new material falling, wind or earthquakes. When an avalanche is triggered by a local disturbance, it is not only material downstream of this disturbance that is dislodged. Material upslope of the disturbance may also collapse, through an upwards propagating erosion wave through the granular layer, or `retrogressive failure', which separates the regions of flowing and static material. This retrogressive failure is critically dependent on physics beyond the $\mu(I)$-rheology and, despite being one of the basic waves in granular flow, has not been modelled in detail before. We use small scale lab experiments, novel theory and numerical simulations to model retrogressive failure, and apply our results to both geophysical and industrial contexts.
Formation of levees, troughs and elevated channels by avalanches on erodible slopes - Andrew Edwards
Snow avalanches are typically initiated on marginally stable slopes with a layer of fresh snow that may easily be incorporated into the avalanche. The net balance of erosion and deposition of snow determines whether an avalanche grows, starves away or propagates steadily.
We present the results of small scale experiments in which particles are released on a rough inclined plane coated with a static erodible layer of the same grains. For thick static layers on steep slopes the initial avalanche grows rapidly in size by entraining grains. On shallower slopes an elevated channel forms and material is eventually brought to rest due to a greater rate of deposition than erosion. On steep slopes with thinner erodible layers it is possible to generate avalanches that have a perfect balance between erosion and deposition, leaving a constant width trough with levees.
We then show, by combining Pouliquen & Forterre (2002)'s friction law with Gray & Edwards (2014)'s depth-averaged mu(I)-rheology, that it is possible to develop a simple 2D shallow water-like avalanche model that qualitatively captures all of the experimental behaviours. Hence this model may have important practical implications for modeling the initiation, growth and decay of snow avalanches for hazard risk assessment.
Segregation-induced granular fingering - Chico Rocha
It is well known that a mixture of grains of different sizes tends to segregate as they avalanche downslope, with large particles rising to the near surface regions, which move faster. As a result, large particles tend to be preferentially transported to flow front, where they can accumulate by being over-run and resegregated to the surface. If the large particles are also more frictional, the flow becomes unstable and breaks- up in a series of fingers: the so-called granular fingering instability. This instability is observed in a wide variety of systems, from geophysical mass flows, such as pyroclastic flows, to small-scale experiments relevant to industry. Although key features of the fingering pattern are predicted by a particle-size segregation model, coupled with a standard depth-averaged avalanche model, stability analysis shows that the equations are ill-posed, leading to unphysical growth of short-wavelength perturbations. Recently, a well-posed model was presented Baker, Johnson and Gray, in which a dissipative viscous-like term derived from the μ(I)-rheology is incorporated to the avalanche model. In this paper we use fully nonlinear simulations of this model to make a first assessment of the fastest growing mode of the frontal instability, which sets the finger wavelength.
Sorting capsules by deformability - Edgar Haener
The deformability of cells is an important biomarker for disease. Artificial capsules are used widely from drug delivery to agriculture. The mechanical properties of these artificial capsules need to be tailored to the application. We study experimentally the flow-induced deformation of liquid-filled ovalbumin-alginate capsules in two sorting devices: a straight channel with a half-cylindrical obstruction and a pinched flow fractioning device (PFF) adapted for use with capsules. In the half-cylinder device, the capsules deform as they encounter the obstruction, and travel around the half-cylinder. The distance from the capsule’s centre of mass to the surface of the half-cylinder depends on deformability, and separation between capsules of different deformability is amplified by diverging streamlines in the channel expansion downstream of the obstruction. We show experimentally that capsules can be sorted according to deformability with their downstream position depending on capillary number only, and we establish the sensitivity of the device to experimental variability. In the PFF device, particles are compressed against a wall using a strong pinching flow. We show that capsule deformation increases with the intensity of the pinching flow, but that the downstream capsule position is not set by deformation in the device. However, when using the PFF device like a T-Junction, we achieve improved sorting resolution compared to the half-cylinder device.
Well-posed continuum equations for granular flow with compressibility and μ(I)-rheology - Tom Barker
Continuum modelling of granular flow has been plagued with the issue of ill-posed equations for a long time. Equations for incompressible, two-dimensional flow based on the Coulomb friction law are ill-posed regardless of the deformation, whereas the rate-dependent μ(I)-rheology is ill-posed when the non-dimensional strain-rate I is too high or too low. Here, incorporating ideas from Critical-State Soil Mechanics, we derive conditions for well-posedness of PDEs that combine compressibility with I-dependent rheology. When the I-dependence comes from a specific friction coefficient μ(I), our results show that, with compressibility, the equations are well-posed for all deformation rates provided that μ(I) satisfies certain minimal, physically natural, inequalities.