Segregation-Induced Granular Fingering

Chico Rocha (The University of Manchester)

ATB Frank Adams 1,

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 (Gray & Ancey 2009). 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 (Pouliquen et al. 1997). 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 (Woodhouse et al. 2012). Recently, a well-posed model was presented (Baker et al. 2016), in which a dissipative viscous-like term derived from the μ(I)-rheology (Gray & Edwards 2014) is incorporated to the avalanche model. We use fully non-linear simulations of this model to make a first assessment of the fastest growing mode of the frontal instability, which sets the finger wavelength.

 

References

Baker, J. L., Johnson, C. G. & Gray, J. M. N. T. (2016), ‘Segregation-induced finger formation in granular free-surface flows’, Journal of Fluid Mechanics 809, 168–212.

Gray, J. & Ancey, C. (2009), ‘Segregation, recirculation and deposition of coarse particles near two-dimensional avalanche fronts’, Journal of Fluid Mechanics 629, 387.

Gray, J. M. N. T. & Edwards, A. N. (2014), ‘A depth-averaged μ(I)-rheology for shallow granular free-surface flows’, Journal of Fluid Mechanics 755, 503–534.

Pouliquen, O., Delour, J. & Savage, S. B. (1997), ‘Fingering in granular flows’, Nature 386(6627), 816. Woodhouse, M. J., Thornton, A. R., Johnson, C. G., Kokelaar, B. P. & Gray, J. M. N. T. (2012), ‘Segregation-induced fingering instabilities in granular free-surface flows’, Journal of fluid mechanics 709, 543–580.

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