WIAS Preprint No. 632, (2001)

Flow instabilities in granular media due to porosity inhomogeneities


  • Wilhelm, Theo
  • Wilmański, Krzysztof

2010 Mathematics Subject Classification

  • 86-99 76E20 73Q05 76S05 76T05


  • Piping, channeling, flow instability in granular materials (fluidization), multicomponent model of saturated soils


The paper concerns a theoretical description of the piping phenomenon appearing in saturated sands at high filtration velocities. Motivated by own experiments we propose a thermodynamical two component model which accounts for a threshold effect at a critical value of the relative velocity of components. This property is incorporated in the source term of momentum balance equations by means of a nonlinear contribution accounting for spatial variations of the porosity. We prove the thermodynamical admissibility of such a model. By means of a linear stability analysis we show the existence of the onse of instability for realistic values of material parameters gained from experiments.

Appeared in

  • Internat. J. Multiphase Flows 28 (2002), pp. 1929--1944

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