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