Ioannis Vardoulakis
Department of Mechanics, Faculty of Applied Mathematics and Physics
National Technical University of Athens
Fluidization of Sands in Artesian Flow Conditions

A two-, three- phase continuum theory for fully fluidized, fluid-flown, granular media is presented. The analysis is restricted to artesian flow conditions and utilizes results from previous studies on fluidization [1-4], erosion and sand production [5,6].

It is demonstrated that at the state of incipient fluidization hydromechanically stable sands undergo a discontinuous phase transition. The stationary fluidized state is characterized by the development of particle repulsion [1] and the effect of weak inertia [7] on the resistance of the fluidized granular bed to flow. Based on Richardson's expansion law it is demonstrated that the adjustment of porosity to small increases in the fluid-flow rate takes place via small-amplitude kinematic porosity rarefaction waves [4]. Linear stability analysis of perturbations out of the state stationary, uniform fluidization shows that granular inertia plays a destabilizing role leading to mathematical ill-posedeness. Mathematical ill-posedeness is removed by considering the effect of mixture's viscosity [8].

Further, the concepts of fluidization and sand transport are utilized to backanalyze the column tests with gap-graded soils [9]. It is shown that the observed abnormal decrease in hydraulic resistivity can be attributed to a progressive partial fluidization of the fine's fraction of the soil, which eventually leads to unplugging of the pore space and to segregation piping-erosion in form of a run-away instability [10].

References
  1. Batchelor, G.K. (1988). A new theory of the instability of a uniform fluidized bed. J. Fluid Mech., 193, 75-110.
  2. Göz, M.F. (1992). On the origin of wave patterns in fluidized beds. J. Fluid Mech., 240, 379-404.
  3. Harris, S.E. and Crighton, D.G. (1994). Solitons, solitary waves, and voidage disturbances in gas-fluidized beds. J. Fluid Mech., 266,243-276.
  4. Vardoulakis, I., Stavropoulou, M. and Skjaerstein, A. (1998). Porosity waves in fluidized sand-column tests. Proc. Royal Soc. London A., 356, 1-18.
  5. Vardoulakis, I., Stavropoulou, M., Papanastasiou P. (1995). Hydromechanical aspects of sand production problem. Transport in Porous Media, 22, 225-244.
  6. Vardoulakis I, Papanastasiou P., Stavropoulou M. (2001). Sand erosion in axial flow conditions. Transport in Porous Media, 45, 261-281.
  7. Skjetne, E. and Auriault, J.L. (1999). New insights on steady, non-linear flow in porous media. Eur. J. Mech. B/ Fluids, 18, 131-145.
  8. Vardoulakis I. (2002a). Fluidization in Artesian Flow Conditions: I. Hydromechanically stable granular media. (submitted for publication).
  9. Skempton, A. W. and Brogan, J. M. (1994). Experiments on piping in sandy gravels. Géotechnique 44, 449-460.
  10. Vardoulakis I. (2002b). Fluidization in Artesian Flow Conditions: II. Hydromechanically unstable granular media. (submitted for publication).
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