Fluidized bed in a confined volume

P. Vainshtein, M. Fichman, M. Shapiro*, L. Moldavsky, C. Gutfinger

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


Coarse solid elastic enough particles form a packed bed in a vertical cylinder confined from below and from above by permeable elastic plates. A gas is forced through the lower plate with a velocity exceeding the terminal (transport) velocity. Adjacent to the lower plate the particles are entrained and impact on the upper plate. As a result, fluidization regimes of still unreported types take place in the confined cylinder. These regimes are analyzed qualitatively by a theoretical model proposed here. This model describes the mean motions of the gas and particles. It includes the mass and momentum equations for the gas and particle phases and the equation of the kinetic energy of particle fluctuations. The system of equations is supplemented by constitutive equations for the averaged drag force, granular pressure, kinetic energy dissipation due to inelastic particle collisions, and energy generation. It is assumed that generation of the kinetic energy is caused by the lateral Magnus force due to particle rotation. Steady state solutions of the equations are obtained, which describe the fluidization regimes in a confined cylinder, namely disperse for a fluidized bed with increasing or decreasing volume fraction and for an inverted packed bed. Experiments are performed to show the existence of the disperse regime of fluidization. Stability of the disperse bed with respect to small perturbations is considered. It is shown that a disperse fluidized bed is unstable for sufficiently concentrated dispersions where the bulk modulus of elasticity of the granular phase is negative. The effect of vibrations of the upper plate upon fluidization regimes is also studied. Resonant frequencies are detected in the concentration region where the bulk modulus of elasticity is positive.

Original languageEnglish
Pages (from-to)1431-1456
Number of pages26
JournalInternational Journal of Multiphase Flow
Issue number6-7
StatePublished - Sep 1999
Externally publishedYes


  • Confined volume
  • Fluidization regimes
  • Fluidized bed


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