The modeling of the fluidization or sedimentation velocity of a suspension of solid particles is revisited by examining experiments conducted in either a liquid or a gas. A general expression is found in the case of negligible fluid inertia, i.e. at low Reynolds or Archimedes number. It is built as the product of the velocity of an isolated particle by three non-dimensional corrections that each takes into account a specific physical mechanism. The first correction reflects the variation of the buoyancy with the particle concentration. The second correction describes how the drag force increases with the concentration in case of negligible particle inertia. The third one accounts for the further increase of the drag when the particle inertia is increased. Remarkably, each correction only relies on a single of the three independent non-dimensional groups that control the problem: (1) the particle volume fraction Φ s ; (2) the ratio Φ s /Φ pack where Φ pack is the bed packing concentration; (3) the Stokes number St 0 , which characterizes the inertia of the particles and controls their agitation. Moreover, the onset of the instability that separates the homogeneous regime from the heterogeneous one is found to be controlled similarly by the Stokes number.Empirical expressions of the corrections are given, which provide a reliable tool to predict fluidization and sedimentation velocities for all values of the three non-dimensional numbers. The present results emphasize the crucial role of particle inertia, which is often disregarded in previous modeling approaches, such as that of Richardson and Zaki.
The investigation of the fall of a sphere at finite Reynolds number in a concentrated suspension of small fluidized particles leads to unexpected results. By analyzing the drag force, it is shown that the average surface stress on the sphere is independent of the size of the sphere. It is proportional to an effective viscosity determined from the sedimentation velocity of the particles multiplied by the velocity of the sphere and divided by the size of the particles. These results question the role of concentration inhomogeneities that occur on a large scale in the overall flow around a moving obstacle and on a small scale near its surface.
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