On the fluidization/sedimentation velocity of a homogeneous suspension in a low-inertia fluid

Abstract

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.

Fall of a large sphere in a suspension of small fluidized particles

“…It is constant for a given fluid-particle system and increases from 1 to 3 as St 0 increases from zero to infinity. Figure 2 shows that the experimental results obtained with the present suspensions collapse on the master curve proposed by [10], which validates the relevance of the viscosity µ m d determined from Eq. 1.…”

“…From the analysis of many fluid-particle systems, it has been shown in [10] that, provided that the fluid inertia is negligible, the fluidization velocity of a suspension can be modeled as…”

“…We used three sets of spherical glass beads of different sizes (GB 1 , GB 2 , GB 3 ) and one set of natural sand grains. Following[10,11], we introduce an effective viscosity of the suspension µ m d determined from the fluidization velocity. Let's consider a spherical bead of diameter d and density ρ d falling at velocity U f into a fluid of viscosity µ m d and density ρ m .…”

Continuum dynamics of suspensions at low Reynolds number

“…Many other groups have offered empirically determined functional forms to try to describe the dependence of sedimentation speed on volume fraction (see e.g. Amin, Girolami & Risso 2021).…”