Sedimentation of gas-fluidized particles with random shape and size

This work deals with the fluidization and sedimentation of fine solid particles, of random shape and size, similar to those commonly involved in geophysical mass flows, such as pyroclastic flows. While heated to avoid the effect of moisture and the formation of clusters, particles were first uniformly fluidized by a hot gas flow, up to a high expansion rate, and then sedimented after stopping the gas supply. Three different materials are explored, involving contrasted geometries, each characterized by a specific particle volume fraction at packing ${\mathrm{\Phi }}_{\mathrm{pack}}$. Within the range of values of the solid volume fraction ${\mathrm{\Phi }}_s/{\mathrm{\Phi }}_{\mathrm{pack}}$ studied here, the dense suspension forms a fully fluidized homogeneous mixture, with no segregation, for which the fluidization and sedimentation velocities are equal. Despite a significant discrepancy between the intrinsic properties of the different materials used, all measured velocities are observed to collapse into a single master curve $f({\mathrm{\Phi }}_s/{\mathrm{\Phi }}_{\mathrm{pack}})$ provided that they are normalized by the relevant scaling. Regarding the sedimentation velocity, ${\mathrm{\Phi }}_{\mathrm{pack}}$ turns out to be sufficient to characterize the material made with a random distribution in particle shape and size.

Figure 1

Pictures and size distributions of ${\mathrm{Ash}}^1$, ${\mathrm{Ash}}^2$, and FCC.

Figure 2

Fluidization and sedimentation processes applied to a bed of particles: (a) the packed state ($U_f<U_{mf}$), (b) the homogeneous fluidization associated with a uniform bed expansion ($U_{mf}<U_f<U_{mb}$), (c) the sedimentation process obtained after cutting the gas supply ($U_{\mathrm{sed}}=U_f$).

Figure 3

Fluidization velocity $U_f$ (light-gray symbols, measured with an accuracy of $\pm 1\%$) and sedimentation velocity $U_{\mathrm{sed}}$ (dark-gray symbols, measured with an accuracy of $\pm 3\%$) as a function of the particle volume fraction ${\mathrm{\Phi }}_s$ (measured with an accuracy of $\pm 2\%$). White symbols represent $U_{mf}$, while blue and pink symbols indicate, respectively, the predictions of Ergun (1952) [12] and Richardson and Zaki (1954) [1] for $U_{mf}$.

Figure 4

Correction coefficient $\alpha$ accounting for the nonsphericity of the particles in the Stokes drag force as a function of the particle aspect ratio $\lambda$.

Figure 5

Apparent bulk viscosity of the suspension normalized by the gas viscosity ${\mu }_m/{\mu }_f$ (determined with an accuracy of $\pm 6\%$), which is the same as the inverse normalized sedimentation velocity ${(U/U_{\mathrm{ref}})}^{-1}$, as a function of normalized solid volume fraction ${\mathrm{\Phi }}_s/{\mathrm{\Phi }}_{\mathrm{pack}}$. Light-blue symbols represent the values at $U_{mf}$. ${\mathrm{\Phi }}_s/{\mathrm{\Phi }}_{\mathrm{pack}}$ is determined with an accuracy of $\pm 1\%$, while ${\mu }_m/{\mu }_f$ have an accuracy of $\pm 6\%$.