Spreading fronts in sedimentation of dilute suspension of spheres

Abstract

The thickness of the diffuse front between a sedimenting dilute suspension and the clear fluid above grows linearly in time due to polydispersity in the size of the particles and due to a hydrodynamic effect in which randomly heavy clusters fall out of the front leaving it depleted. Experiments and simplified point-particle numerical simulations agree that these two effects are not simply linearly additive.

The remarkable longevity of submarine plumes: Implications for the hydrothermal input of iron to the deep-ocean

“…This relationship is found to capture the behavior of our experimental materials in a simplified 2D Hele-Shaw geometry in the limit of dilute suspension (5 × 10 −4 < C < 5 × 10 −2 ) such as a = 1.2 with R 2 = 0.953. Moreover, it is fully consistent with previous experimental results on particle sedimentation in dilute suspensions (Bergougnoux et al, 2003;Chehata Gomez et al, 2008, 2009.…”

“…The effect of multiple scattering is considered to be small (within the error bars in Fig. 4 of the paper) at the low concentration used in this study, which is consistent with our 2D experiments and previous published work (Bergougnoux et al, 2003;Chehata Gomez et al, 2008, 2009). …”

Concentration instability of sedimenting spheres in a second-order fluid

“…In the Newtonian case [ Fig. 4(a)], a diffuse concentration front is found to develop and spread at the interface with the clear fluid, as previously characterized in experiments and simulations; 8,12,48 however, the concentration profile remains nearly uniform and equal to the mean concentration in the bulk of the suspension away from the front, except in the late stages of the sedimentation process when the front becomes very broad. In a viscoelastic fluid [Figs.…”

“…While this differs from the no-slip boundary condition applying at the walls of a rigid container, it has the advantage of allowing for a very efficient spectral solution while preventing fluid penetration at the boundaries, a feature that has previously been shown to be critical in sedimentation simulations. 7 Previous simulations of sphere suspensions, 8,12,48 as well as spheroid suspensions, 32,33 have demonstrated that this boundary condition is sufficient to capture most salient features observed in sedimentation experiments, including the decay of velocity fluctuations in sphere suspensions, 12 and a wavenumber selection for density fluctuations in spheroid suspensions. 33 Note, however, that owing to the freeshear-stress condition there is no resistance to tangential flow close the the boundaries, which may have a quantitative effect on velocity fluctuations in the suspensions.…”

Numerical and experimental analysis of the sedimentation of spherical colloidal suspensions under centrifugal force

“…Polydispersity in the particle size, and Brownian motion of colloidal sized particles, may cause the thickness of this interface to increase in time. 7 Sedimentation continues until all of the dispersed phase is contained within the sediment bed, with only clear fluid above. When this is the case, complete phase separation has occurred.…”