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Abstract The dynamics of geophysical dilute turbulent gas‐particles mixtures depends to a large extent on particle concentration, which in turn depends predominantly on the particle settling velocity. We experimentally investigate air‐particle mixtures contained in a vertical pipe in which the velocity of an ascending air flux matches the settling velocity of glass particles. To obtain local particle concentrations in these mixtures, we use acoustic probing and air pressure measurements and show that these independent techniques yield similar results for a range of particle sizes and particle concentrations. Moreover, we find that in suspensions of small particles (78 μm) the settling velocity increases with the local particle concentration due to the formation of particle clusters. These clusters settle with a velocity that is four times faster than the terminal settling velocity of single particles, and they double settling speeds of the suspensions. In contrast, in suspensions of larger particles (467 μm) the settling velocity decreases with increasing particle concentration. Although particle clusters are still present in this case, the settling velocity is decreased by 30%, which is captured by a hindered settling model. These results suggest an interplay between hindered settling and cluster‐induced enhanced settling, which in our experiments occur respectively at Stokes number O(100) and O(1). We discuss implications for volcanic plumes and pyroclastic currents. Our study suggests that clustering and related enhanced or hindered particle settling velocities should be considered in models of volcanic phenomena and that drag law corrections are needed for reliable predictions and hazard assessment.
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Preferential concentration driven instability of sheared gas–solid suspensions
We examine the linear stability of a homogeneous gas–solid suspension of small Stokes number particles, with a moderate mass loading, subject to a simple shear flow. The modulation of the gravitational force exerted on the suspension, due to preferential concentration of particles in regions of low vorticity, in response to an imposed velocity perturbation, can lead to an algebraic instability. Since the fastest growing modes have wavelengths small compared with the characteristic length scale ( $$U_{g}/{\it\Gamma}$$ ) and oscillate with frequencies large compared with $${\it\Gamma}$$ , $$U_{g}$$ being the settling velocity and $${\it\Gamma}$$ the shear rate, we apply the WKB method, a multiple scale technique. This analysis reveals the existence of a number density mode which travels due to the settling of the particles and a momentum mode which travels due to the cross-streamline momentum transport caused by settling. These modes are coupled at a turning point which occurs when the wavevector is nearly horizontal and the most amplified perturbations are those in which a momentum wave upstream of the turning point creates a downstream number density wave. The particle number density perturbations reach a finite, but large amplitude that persists after the wave becomes aligned with the velocity gradient. The growth of the amplitude of particle concentration and fluid velocity disturbances is characterised as a function of the wavenumber and Reynolds number ( $$\mathit{Re}=U_{g}^{2}/{\it\Gamma}{\it\nu}$$ ) using both asymptotic theory and a numerical solution of the linearised equations.
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- Award ID(s):
- 1233793
- PAR ID:
- 10025838
- Date Published:
- Journal Name:
- Journal of Fluid Mechanics
- Volume:
- 770
- ISSN:
- 0022-1120
- Page Range / eLocation ID:
- 85 to 123
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1017/jfm.2015.136
