No data available.

Please log in to see this content.

You have no subscription access to this content.

No metrics data to plot.

The attempt to load metrics for this article has failed.

The attempt to plot a graph for these metrics has failed.

Falling plumes of point particles in viscous fluid

Rent:

Rent this article for

USD

10.1063/1.4769125

### Abstract

The growth of radial bulges on the conduit of a falling viscous plume of particles, reported by Pignatel *et al.* for a finite starting plume [F. Pignatel, M. Nicolas, É. Guazzelli, and D. Saintillan, “Falling jets of particles in viscous fluids,” Phys. Fluids21, 123303 (2009)10.1063/1.3276235], is investigated both numerically and analytically. As a model for the plume conduit, an infinite vertical cylinder of identical non-Brownian point particles falling under gravity in Stokes flow is considered. Numerically, this is implemented with periodic boundary conditions of a large, but finite, period. The quasi-periodic numerical simulations exhibit qualitatively similar behaviour to that previously observed for the finite plume, demonstrating that neither the plume head nor the plume source play a role in the growth of the radial bulges. This growth is instead shown to be due to fluctuations in the average number density of particles along the plume about its mean value *n*, which leads to an initial growth rate proportional to *n* ^{−1/2}. The typical length scale of the bulges, which is of the order of 10 plume radii, results from the particle plume responding most strongly to density fluctuations in the axial direction on this scale. Large radial bulges undergo a nonlinear wave-breaking mechanism, which entrains ambient fluid and reduces the magnitude of perturbations on the plume surface. This contributes towards an outwards diffusion of the plume in which the increase in radius, at sufficiently large times, is proportional to *t* ^{2/3}.

© 2012 American Institute of Physics

Received 27 April 2012
Accepted 30 July 2012

Acknowledgments:
A.C. is grateful for support from an EPSRC studentship.

Article outline:

I. INTRODUCTION

II. PROBLEM DESCRIPTION

III. NUMERICAL METHOD

A. Temporal evolution

B. Statistical measures of macroscopic properties

IV. NUMERICAL RESULTS

A. Instability growth

B. Axial length scale of disturbances

C. Long-term growth of *R* ^{2}

D. Entrainment

E. Long-time growth of σ_{avg}

V. THEORY

A. Initial length scales and growth rates

B. Initial growth of σ

C. The continuum limit

D. Time scales for initial growth

E. Long-time evolution

VI. CONCLUSIONS

/content/aip/journal/pof2/24/12/10.1063/1.4769125

http://aip.metastore.ingenta.com/content/aip/journal/pof2/24/12/10.1063/1.4769125

Article metrics loading...

/content/aip/journal/pof2/24/12/10.1063/1.4769125

2012-12-01

2014-04-25

Full text loading...

### Most read this month

Article

content/aip/journal/pof2

Journal

5

3

Commenting has been disabled for this content