Hostname: page-component-78c5997874-xbtfd Total loading time: 0 Render date: 2024-11-04T21:41:41.060Z Has data issue: false hasContentIssue false
  • English
  • Français

Fast equilibration dynamics of viscous particle-laden flow in an inclined channel

Published online by Cambridge University Press:  19 September 2019

Jeffrey Wong Open the ORCID record for Jeffrey Wong [Opens in a new window] ,
Michael Lindstrom  and
Andrea L. Bertozzi
Jeffrey Wong*
Affiliation:
Department of Mathematics, Duke University, Durham, NC 27708, USA Department of Mathematics, University of California, Los Angeles, CA 90095, USA
Michael Lindstrom
Affiliation:
Department of Mathematics, University of California, Los Angeles, CA 90095, USA
Andrea L. Bertozzi
Affiliation:
Department of Mathematics, University of California, Los Angeles, CA 90095, USA Department of Mechanical and Aerospace Engineering, University of California, Los Angeles, CA 90095, USA
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

A viscous suspension of negatively buoyant particles released into a wide, open channel on an incline will stratify in the normal direction as it flows. We model the early dynamics of this stratification under the effects of sedimentation and shear-induced migration. Prior work focuses on the behaviour after equilibration where the bulk suspension either separates into two distinct fronts (settled) or forms a single, particle-laden front (ridged), depending on whether the initial concentration of particles exceeds a critical threshold. From past experiments, it is also clear that this equilibration time scale grows considerably near the critical concentration. This paper models the approach to equilibrium. We present a theory of the dramatic growth in this equilibration time when the mixture concentration is near the critical value, where the balance between settling and shear-induced resuspension reverses.

JFM classification

Interfacial Flows (free surface): Thin films Low-Reynolds-number flows: Lubrication theory
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 879 , 25 November 2019 , pp. 28 - 53
Check for updates
Copyright
© 2019 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Abousnina, R. M., Manalo, A., Shiau, J. & Lokuge, W. 2015 Effects of light crude oil contamination on the physical and mechanical properties of fine sand. Intl J. Soil Sedim. Contam. 24 (8), 833–845.10.1080/15320383.2015.1058338Google Scholar
Arnold, D. J., Stokes, Y. M. & Green, J. E. F. 2015 Thin-film flow in helically-wound rectangular channels of arbitrary torsion and curvature. J. Fluid Mech. 764, 76–94.10.1017/jfm.2014.703Google Scholar
Berres, S., Bürger, R. & Tory, E. M. 2005 Applications of polydisperse sedimentation models. Chem. Engng J. 111 (2-3), 105–117.10.1016/j.cej.2005.02.006Google Scholar
Boyer, F., Pouliquen, O. & Guazzelli, É. 2011 Dense suspensions in rotating-rod flows: normal stresses and particle migration. J. Fluid Mech. 686, 5–25.10.1017/jfm.2011.272Google Scholar
Chen, Y., Malambri, F. & Lee, S. 2018 Viscous fingering of a draining suspension. Phys. Rev. Fluids 3 (9), 094001.10.1103/PhysRevFluids.3.094001Google Scholar
Cook, B. P., Bertozzi, A. L. & Hosoi, A. E. 2008 Shock solutions for particle-laden thin films. SIAM J. Appl. Maths 68 (3), 760–783.10.1137/060677811Google Scholar
Dbouk, T., Lobry, L. & Lemaire, E. 2013 Normal stresses in concentrated non-Brownian suspensions. J. Fluid Mech. 715, 239–272.10.1017/jfm.2012.516Google Scholar
Delannay, R., Valance, A., Mangeney, A. & Richard, P. 2017 Granular and particle-laden flows: from laboratory experiments to field observations. J. Phys. D: Appl. Phys. 50 (5), 053001.10.1088/1361-6463/50/5/053001Google Scholar
Huppert, H. E. 1982 Flow and instability of a viscous current down a slope. Nature 300 (5891), 427–429.10.1038/300427a0Google Scholar
Katz, O. & Aharonov, E. 2006 Landslides in vibrating sand box: What controls types of slope failure and frequency magnitude relations? Earth Planet. Sci. Lett. 247 (3–4), 280–294.10.1016/j.epsl.2006.05.009Google Scholar
Lareo, C., Fryer, P. J. & Barigou, M. 1997 The fluid mechanics of two-phase solid–liquid food flows: a review. Food Bioprod. Process. 75 (2), 73–105.10.1205/096030897531405Google Scholar
Lee, S., Stokes, Y. & Bertozzi, A. L. 2014 Behavior of a particle-laden flow in a spiral channel. Phys. Fluids 26 (4), 1661–1673.10.1063/1.4872035Google Scholar
Leighton, D. & Acrivos, A. 1987 Shear-induced migration of particles in concentrated suspensions. J. Fluid Mech. 181, 415–439.10.1017/S0022112087002155Google Scholar
Leonardi, A.2015 Numerical simulation of debris flow and interaction between flow and obstacle via dem. PhD thesis, ETH Zurich.Google Scholar
Miller, R. M. & Morris, J. F. 2006 Normal stress-driven migration and axial development in pressure-driven flow of concentrated suspensions. J. Non-Newtonian Fluid Mech. 135 (2), 149–165.10.1016/j.jnnfm.2005.11.009Google Scholar
Morris, J. F. & Boulay, F. 1999 Curvilinear flows of noncolloidal suspensions: the role of normal stresses. J. Rheol. 43 (5), 1213–1237.10.1122/1.551021Google Scholar
Murisic, N., Ho, J., Hu, V., Latterman, P., Koch, T., Lin, K., Mata, M. & Bertozzi, A. L. 2011 Particle-laden viscous thin-film flows on an incline: experiments compared with an equilibrium theory based on shear-induced migration and particle settling. Physica D 240 (20), 1661–1673.Google Scholar
Murisic, N., Pausader, B., Peschka, D. & Bertozzi, A. L. 2013 Dynamics of particle settling and resuspension in viscous liquid films. J. Fluid Mech. 717, 203–231.10.1017/jfm.2012.567Google Scholar
Nott, P. R., Guazzelli, E. & Pouliquen, O. 2011 The suspension balance model revisited. Phys. Fluids 23 (4), 043304.10.1063/1.3570921Google Scholar
Oron, A., Davis, S. H. & Bankoff, S. G. 1997 Long-scale evolution of thin liquid films. Rev. Mod. Phys. 69 (3), 931–980.10.1103/RevModPhys.69.931Google Scholar
Ramachandran, A. & Leighton, D. T. 2008 The influence of secondary flows induced by normal stress differences on the shear-induced migration of particles in concentrated suspensions. J. Fluid Mech. 603, 207–243.10.1017/S0022112008000980Google Scholar
Taylor, G. I. 1954 The dispersion of matter in turbulent flow through a pipe. Proc. R. Soc. Lond. A 223 (1155), 446–468.Google Scholar
Taylor, J. E., Van Damme, I., Johns, M. L., Routh, A. F. & Wilson, D. I. 2009 Shear rheology of molten crumb chocolate. J. Food Sci. 74 (2), E55–E61.10.1111/j.1750-3841.2008.01041.xGoogle Scholar
Timberlake, B. D. & Morris, J. F. 2005 Particle migration and free-surface topography in inclined plane flow of a suspension. J. Fluid Mech. 538, 309–341.10.1017/S0022112005005471Google Scholar
Wang, L. & Bertozzi, A. L. 2014 Shock solutions for high concentration particle-laden thin films. SIAM J. Appl. Maths 74 (2), 322–344.10.1137/130917740Google Scholar
Ward, T., Wey, C., Glidden, R., Hosoi, A. E. & Bertozzi, A. L. 2009 Experimental study of gravitation effects in the flow of a particle-laden thin film on an inclined plane. Phys. Fluids 21 (8), 083305.10.1063/1.3208076Google Scholar
Zettl, A. 2005 Sturm-Liouville Theory. American Mathematical Society.Google Scholar
Zhou, J., Dupuy, B., Bertozzi, A. L. & Hosoi, A. E. 2005 Theory for shock dynamics in particle-laden thin films. Phys. Rev. Lett. 94 (11), 117–803.10.1103/PhysRevLett.94.117803Google Scholar