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Interfacial instabilities in sediment suspension flows

Published online by Cambridge University Press:  08 October 2014

Maryam Abedi ,
Mir Abbas Jalali  and
Maniya Maleki
Maryam Abedi
Affiliation:
Department of Mechanical Engineering, Sharif University of Technology, Azadi Avenue, Tehran, Iran
Mir Abbas Jalali*
Affiliation:
Department of Mechanical Engineering, Sharif University of Technology, Azadi Avenue, Tehran, Iran Department of Astronomy, University of California, Berkeley, CA 94720-3411, USA
Maniya Maleki
Affiliation:
Department of Physics, Institute for Advanced Studies in Basic Sciences, Zanjan 45137-66731, Iran
*
†Email address for correspondence: mjalali@berkeley.edu
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Abstract

We report the existence of interfacial instability in the two-dimensional channel flow of a sediment suspension whose particles diffuse in the carrier fluid due to shear-induced collisions. We derive partial differential equations that govern the deformations of the interface between the sediment suspension and the clear fluid, and devise a perturbation method that preserves the positivity of the particle volume fraction. We solve perturbed momentum, particle transport and deforming interface equations to show that a Kelvin–Helmholtz-type unstable wave develops at the interface for wavelengths longer than a critical value. Short-wavelength oscillations of the interface are damped due to shear-induced diffusion of particles. We also show that the lowest critical Reynolds number, above which the interface is unstable, occurs for intermediate values of the total volume fraction of particles.

JFM classification

Instability: Instability Multiphase and Particle-laden Flows: Multiphase and Particle-laden Flows Complex Fluids: Suspensions
Type
Papers
Information
Journal of Fluid Mechanics , Volume 758 , 10 November 2014 , pp. 312 - 326
Copyright
© 2014 Cambridge University Press 

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References

Aussillous, P., Chauchat, J., Pailha, M., Médale, M. & Guazzelli, M. 2013 Investigation of the mobile granular layer in bedload transport by laminar shearing flows. J. Fluid Mech. 736, 594–615.CrossRefGoogle Scholar
Charru, F. & Mouilleron-Arnould, H. 2002 Instability of a bed of particles sheared by a viscous flow. J. Fluid Mech. 452, 303–323.CrossRefGoogle Scholar
Cook, B. P. 2008 Theory for particle settling and shear-induced migration in thin-film liquid flow. Phys. Rev. E 78, 045303(R).CrossRefGoogle ScholarPubMed
Dongarra, J. J., Straughan, B. & Walker, D. W. 1996 Chebyshev tau/QZ algorithm methods for calculating spectra of hydrodynamic stability problems. J. Appl. Numer. Math. 22, 399–435.CrossRefGoogle Scholar
Govindarajan, R. 2004 Effect of miscibility on the linear instability of two-fluid channel flow. Intl J. Multiphase Flow 30 (10), 1177–1192.Google Scholar
Hooper, A. P. & Boyd, W. G. C. 1983 Shear-flow instability at the interface between two viscous fluids. J. Fluid Mech. 128, 507–528.CrossRefGoogle Scholar
Khoshnood, A. & Jalali, M. A. 2012 Long-lived and unstable modes of Brownian suspensions in microchannels. J. Fluid Mech. 701, 407–418.CrossRefGoogle Scholar
Kouakou, K. K. J. & Lagrée, P. Y. 2005 Stability of an erodible bed in various shear flows. Eur. Phys. J. 47, 115–125.CrossRefGoogle Scholar
Kuru, W. C., Leighton, D. T. & McCready, M. J. 1995 Formation of waves on a horizontal erodible bed of particles. Intl J. Multiphase Flow 21 (6), 1123–1140.CrossRefGoogle Scholar
Langlois, V. & Valance, A. 2007 Initiation and evolution of current ripples on a flat sand bed under turbulent water flow. Eur. Phys. J. E 22, 201–208.CrossRefGoogle ScholarPubMed
Lenoble, M., Snabre, P. & Pouligny, B. 2005 The flow of a very concentrated slurry in a parallel-plate device: influence of gravity. Phys. Fluids 17 (7), 073303.CrossRefGoogle Scholar
Maleki, M., Pacheco, H., Suárez, C. R. & Clément, E. 2009 Interfacial instability of a confined suspension under oscillating shear. In Traffic and Granular Flow ’07, pp. 621–627. Springer.CrossRefGoogle Scholar
Miskin, I., Elliott, L. & Ingham, D. B. 1999 Stability in a fully-developed two-dimensional resuspension flow. Intl J. Multiphase Flow 25 (3), 501–530.Google Scholar
Miskin, I., Elliott, L., Ingham, D. B. & Hommand, P. S. 1996 Steady suspension flows into two-dimensional horizontal and inclined channels. Intl J. Multiphase Flow 22 (6), 123–1246.Google Scholar
Norman, J. T., Nayak, H. V. & Bonnecaze, R. T. 2005 Migration of buoyant particles in low-Reynolds-number pressure-driven flows. J. Fluid Mech. 523, 1–35.Google Scholar
Orszag, S. A. 1971 Accurate solution of the Orr–Sommerfeld stability equation. J. Fluid Mech. 50, 689–703.CrossRefGoogle Scholar
Ouriemi, M., Aussillous, P. & Guazzelli, E. 2009 Sediment dynamics. Part 2. Dune formation in pipe flow. J. Fluid Mech. 636, 321–336.CrossRefGoogle Scholar
Ouriemi, M., Aussillous, P., Medale, M., Peysson, Y. & Guazzelli, E. 2007 Determination of the critical Shields number for particle erosion. Phys. Fluids 19, 061706.CrossRefGoogle Scholar
Papista, E., Dimitrakis, D. & Yiantsios, S. G. 2011 Direct numerical simulation of incipient sediment motion and hydraulic conveying. Ind. Engng Chem. Res. 50 (2), 630–638.Google Scholar
Phillips, R. J., Armstrong, R. C. & Brown, R. A. 1992 A constitutive equation for concentrated suspensions that accounts for shear-induced particle migration. Phys. Fluids 4, 30–40.CrossRefGoogle Scholar
Schaflinger, U. 1994 Interfacial instabilities in a stratified flow of two superposed fluids. Fluid Dyn. Res. 13 (6), 299–316.CrossRefGoogle Scholar
Schaflinger, U., Acrivos, A. & Stibi, H. 1995 An experimental study of viscous resuspension in a pressure-driven plane channel flow. Intl J. Multiphase Flow 21 (4), 693–704.CrossRefGoogle Scholar
Schaflinger, U., Acrivos, A. & Zhang, K. 1990 Viscous resuspension of a sediment within a laminar and stratified flow. Intl J. Multiphase Flow 16 (4), 567–578.CrossRefGoogle Scholar
Talon, L. & Meiburg, E. 2011 Plane Poiseuille flow of miscible layers with different viscosities: instabilities in the Stokes flow regime. J. Fluid Mech. 686, 484–506.CrossRefGoogle Scholar
Valance, A. & Langlois, V. 2005 Ripple formation over a sand bed submitted to a laminar shear flow. Eur. Phys. J. B 43 (2), 283–294.Google Scholar
Yiantsios, S. G. & Higgins, B. G. 1988 Linear stability of plane Poiseuille flow of two superposed fluids. Phys. Fluids 31, 3225–3238.CrossRefGoogle Scholar
Yih, C. S. 1967 Instability due to viscosity stratification. J. Fluid Mech. 27 (2), 337–352.Google Scholar
Zhang, K., Acrivos, A. & Schaflinger, U. 1992 Stability in a two-dimensional Hagen–Poiseuille resuspension flow. Intl J. Multiphase Flow 18 (1), 51–63.Google Scholar