Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-11-28T18:07:27.388Z Has data issue: false hasContentIssue false
  • English
  • Français

Long-lived and unstable modes of Brownian suspensions in microchannels

Published online by Cambridge University Press:  10 May 2012

Atefeh Khoshnood  and
Mir Abbas Jalali
Atefeh Khoshnood
Affiliation:
Computational Mechanics Laboratory, Department of Mechanical Engineering, Sharif University of Technology, Azadi Avenue, PO Box 11155-9567, Tehran, Iran Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544-5263, USA
Mir Abbas Jalali*
Affiliation:
Computational Mechanics Laboratory, Department of Mechanical Engineering, Sharif University of Technology, Azadi Avenue, PO Box 11155-9567, Tehran, Iran
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We investigate the stability of the pressure-driven, low-Reynolds-number flow of Brownian suspensions with spherical particles in microchannels. We find two general families of stable/unstable modes: (i) degenerate modes with symmetric and antisymmetric patterns; (ii) single modes that are either symmetric or antisymmetric. The concentration profiles of degenerate modes have strong peaks near the channel walls, while single modes diminish there. Once excited, both families would be detectable through high-speed imaging. We find that unstable modes occur in concentrated suspensions whose velocity profiles are sufficiently flattened near the channel centreline. The patterns of growing unstable modes suggest that they are triggered due to Brownian migration of particles between the central bulk that moves with an almost constant velocity, and a highly-sheared low-velocity region near the wall. Modes are amplified because shear-induced diffusion cannot efficiently disperse particles from the cavities of the perturbed velocity field.

JFM classification

Instability: Instability Micro-/Nano-fluid dynamics: Microfluidics Complex Fluids: Suspensions
Type
Papers
Information
Journal of Fluid Mechanics , Volume 701 , 25 June 2012 , pp. 407 - 418
Copyright
Copyright © Cambridge University Press 2012

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

1. Brown, J. R., Fridjonsson, E. O., Seymour, J. D. & Codd, S. L. 2009 Nuclear magnetic resonance measurement of shear-induced particle migration in Brownian suspensions. Phys. Fluids 21, 093301.CrossRefGoogle Scholar
2. Carpen, I. C. & Brady, J. F. 2002 Gravitational instability in suspension flow. J. Fluid Mech. 472, 201–210.CrossRefGoogle Scholar
3. Dongarra, J. J., Straughan, B. & Walker, D. W. 1996 Chebyshev tau/QZ algorithm methods for calculating spectra of hydrodynamic stability problems. J. Appl. Numer. Maths 22, 399–435.CrossRefGoogle Scholar
4. Frank, M., Anderson, D., Weeks, E. R. & Morris, J. F. 2003 Particle migration in pressure-driven flow of a Brownian suspension. J. Fluid Mech. 493, 363–378.CrossRefGoogle Scholar
5. Govindarajan, R., Nott, P. R. & Ramaswamy, S. 2001 Theory of suspension segregation in partially filled horizontal rotating cylinders. Phys. Fluids 13, 3517–3520.CrossRefGoogle Scholar
6. Gradshteyn, I. S. & Ryzhik, I. M. 2007 Table of Integrals, Series, and Products, 7th edn. Academic.Google Scholar
7. Helton, K. L. & Yager, P. 2007 Interfacial instabilities affect microfluidic extraction of small molecules from non-Newtonian fluids. Lab on a Chip 7, 1581–1588.CrossRefGoogle ScholarPubMed
8. Kauzlarić, D., Pastewka, L., Meyer, H., Heldele, R., Schulz, M., Weber, O., Piotter, V., Hausselt, J., Greiner, A. & Korvink, J. G. 2011 Smoothed particle hydrodynamics simulation of shear-induced powder migration in injection moulding. Phil. Trans. R. Soc. Lond. A 369, 2320–2328.Google ScholarPubMed
9. Klinkenberg, J., de Lange, H. C. & Brandt, L. 2011 Modal and non-modal stability of particle-laden channel flow. Phys. Fluids 23, 064110.CrossRefGoogle Scholar
10. Kromkamp, J., van der Padt, A., Schroen, C. G. P. H. & Boom, R. M. 2006 Shear induced fractionation of particles. Patent EP1 673 957 A1, European Patent Office.Google Scholar
11. Leighton, D. & Acrivos, A. 1987 The shear-induced migration of particles in concentrated suspensions. J. Fluid Mech. 181, 415–439.CrossRefGoogle Scholar
12. Merhi, D., Lemaire, E., Bossis, G. & Moukalled, F. 2005 Particle migration in a concentrated suspension flowing between rotating parallel plates: investigation of diffusion flux coefficients. J. Rheol. 49, 1429–1448.CrossRefGoogle Scholar
13. 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, 149–165.CrossRefGoogle Scholar
14. Morris, J. F. & Boulay, F. 1999 Curvilinear flows of noncolloidal suspensions: the role of normal stresses. J. Rheol. 43, 1213–1237.CrossRefGoogle Scholar
15. Nott, P. R. & Brady, J. F. 1994 Pressure-driven flow of suspensions: simulation and theory. J. Fluid Mech. 275, 157–199.CrossRefGoogle Scholar
16. Orszag, S. A. 1971 Accurate solution of the Orr–Sommerfeld stability equation. J. Fluid Mech. 50, 689–703.CrossRefGoogle Scholar
17. 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 A 4, 30–40.CrossRefGoogle Scholar
18. Rao, R. R., Mondy, L. A. & Altobelli, S. A. 2007 Instabilities during batch sedimentation in geometries containing obstacles: a numerical and experimental study. Intl J. Numer. Meth. Fluids 55, 723–735.CrossRefGoogle Scholar
19. Rudyak, V. Ya., Isakov, E. B. & Bord, E. G. 1997 Hydrodynamic stability of the Poiseuille flow of dispersed fluid. J. Aerosol Sci. 28, 53–66.CrossRefGoogle Scholar
20. Rusconi, R. & Stone, H. A. 2008 Shear-induced diffusion of platelike particles in microchannels. Phys. Rev. Lett. 101, 254502.CrossRefGoogle ScholarPubMed
21. Semwogerere, D., Morris, J. F. & Weeks, E. R. 2007 Development of particle migration in pressure-driven flow of a Brownian suspension. J. Fluid Mech. 581, 437–451.CrossRefGoogle Scholar
22. Semwogerere, D. & Weeks, E. R. 2008 Shear-induced particle migration in binary colloidal suspensions. Phys. Fluids 20, 043306.CrossRefGoogle Scholar
23. Stickel, J. J. & Powell, R. L. 2005 Fluid mechanics and rheology of dense suspensions. Annu. Rev. Fluid Mech. 37, 129–149.CrossRefGoogle Scholar
24. Vollebregt, H. M., van der Sman, R. G. M. & Boom, R. M. 2010 Suspension flow modelling in particle migration and microfiltration. Soft Matt. 6, 6052–6064.CrossRefGoogle Scholar
25. Yiantsios, S. G. 2006 Plane Poiseuille flow of a sedimenting suspension of Brownian hard-sphere particles: hydrodynamic stability and direct numerical simulations. Phys. Fluids 18, 054103.CrossRefGoogle Scholar
26. Yurkovetsky, Y. & Morris, J. F. 2008 Particle pressure in sheared Brownian suspensions. J. Rheol. 52, 141–164.CrossRefGoogle Scholar