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Long-lived and unstable modes of Brownian suspensions in microchannels

  • Atefeh Khoshnood (a1) (a2) and Mir Abbas Jalali (a1)


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.


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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.
2. Carpen, I. C. & Brady, J. F. 2002 Gravitational instability in suspension flow. J. Fluid Mech. 472, 201210.
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, 399435.
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, 363378.
5. Govindarajan, R., Nott, P. R. & Ramaswamy, S. 2001 Theory of suspension segregation in partially filled horizontal rotating cylinders. Phys. Fluids 13, 35173520.
6. Gradshteyn, I. S. & Ryzhik, I. M. 2007 Table of Integrals, Series, and Products, 7th edn. Academic.
7. Helton, K. L. & Yager, P. 2007 Interfacial instabilities affect microfluidic extraction of small molecules from non-Newtonian fluids. Lab on a Chip 7, 15811588.
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, 23202328.
9. Klinkenberg, J., de Lange, H. C. & Brandt, L. 2011 Modal and non-modal stability of particle-laden channel flow. Phys. Fluids 23, 064110.
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.
11. Leighton, D. & Acrivos, A. 1987 The shear-induced migration of particles in concentrated suspensions. J. Fluid Mech. 181, 415439.
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, 14291448.
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, 149165.
14. Morris, J. F. & Boulay, F. 1999 Curvilinear flows of noncolloidal suspensions: the role of normal stresses. J. Rheol. 43, 12131237.
15. Nott, P. R. & Brady, J. F. 1994 Pressure-driven flow of suspensions: simulation and theory. J. Fluid Mech. 275, 157199.
16. Orszag, S. A. 1971 Accurate solution of the Orr–Sommerfeld stability equation. J. Fluid Mech. 50, 689703.
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, 3040.
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, 723735.
19. Rudyak, V. Ya., Isakov, E. B. & Bord, E. G. 1997 Hydrodynamic stability of the Poiseuille flow of dispersed fluid. J. Aerosol Sci. 28, 5366.
20. Rusconi, R. & Stone, H. A. 2008 Shear-induced diffusion of platelike particles in microchannels. Phys. Rev. Lett. 101, 254502.
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, 437451.
22. Semwogerere, D. & Weeks, E. R. 2008 Shear-induced particle migration in binary colloidal suspensions. Phys. Fluids 20, 043306.
23. Stickel, J. J. & Powell, R. L. 2005 Fluid mechanics and rheology of dense suspensions. Annu. Rev. Fluid Mech. 37, 129149.
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, 60526064.
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.
26. Yurkovetsky, Y. & Morris, J. F. 2008 Particle pressure in sheared Brownian suspensions. J. Rheol. 52, 141164.
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Long-lived and unstable modes of Brownian suspensions in microchannels

  • Atefeh Khoshnood (a1) (a2) and Mir Abbas Jalali (a1)


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