Hostname: page-component-78c5997874-8bhkd Total loading time: 0 Render date: 2024-11-05T09:36:59.214Z Has data issue: false hasContentIssue false
  • English
  • Français

Numerical simulations of concentrated suspensions of monodisperse particles in a Poiseuille flow

Published online by Cambridge University Press:  03 August 2011

KYONGMIN YEO  and
MARTIN R. MAXEY
KYONGMIN YEO
Affiliation:
Division of Applied Mathematics, Brown University, Providence, RI 02912, USA
MARTIN R. MAXEY*
Affiliation:
Division of Applied Mathematics, Brown University, Providence, RI 02912, USA
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The dynamics of concentrated suspensions of non-colloidal, monodisperse particles in plane Poiseuille flows are investigated by fully three-dimensional numerical simulations for bulk volume fractions of 0.20–0.40 of neutrally-buoyant particles. The ensemble averages of the volume fraction and particle velocity profiles are consistent with previous experiments. A statistical analysis indicates that there is an intermediate region between particle layers near the wall and a plug region in the core, in which the behaviour of ensemble-averaged suspension field can be approximated by a continuum theory. In the intermediate region, the wall-normal and spanwise velocity fluctuations, angular velocity in the vorticity direction and particle shear stress are found to be linear functions of the distance from the wall. The particle normal stresses in the intermediate region are almost uniform, consistent with the concept of normal-stress-driven particle migration. The intermediate region decreases in extent and the width of the core region increases for larger bulk volume fractions. There is a remarkable similarity between the particle–phase pressure profiles scaled by the local shear rate for different bulk volume fractions. The particle pressure profiles in the intermediate region are compared with the rheological model proposed by Morris & Boulay (1999). The effective viscosity, evaluated from the ratio of the total shear stress to the fluid-phase shear stress, shows a good agreement with empirical viscosity relations in Couette-flow suspensions. In the present study, both non-local dynamics and finite-size effects of the particles are evident in the core of the channel. These effects are more pronounced at larger volume fractions.

JFM classification

Low-Reynolds-number flows: Low-Reynolds-number flows Micro-/Nano-fluid dynamics: Microfluidics Complex Fluids: Suspensions
Type
Papers
Information
Journal of Fluid Mechanics , Volume 682 , 10 September 2011 , pp. 491 - 518
Copyright
Copyright © Cambridge University Press 2011

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

REFERENCES

Backer, J. A., Lowe, C. P., Hoefsloot, H. C. J. & Iedema, P. D. 2005 Poiseuille flow to measure the viscosity of particle model fluids. J. Chem. Phys. 122, 154503.Google Scholar
Batchelor, G. K. 1970 The stress system in a suspension of force-free particles. J. Fluid Mech. 41, 545–570.Google Scholar
Batchelor, G. K. & Green, J. T. 1972 a The determination of the bulk stress in a suspension of spherical particles to order c 2. J. Fluid Mech. 56, 401–427.Google Scholar
Batchelor, G. K. & Green, J. T. 1972 b The hydrodynamic interaction of two small freely-moving spheres in a linear flow field. J. Fluid Mech. 56, 375–400.CrossRefGoogle Scholar
Brady, J. F. 2001 Computer simulation of viscous suspensions. Chem. Engng Sci. 56, 2921–2926.Google Scholar
Cokelet, G. R. 1999 Viscometric, in vitro and in vivo blood viscosity relationships: how are they related? Biorheology 36, 343–358.Google Scholar
Dance, S. L. & Maxey, M. R. 2003 Incorporation of lubrication effects into force-coupling method for particulate two-phase flow. J. Comput. Phys. 189, 212–238.Google Scholar
Deboeuf, A., Gauthier, G., Martin, J., Yurkovetsky, Y. & Morris, J. F. 2009 Particle pressure in a sheared suspension: A bridge from osmosis to granular dilatancy. Phys. Rev. Lett. 102, 108301.Google Scholar
Dratler, D. I. & Schowalter, W. R. 1996 Dynamic simulation of suspensions of non-Brownian hard spheres. J. Fluid Mech. 325, 53–77.Google Scholar
Drazer, G., Koplik, J., Khusid, B. & Acrivos, A. 2004 Microstructure and velocity fluctuations in sheared suspensions. J. Fluid Mech. 511, 237–263.Google Scholar
Drew, D. A. 1983 Mathematical modeling of two-phase flow. Annu. Rev. Fluid Mech. 15, 261–291.Google Scholar
Ganatos, P., Weinbaum, S. & Preffer, R. 1982 Gravitational and zero-drag motion of a sphere of arbitrary size in an inclined channel at low Reynolds number. J. Fluid Mech. 124, 27–43.Google Scholar
Gao, C., Kulkarni, S. D., Morris, J. F. & Gilchrist, J. F. 2010 Direct investigation of anisotropic suspension structure in pressure-driven flow. Phys. Rev. E 81, 041403.Google Scholar
Gao, C., Xu, B. & Gilchrist, J. F. 2009 Mixing and segregation of microspheres in microchannel flows of mono- and bidisperse suspensions. Phys. Rev. E 79, 036311.Google Scholar
Goddard, J. D. 2006 A dissipative anisotropic fluid model for non-colloidal particle dispersions. J. Fluid Mech. 568, 1–17.Google Scholar
Guasto, J. S., Ross, A. S. & Gollub, J. P. 2010 Hydrodynamic irreversibility in particle suspensions with nonuniform strain. Phys. Rev. E 81, 061401.Google Scholar
Hampton, R. E., Mammoli, A. A., Graham, A. L., Tetlow, N. & Altobelli, S. A. 1997 Migration of particles undergoing pressure-driven flow in a circular conduit. J. Rheol. 41, 621–640.CrossRefGoogle Scholar
Isa, L., Besseling, R. & Poon, W. C. K. 2008 Shear zones and wall slip in the capillary flow of concentrated colloidal suspensions. Phys. Rev. Lett. 98, 198305.Google Scholar
Karnis, A., Goldsmith, H. L. & Mason, S. G. 1966 The kinetics of flowing dispersions: Concentrated suspensions of rigid particles. J. Colloid Interface Sci. 22, 531–553.Google Scholar
Koh, C. J., Hookham, P. A. & Leal, L. G. 1994 An experimental investigation of concentrated suspension flow in a rectangular channel. J. Fluid Mech. 266, 1–32.Google Scholar
Krieger, I. M. & Dogherty, T. J. 1959 A mechanism for non-Newtonian flow in suspensions of rigid spheres. Trans. Soc. Rheol. 3, 137–152.CrossRefGoogle Scholar
Kromkamp, J., van den Ende, D., Kandhai, D., van der Sman, R. & Boom, R. 2006 Lattice Boltzmann simulation of 2D and 3D non-Brownian suspensions in Couette flow. Chem. Engng Sci. 61, 858–873.Google Scholar
Kulkarni, P. M. & Morris, J. F. 2008 Suspension properties at finite Reynolds number from simulated shear flow. Phys. Fluids 20, 040602.Google Scholar
Kulkarni, S. D. & Morris, J. F. 2009 Ordering transition and structural evolution under shear in Brownian suspensions. J. Rheol. 53, 417–439.Google Scholar
Leighton, D. & Acrivos, A. 1987 The shear-induced migration of particles in concentrated suspensions. J. Fluid Mech. 181, 415–439.CrossRefGoogle Scholar
Lhuillier, D. 2009 Migration of rigid particles in non-Brownian viscous suspensions. Phys. Fluids 21, 023302.Google Scholar
Lomholt, S. & Maxey, M. R. 2003 Force-coupling method for particulate two-phase flow: Stokes flow. J. Comput. Phys. 184, 381–405.Google Scholar
Lyon, M. K. & Leal, L. G. 1998 An experimental study of the motion of concentrated suspensions in two-dimensional channel flow. Part 1. Monodisperse systems. J. Fluid Mech. 363, 25–56.Google Scholar
Marchioro, M., Tanksley, M. & Prosperetti, A. 1999 Mixture pressure and stress in disperse two-phase flow. Intl J. Multiphase flow 25, 1395–1429.CrossRefGoogle Scholar
Marchioro, M., Tanksley, M. & Prosperetti, A. 2000 Flow of spatially non-uniform suspensions. Part I: Phenomenology. Intl J. Multiphase Flow 26, 783–831.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, 149–165.Google Scholar
Morris, J. F. 2001 Anomalous migration in simulated oscillatory pressure-driven flow of a concentrated suspension. Phys. Fluids 13, 2457–2462.Google Scholar
Morris, J. F. 2009 A review of microstructure in concentrated suspensions and its implications for rheology and bulk flow. Rheol. Acta 48, 909–923.Google Scholar
Morris, J. F. & Boulay, F. 1999 Curvilinear flows of noncolloidal suspensions: The role of normal stresses. J. Rheol. 43, 1213–1237.Google Scholar
Nguyen, N.-Q. & Ladd, A. J. C. 2002 Lubrication corrections for lattice-Boltzmann simulations of particle suspensions. Phys. Rev. E 66, 046708.Google Scholar
Nott, P. R. & Brady, J. F. 1994 Pressure-driven flow of suspensions: simulation and theory. J. Fluid Mech. 275, 157–199.Google Scholar
Pan, W., Caswell, B. & Karniadakis, G. E. 2010 Rheology, microstructure and migration in Brownian colloidal suspensions. Langmuir 26, 133–142.Google Scholar
Psaltis, D., Quake, S. R. & Yang, C. 2006 Developing optofluidic technology through the fusion of microfluidics and optics. Nature 442, 381–386.Google Scholar
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.Google Scholar
Sierou, A. & Brady, J. F. 2002 Rheology and microstructure in concentrated noncolloidal suspensions. J. Rheol. 46, 1031–1056.Google Scholar
Singh, A. & Nott, P. R. 2000 Normal stresses and microstructure in bounded sheared suspensions via Stokesian dynamics simulations. J. Fluid Mech. 412, 279–301.Google Scholar
Stickel, J. J. & Powell, R. L. 2005 Fluid mechanics and rheology of dense suspensions. Annu. Rev. Fluid Mech. 37, 129–149.Google Scholar
Verberg, R. & Koch, D. L. 2006 Rheology of particle suspensions with low to moderate fluid inertia at finite particle inertia. Phys. Fluids 18, 083303.Google Scholar
Wilson, H. J. 2005 An analytic form for the pair distribution function and rheology of a dilute suspension of rough spheres in plane strain flow. J. Fluid Mech. 534, 97–114.Google Scholar
Yapici, K., Powell, R. L. & Philips, R. J. 2009 Particle migration and suspension structure in steady and oscillatory plane Poiseuille flow. Phys. Fluids 21, 053302.Google Scholar
Yeo, K. 2011 Ph.D thesis, Brown University.Google Scholar
Yeo, K. & Maxey, M. R. 2010 a Anomalous diffusion in wall-bounded non-Brownian suspensions under steady shear. Europhys. Lett. 92, 24008.Google Scholar
Yeo, K. & Maxey, M. R. 2010 b Dynamics of concentrated suspensions of non-colloidal particles in Couette flow. J. Fluid Mech. 649, 205–231.Google Scholar
Yeo, K. & Maxey, M. R. 2010 c Ordering transitions of non-Brownian suspensions in confined steady shear flow. Phys. Rev. E 81, 051502.Google Scholar
Yeo, K. & Maxey, M. R. 2010 d Simulation of concentrated suspensions using the force-coupling method. J. Comput. Phys. 229, 2401–2421.Google Scholar
Yurkovetsky, Y. 1997 PhD thesis, California Institute of Technology.Google Scholar
Zarraga, I. E., Hill, D. A. & Leighton, D. T. 2000 The characterization of the total stress of concentrated suspensions of noncolloidal spheres in Newtonian fluids. J. Rheol. 44, 185–220.Google Scholar
Zhang, Q. & Prosperetti, A. 2010 Physics-based analysis of the hydrodynamic stress in a fluid–particle system. Phys. Fluids 22, 033306.Google Scholar