DOI: 10.1017/s0022112096002170. Stokesian Dynamics simulation of Brownian suspensions

Stokesian Dynamics simulation of Brownian suspensions

10.1017/s0022112096002170

Crossref journal-article

Cambridge University Press (CUP)

Journal of Fluid Mechanics (56)

Abstract

The non-equilibrium behaviour of concentrated colloidal dispersions is studied by Stokesian Dynamics, a general molecular-dynamics-like technique for simulating particles suspended in a viscous fluid. The simulations are of a suspension of monodisperse Brownian hard spheres in simple shear flow as a function of the Péclet number, Pe, which measures the relative importance of shear and Brownian forces. Three clearly defined regions of behaviour are revealed. There is first a Brownian-motion-dominated regime (Pe ≤ 1) where departures from equilibrium in structure and diffusion are small, but the suspension viscosity shear thins dramatically. When the Brownian and hydrodynamic forces balance (Pe ≈ 10), the dispersion forms a new ‘phase’ with the particles aligned in ‘strings’ along the flow direction and the strings are arranged hexagonally. This flow-induced ordering persists over a range of Pe and, while the structure and diffusivity now vary considerably, the rheology remains unchanged. Finally, there is a hydrodynamically dominated regime (Pe > 200) with a dramatic change in the long-time self-diffusivity and the rheology. Here, as the Péclet number increases the suspension shear thickens owing to the formation of large clusters. The simulation results are shown to agree well with experiment.

Bibliography

Phung, T. N., Brady, J. F., & Bossis, G. (1996). Stokesian Dynamics simulation of Brownian suspensions. Journal of Fluid Mechanics, 313, 181â207.

Authors 3

Thanh N. Phung (first)
John F. Brady (additional)
Georges Bossis (additional)

References 46 Referenced 265

Brady, J. F. , Lester, J. , Phillips, R. & Bossis, G. 1988 Dynamic simulation of hydrodynamically interacting suspensions.J. Fluid Mech. 195,257.
Phung, T. N. & Brady, J. F. 1992 Microstructured fluids: structure, diffusion and rheology of colloidal dispersions. In Slow Dynamics in Condensed Matter (ed. Kawasaki Tokuyama & Kawakatsu ), p.391. AIP Conference Proc. 256. (10.1063/1.42337)
Leighton, D. & Acrivos, A. 1987 Measurement of self-diffusion in concentrated suspensions of spheres.J. Fluid Mech. 177,109.
Bossis, G. , Meunier, A. & Brady, J. F. 1991 Hydrodynamic stress of fractal aggregates of spheres.J. Chem. Phys. 94,5064.
Jeffrey, D. J. , Morris, J. F. & Brady, J. F. 1993 The pressure moments for two rigid spheres in low-Reynolds-number flow.Phys. Fluids A5,2317.
Xue, W. & Grest, G. S. 1990 Shear-induced alignment of colloidal particles in the presence of a shear flow.Phys. Rev. Lett. 64,419.
Phung, T. N. , Brady, J. F. & Bossis, G. 1996a Stokesian Dynamics simulation of colloidal dispersions. I. Moderately concentrated hard-sphere suspensions.J. Rheol. (to be submitted). (10.1017/S0022112096002170)
Bender, J. W. & Wagner, N. J. 1995 Optical measurement of the contribution of colloidal forces to the rheology of concentrated suspensions J. Colloid Interface Sci. 172,171.
Ackerson, B. J. & Pusey, P. N. 1988 Shear-induced order in suspensions of hard spheres.Phys. Rev. Lett. 61,1033.
Laun, H. M. , Bung, R. , Hess, S. , Loose, W. , Hess, O. , Hahn, K. , Hädicke, E. , Hingmann, R. , Schmidt, F. & Linder, P. 1992 Rheological and small angle neutron scattering investigation of shear-induced particle structures of concentrated polymer dispersions submitted to plane Poiseuille and Couette flow.J. Rheol. 36,743. (10.1122/1.550314)
Morris, J. F. , & Brady, J. F. 1996b Microstructure of strongly-sheared suspensions and its impact on rheology and diffusion.J. Fluid Mech. (to be submitted).
MacKay, M. E. & Kaffashi, B. 1995 Stress jumps of colloidal suspensions, measurements of the elastic-like and viscous-like stress components.J. Colloid Interface Sci. 174,117.
Bossis, G. & Brady, J. F. 1984 Dynamic simulation of sheared suspensions. I. General method.J. Chem. Phys. 80,5141.
Durlofsky, L. J. , Brady, J. F. & Bossis, G. 1987 Dynamic simulation of hydrodynamically interacting particles.J. Fluid Mech. 180,21.
Wagner, N. J. & Ackerson, B. J. 1992 Analysis of nonequilibrium structures of shearing colloidal suspensions.J. Chem. Phys. 97,1473.
Heyes, D. M. 1988 Shear thinning of dense suspensions modeled by Brownian dynamics.Phys. Lett. 132,399.
Bossis, G. & Brady, J. F. 1989 The rheology of Brownian suspensions.J. Chem. Phys. 91,1866.
Phillips, R. , Brady, J. F. & Bossis, G. 1988 Hydrodynamic transport properties of hard-sphere dispersions. I. Suspensions of freely mobile particles.Phys. Fluids 31,3462.
Batchelor, G. K. 1977 The effect of Brownian motion on the bulk stress in a suspension of spherical particles.J. Fluid Mech. 83,97.
O'Brien, R. W. 1979 A method for the calculation of the effective transport properties of interacting particles.J. Fluid Mech. 56,401.
Werff, J. C. van der , Kruif, C. G. de , Blom, C. & Mellema, J. 1989 Linear viscoelastic behaviour of dense hard-sphere dispersions.Phys. Rev. A39,67.
Thomas, D. G. 1965 Transport characteristics of suspensions. VIII. A note on the viscosity of Newtonian suspensions of uniform spherical particles.J. Colloid Interface Sci. 20,267.
Eckstein, E. C. , Bailey, D. G. & Shapiro, A. H. 1977 Self-diffusion in shear flow of a suspension.J. Fluid Mech. 79,191.
Phung, T. N. , Brady, J. F. & Bossis, G. 1996b Stokesian Dynamics simulation of colloidal dispersions. II. Very concentrated hard-sphere suspensions.J. Rheol. (to be submitted). (10.1017/S0022112096002170)
Pusey, P. N. 1991 Colloidal suspensions. In Liquids, Freezing and Glass Transition (ed. J. P. Hansen , D. Levesque & J. Zinn-Justin ).Elsevier.
Elrick, D. E. 1962 Source functions for diffusion in uniform shear flow.Austral. J. Phys. 15,283.
Bossis, G. & Brady, J. F. 1987 Self-diffusion of Brownian particles in concentrated suspensions under shear.J. Chem. Phys. 87,5437.
Morris, J. F. , & Brady, J. F. 1996a Self-diffusion in sheared suspensions.J. Fluid Mech. 312,223–252.
Dhaene, P. , Mewis, J. & Fuller, G. G. 1993 Scattering dichroism measurements of flow-induced structure of a shear thickening suspension.J.Colloid Interface Sci. 156,350.
Brady, J. F. 1993b The rheological behaviour of concentrated colloidal dispersions.J. Chem. Phys. 99,567.
Brady, J. F. & Bossis, G. 1985 The rheology of concentrated suspensions of spheres in simple shear flow by numerical simulation.J. Fluid Mech. 155,105.
Hess, S. 1985 Shear-induced melting and reentrant positional ordering in a system of spherical particles.Intl J. Thermophys. 6,657.
Werff, J. C. van der & Kruif, C. G. de 1989 Hard-sphere colloidal dispersions: the scaling of rheological properties with particle size, volume fraction, and shear rate.J. Rheol. 33,421. (10.1122/1.550062)
Brady, J. F. 1994 The long-time self-diffusivity in concentrated colloidal dispersions.J. Fluid Mech. 272,109.
Phan, S. E. & Leighton, D. L. 1993 Measurement of the shear-induced tracer diffusivity in concentrated suspensions.J. Fluid Mech. (submitted).
Grassia, P. S. , Hinch, E. J. & Nitsche, L. C. 1995 Computer simulations of Brownian motion in complex systems.J. Fluid Mech. 282,373.
Heyes, D. M. 1986 Some physical consequences of large shear rates on simple fluids.J. Chem. Phys. 85,997.
Rallison, J. M. & Hinch, E. J. 1986 The effect of particle interactions on dynamic light scattering from a dilute solution.J. Fluid Mech. 167,131.
Phung, T. N. 1993 Behaviour of concentrated colloidal suspensions by Stokesian Dynamics simulation PhD Thesis,California Institute of Technology.
Brady, J. F. 1993a Brownian motion, hydrodynamics, and the osmotic pressure.J. Chem. Phys. 98,3335.
Ackerson, B. J. 1990 Shear induced order and shear processing of model hard sphere suspensions J. Rheol. 34,553.
Erpenbeck, J. J. 1984 Shear viscosity of the hard-sphere fluid via nonequilibrium molecular dynamics.Phys. Rev. Lett. 52,1333.
Megen, W. van , Underwood, S. M. & Snook, I. 1986 Tracer diffusion in concentrated colloidal dispersions.J. Chem. Phys. 85,4065.
Kruif, C. G. de , Iersel, E. M. F. van , Vrij, A. & Russel, W. B. 1985 Hard sphere colloidal dispersion: viscosity as a function of shear rate and volume fraction.J. Chem. Phys. 83,4717.
Brady, J. F. & Vicic, M. 1995 Normal stresses in colloidal dispersions.J. Rheol. 39,545.
Brady, J. F. & Bossis, G. 1988 Stokesian dynamics.Ann. Rev. Fluid Mech. 20,111.

Dates

Type	When
Created	19 years, 3 months ago (April 27, 2006, 6:22 p.m.)
Deposited	6 years, 2 months ago (June 6, 2019, 5:18 p.m.)
Indexed	2 weeks, 5 days ago (Aug. 2, 2025, 12:19 a.m.)
Issued	29 years, 3 months ago (April 25, 1996)
Published	29 years, 3 months ago (April 25, 1996)
Published Online	19 years, 3 months ago (April 26, 2006)
Published Print	29 years, 3 months ago (April 25, 1996)

Funders 0

None

BibTeX

@article{Phung_1996, title={Stokesian Dynamics simulation of Brownian suspensions}, volume={313}, ISSN={1469-7645}, url={http://dx.doi.org/10.1017/s0022112096002170}, DOI={10.1017/s0022112096002170}, journal={Journal of Fluid Mechanics}, publisher={Cambridge University Press (CUP)}, author={Phung, Thanh N. and Brady, John F. and Bossis, Georges}, year={1996}, month=apr, pages={181–207} }

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    },
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      "unstructured": "Brady, J. F. & Vicic, M. 1995 Normal stresses in colloidal dispersions.J. Rheol. 39,545."
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      "unstructured": "Brady, J. F. & Bossis, G. 1988 Stokesian dynamics.Ann. Rev. Fluid Mech. 20,111."
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