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3 - Brownian hard spheres

Published online by Cambridge University Press:  05 December 2011

Jan Mewis
Affiliation:
Katholieke Universiteit Leuven, Belgium
Norman J. Wagner
Affiliation:
University of Delaware
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Publisher: Cambridge University Press
Print publication year: 2011

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References

Laun, H. M.Rheological properties of aqueous polymer dispersionsAngew Makromol Chem 123 1984CrossRefGoogle Scholar
Woods, M. E.Krieger, I. M.Rheological studies on dispersions of uniform colloidal spheres: 1. Aqueous dispersions in steady shear flowJ Colloid Interface Sci 34 1970CrossRefGoogle Scholar
Krieger, I. M.Rheology of monodisperse laticesAdv Colloid Interface Sci 3 1972 111CrossRefGoogle Scholar
de Kruif, C. G.van Iersel, E. M. F.Vrij, A.Russel, W. B.Hard-sphere colloidal dispersions: Viscosity as a function of shear rate and volume fractionJ Chem Phys 83 1985 4717CrossRefGoogle Scholar
Shikata, T.Pearson, D. S.Viscoelastic behavior of concentrated spherical suspensionsJ Rheol 38 1994CrossRefGoogle Scholar
Lee, M.Alcoutlabi, M.Magda, J. J.The effect of the shear-thickening transition of model colloidal spheres on the sign of N−1 and on the radial pressure profile in torsional shear flowsJ Rheol 50 2006 293CrossRefGoogle Scholar
McQuarrie, D. A.Statistical MechanicsSausalito, CAUniversity Science Books 2000Google Scholar
Carnahan, N. F.Starling, K. E.Equation of state for noninteracting rigid spheresJ Chem Phys 51 1969CrossRefGoogle Scholar
Verlet, L.Weis, J. J.Equilibrium theory of simple liquidsPhys Rev A 5 1972CrossRefGoogle Scholar
Alder, B. J.Hoover, W. G.Young, D. A.Studies in molecular dynamics: V. High-density equation of state and entropy for hard disks and spheresJ Chem Phys 49 1968CrossRefGoogle Scholar
Cheng, Z.Chaikin, P. M.Russel, W. B.Phase diagram of hard spheresMater Des 22 2001 529CrossRefGoogle Scholar
Phan, S. E.Russel, W. B.Cheng, Z. D.Phase transition, equation of state, and limiting shear viscosities of hard sphere dispersionsPhys Rev E 54 1996 6633CrossRefGoogle ScholarPubMed
Pusey, P. N.van Megen, W.Phase-behavior of concentrated suspensions of nearly hard colloidal spheresNature 320 1986 340CrossRefGoogle Scholar
Antl, L.Goodwin, J. W.Hill, R. D.The preparation of poly(methyl methacrylate) latices in nonaqueous mediaColloids Surf 17 1986 67CrossRefGoogle Scholar
Underwood, S. M.Taylor, J. R.van Megen, W.Sterically stabilized colloidal particles as model hard spheresLangmuir 10 1994 3550CrossRefGoogle Scholar
Eberle, A. P. R.Wagner, N. J.Akgun, B.Satija, S. K.Temperature-dependent nanostructure of an end-tethered octadecane brush in tetradecane and nanoparticle phase behaviorLangmuir 26 2010 3003CrossRefGoogle ScholarPubMed
van Helden, A. K.Jansen, J. W.Vrij, A.Preparation and characterization of spherical monodisperse silica dispersions in non-aqueous solventsJ Colloid Interface Sci 81 1981 354CrossRefGoogle Scholar
Vrij, A.Jansen, J. W.Dhont, J. K. G.Pathmamanoharan, C.Kopswerkhoven, M. M.Fijnaut, H. M.Light-scattering of colloidal dispersions in non-polar solvents at finite concentrations: Silica spheres as model particles for hard-sphere interactionsFaraday Discuss 76 1983 19CrossRefGoogle Scholar
Prasad, V.Semwogerere, D.Weeks, E. R.Confocal microscopy of colloidsJ Phys: Condens Matter 19 2007Google Scholar
Dullens, R. P. A.Aarts, D.Kegel, W. K.Direct measurement of the free energy by optical microscopyProc Natl Acad Sci USA. 103 2006 529CrossRefGoogle ScholarPubMed
Batchelor, G. K.Brownian diffusion of particles with hydrodynamic interactionsJ Fluid Mech 74 1976 1CrossRefGoogle Scholar
Batchelor, G. K.The effect of Brownian motion on the bulk stress in a suspension of spherical particlesJ Fluid Mech 83 1977CrossRefGoogle Scholar
Batchelor, G. K.The stress system in a suspension of force-free particlesJ Fluid Mech 41 1970 545CrossRefGoogle Scholar
Batchelor, G. K.Transport properties of two-phase materials with random structureAnnu Rev Fluid Mech 6 1974 227CrossRefGoogle Scholar
Batchelor, G. K.Green, J. T.The hydrodynamic interaction of two small freely-moving spheres in a linear flow fieldJ Fluid Mech 56 1972 375CrossRefGoogle Scholar
Batchelor, G. K.Green, J. T.The determination of the bulk stress in a suspension of spherical particles to order 2J Fluid Mech 56 1972 401CrossRefGoogle Scholar
Barenblatt, G. I.George Keith Batchelor (1920–2000) and David George Crighton (1942–2000), applied mathematiciansNotices of the AMS 48 2001 800Google Scholar
Huppert, H. E.George Keith Batchelor, 8 March 1920–30 March 2000, founding editor, Journal of Fluid Mechanics, 1956J Fluid Mech 421 2000 1CrossRefGoogle Scholar
Cichocki, B.Felderhof, B. U.Long-time self-diffusion coefficient and zero-frequency viscosity of dilute suspensions of spherical Brownian particlesJ Chem Phys 89 1988 3705CrossRefGoogle Scholar
Wagner, N. J.Woutersen, A. T. J. M.The viscosity of bimodal and polydisperse suspensions of hard spheres in the dilute limitJ Fluid Mech 278 1994 267CrossRefGoogle Scholar
Bergenholtz, J.Brady, J. F.Vicic, M.The non-Newtonian rheology of dilute colloidal suspensionsJ Fluid Mech 456 2002 239CrossRefGoogle Scholar
Foss, D. R.Brady, J. F.Structure, diffusion and rheology of Brownian suspensions by Stokesian dynamics simulationJ Fluid Mech 407 2000 167CrossRefGoogle Scholar
Leshansky, A. M.Morris, J. F.Brady, J. F.Collective diffusion in sheared colloidal suspensionsJ Fluid Mech 597 2008 305CrossRefGoogle Scholar
Pusey, P. N.van Megen, W.Observation of a glass-transition in suspensions of spherical colloidal particlesPhys Rev Lett 59 1987 2083CrossRefGoogle ScholarPubMed
Cheng, Z. D.Zhu, J. X.Chaikin, P. M.Phan, S. E.Russel, W. B.Nature of the divergence in low shear viscosity of colloidal hard-sphere dispersionsPhys Rev E 65 2002CrossRefGoogle ScholarPubMed
Meeker, S. P.Poon, W. C. K.Pusey, P. N.Concentration dependence of the low-shear viscosity of suspensions of hard-sphere colloidsPhys Rev E 55 1997 5718CrossRefGoogle Scholar
Lionberger, R. A.Russel, W. B.A Smoluchowski theory with simple approximations for hydrodynamic interactions in concentrated dispersionsJ Rheol 41 1997 399CrossRefGoogle Scholar
Banchio, A. J.Brady, J. F.Accelerated Stokesian dynamics: Brownian motionJ Chem Phys 118 2003 10323CrossRefGoogle Scholar
Brady, J. F.The rheological behavior of concentrated colloidal dispersionsJ Chem Phys 99 1993 567CrossRefGoogle Scholar
Segrè, P. N.Meeker, S. P.Pusey, P. N.Poon, W. C. K.Viscosity and structural relaxation in suspensions of hard-sphere colloids: ReplyPhys Rev Lett 77 1996Google Scholar
Maranzano, B. J.Wagner, N. J.The effects of interparticle interactions and particle size on reversible shear thickening: Hard-sphere colloidal dispersionsJ Rheol 45 2001 1205CrossRefGoogle Scholar
Maranzano, B. J.Wagner, N. J.Flow-small angle neutron scattering measurements of colloidal dispersion microstructure evolution through the shear thickening transitionJ Chem Phys 117 22 2002CrossRefGoogle Scholar
Buscall, R.D’Haene, P.Mewis, J.Maximum density for flow of dispersions of near monodisperse spherical-particlesLangmuir 10 1994 1439CrossRefGoogle Scholar
Lionberger, R. A.Russel, W. B.Microscopic theories of the rheology of stable colloidal dispersionsPrigogine, I.Rice, S. A.Advances in Chemical PhysicsNew YorkJohn Wiley & Sons 2000 399Google Scholar
Banchio, A. J.Bergenholtz, J.Nägele, G.Rheology and dynamics of colloidal suspensionsPhys Rev Lett 82 1999 1792CrossRefGoogle Scholar
Siebenburger, M.Fuchs, M.Winter, H.Ballauff, M.Viscoelasticity and shear flow of concentrated, noncrystallizing colloidal suspensions: Comparison with mode-coupling theoryJ Rheol 53 2009 707CrossRefGoogle Scholar
Saltzman, E. J.Schweizer, K. S.Large-amplitude jumps and non-Gaussian dynamics in highly concentrated hard sphere fluidsPhys Rev E 77 2008CrossRefGoogle ScholarPubMed
Banchio, A. J.Nägele, G.Bergenholtz, J.Viscoelasticity and generalized Stokes-Einstein relations of colloidal dispersionsJ Chem Phys 111 1999 8721CrossRefGoogle Scholar
Sigurgeirsson, H.Heyes, D. M.Transport coefficients of hard sphere fluidsMol Phys 101 2003 469CrossRefGoogle Scholar
Eyring, H.Hirschfelder, J.The theory of the liquid stateJ Phys Chem 41 1937 249CrossRefGoogle Scholar
Hirschfelder, J. O.Curtiss, C. F.Bird, R. B.The Molecular Theory of Gases and LiquidsNew YorkJohn Wiley & Sons 1954Google Scholar
Lionberger, R. A.Russel, W. B.High-frequency modulus of hard-sphere colloidsJ Rheol 38 1994 1885CrossRefGoogle Scholar
Wagner, N. J.The high-frequency shear modulus of colloidal suspensions and the effects of hydrodynamic interactionsJ Colloid Interface Sci 161 1993 169CrossRefGoogle Scholar
Jones, D. A. R.Leary, B.Boger, D. V.The rheology of a concentrated colloidal suspension of hard spheresJ Colloid Interface Sci 147 1991 479CrossRefGoogle Scholar
D’Haene, P.Rheology of Polymerically Stabilized SuspensionsKatholieke Universiteit Leuven 1992Google Scholar
Fritz, G.Maranzano, B. J.Wagner, N. J.Willenbacher, N.High frequency rheology of hard sphere colloidal dispersions measured with a torsional resonatorJ Non-Newtonian Fluid Mech 102 2002 149CrossRefGoogle Scholar
van der Werff, J. C.de Kruif, C. G.Hard-sphere colloidal dispersions: The scaling of rheological properties with particle size, volume fraction, and shear rateJ Rheol 33 1989 421CrossRefGoogle Scholar
Ladd, A. J. C.Hydrodynamic transport coefficients of random dispersions of hard spheresJ Chem Phys 93 1990 3484CrossRefGoogle Scholar
de Kruif, C. G.van Iersel, E. M. F.Vrij, A.Russel, W. B.Hard sphere colloidal dispersions: viscosity as a function of shear rate and volume fractionJ Chem Phys 83 1985 4717CrossRefGoogle Scholar
Ballesta, P.Besseling, R.Isa, L.Petekidis, G.Poon, W. C. K.Slip and flow of hard-sphere colloidal glassesPhys Rev Lett 101 2008CrossRefGoogle ScholarPubMed
Di Cola, E.Moussaid, A.Sztucki, M.Narayanan, T.Zaccarelli, E.Correlation between structure and rheology of a model colloidal glassJ Chem Phys 131 2009CrossRefGoogle ScholarPubMed
Wagner, N. J.Russel, W. B.Light-scattering measurements of a hard-sphere suspension under shearPhys Fluids A 2 1990 491CrossRefGoogle Scholar
Kalman, D.Microstructure and Rheology of Concentrated Suspensions of Near Hard-Sphere ColloidsUniversity of Delaware 2010Google Scholar
Henderson, S. I.van Megen, W.Metastability and crystallization in suspensions of mixtures of hard spheresPhys Rev Lett 80 1998 877CrossRefGoogle Scholar
van Megen, W.Pusey, P. N.Dynamic light-scattering study of the glass transition in a colloidal suspensionPhys Rev A 43 1991 5429CrossRefGoogle Scholar
van Megen, W.Underwood, S. M.Glass-transition in colloidal hard spheres: Measurement and mode-coupling theory analysis of the coherent intermediate scattering funcitonPhys Rev E 49 1994 4206CrossRefGoogle Scholar
Martinez, V. A.Bryant, G.van Megen, W.Slow dynamics and aging of a colloidal hard sphere glassPhys Rev Lett 101 13 2008CrossRefGoogle ScholarPubMed
van Megen, W.Williams, S. R.Probing the equilibrium dynamics of colloidal hard spheres above the mode-coupling glass transitionPhys Rev Lett 104 16 2010CrossRefGoogle ScholarPubMed
van Megen, W.Martinez, V. A.Bryant, G.Arrest of flow and emergence of activated processes at the glass transition of a suspension of particles with hard sphere-like interactionsPhys Rev Lett 102 16 2009CrossRefGoogle Scholar
Brambilla, G.El Masri, D.Pierno, M.Probing the equilibrium dynamics of colloidal hard spheres above the mode-coupling glass transitionPhys Rev Lett 102 8 2009CrossRefGoogle ScholarPubMed
Koumakis, N.Schofield, A. B.Petekidis, G.Effects of shear induced crystallization on the rheology and aging of hard sphere glassesSoft Matter 4 2008 2008CrossRefGoogle Scholar
Mason, T. G.Weitz, D. A.Linear viscoelasticity of colloidal hard-sphere suspensions near the glass-transitionPhys Rev Lett 75 1995 2770CrossRefGoogle ScholarPubMed
Gotze, W.Recent tests of the mode-coupling theory for glassy dynamicsJ Phys: Condens Matter 11 1999 A1Google Scholar
Winter, H. H.Siebenburger, M.Hajnal, D.Henrich, O.Fuchs, M.Ballauff, M.An empirical constitutive law for concentrated colloidal suspensions in the approach of the glass transitionRheol Acta 48 2009 747CrossRefGoogle Scholar
Crassous, J. J.Siebenburger, M.Ballauff, M.Shear stresses of colloidal dispersions at the glass transition in equilibrium and in flowJ Chem Phys 128 2008CrossRefGoogle ScholarPubMed
Brader, J. M.Cates, M. E.Fuchs, M.First-principles constitutive equation for suspension rheologyPhys Rev Lett 101 2008CrossRefGoogle ScholarPubMed
Fuchs, M.Ballauff, M.Flow curves of dense colloidal dispersions: Schematic model analysis of the shear-dependent viscosity near the colloidal glass transitionJ Chem Phys 122 2005CrossRefGoogle ScholarPubMed
Banchio, A. J.Nägele, G.Bergenholtz, J.Collective diffusion, self-diffusion and freezing criteria of colloidal suspensionsJ Chem Phys 113 2000 3381CrossRefGoogle Scholar
Pusey, P. N.Zaccarelli, E.Valeriani, C.Sanz, E.Poon, W. C. K.Cates, M. E.Hard spheres: Crystallization and glass formationPhil Trans R Soc A 367 1909 4993CrossRefGoogle Scholar
von Smoluchowski, M.Theoretical observations on the viscosity of colloidesKolloid-Z 18 1916 190Google Scholar
von Smoluchowski, M.Experiments on a mathematical theory of kinetic coagulation of colloid solutionsZ Phys Chem Stoechiom Verwandtschafts 92 1917 129Google Scholar
Wagner, N. J.The Smoluchowski equation for colloidal suspensions developed and analyzed through the GENERIC formalismJ Non-Newtonian Fluid Mech 96 2001 177CrossRefGoogle Scholar
Russel, W. B.Saville, D. A.Schowalter, W. R.Colloidal DispersionsCambridgeCambridge University Press 1989CrossRefGoogle Scholar
Brady, J. F.Brownian motion, hydrodynamics, and the osmotic pressureJ Chem Phys 98 1993 3335CrossRefGoogle Scholar
Hall, K. R.Another hard-sphere equation of stateJ Chem Phys 57 1972CrossRefGoogle Scholar

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  • Brownian hard spheres
  • Jan Mewis, Katholieke Universiteit Leuven, Belgium, Norman J. Wagner, University of Delaware
  • Book: Colloidal Suspension Rheology
  • Online publication: 05 December 2011
  • Chapter DOI: https://doi.org/10.1017/CBO9780511977978.006
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  • Brownian hard spheres
  • Jan Mewis, Katholieke Universiteit Leuven, Belgium, Norman J. Wagner, University of Delaware
  • Book: Colloidal Suspension Rheology
  • Online publication: 05 December 2011
  • Chapter DOI: https://doi.org/10.1017/CBO9780511977978.006
Available formats
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Save book to Google Drive

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  • Brownian hard spheres
  • Jan Mewis, Katholieke Universiteit Leuven, Belgium, Norman J. Wagner, University of Delaware
  • Book: Colloidal Suspension Rheology
  • Online publication: 05 December 2011
  • Chapter DOI: https://doi.org/10.1017/CBO9780511977978.006
Available formats
×