Book contents
- Frontmatter
- Contents
- Preface
- General list of symbols
- Useful physical constants and values
- 1 Introduction to colloid science and rheology
- 2 Hydrodynamic effects
- 3 Brownian hard spheres
- 4 Stable systems
- 5 Non-spherical particles
- 6 Colloidal attractions and flocculated dispersions
- 7 Thixotropy
- 8 Shear thickening
- 9 Rheometry of suspensions
- 10 Suspensions in viscoelastic media
- 11 Advanced topics
- Index
- References
2 - Hydrodynamic effects
Non-colloidal particles
Published online by Cambridge University Press: 05 December 2011
Book contents
- Frontmatter
- Contents
- Preface
- General list of symbols
- Useful physical constants and values
- 1 Introduction to colloid science and rheology
- 2 Hydrodynamic effects
- 3 Brownian hard spheres
- 4 Stable systems
- 5 Non-spherical particles
- 6 Colloidal attractions and flocculated dispersions
- 7 Thixotropy
- 8 Shear thickening
- 9 Rheometry of suspensions
- 10 Suspensions in viscoelastic media
- 11 Advanced topics
- Index
- References
Summary
Introduction
The primary topic of this book is suspensions comprised of solid particles suspended in a liquid. When such materials are subjected to shear forces, the deformation is borne by the liquid phase, and it is in that phase and its interface with the particles that the flow causes energy to be dissipated. Therefore, the hydrodynamics of the liquid phase will always play a role in the rheology of a suspension, even in those cases where other phenomena, such as colloidal interparticle forces, contribute to the stresses. Therefore, a systematic study of the various parameters that govern suspension rheology starts with the hydrodynamic contribution, i.e., the contribution to the suspension stress that derives directly from the dissipation in the liquid phase of the suspension. As noted in the introduction, the flows of interest will be laminar and the particle Reynolds number will be sufficiently small that Stokes flow will be assumed, i.e., particle inertia will not be considered in the general treatment.
In suspensions of large, non-colloidal particles, i.e., with characteristic dimensions of a few micrometers or more, the contributions to the suspension stress from Brownian motion and from interparticle forces such as electrostatic interactions can often be ignored. Hence, such suspensions can be used to study hydrodynamic effects without interference from the other phenomena. However, because non-colloidal suspensions do not display Brownian motion, there is no diffusion to help generate an equilibrium structure. This causes some experimental and theoretical problems, as will be discussed. Therefore, some features are introduced in this chapter, to be elaborated on in Chapter 3 which explicitly treats Brownian motion. In the present chapter and in Chapters 3 and 4, only suspensions of spherical particles will be considered, in order to avoid at this stage the complexity introduced by shape effects. Non-spherical particles and the resulting shape effects will be treated in Chapter 5. Likewise, the complexities resulting from the use of non-Newtonian suspending media are not considered here. A number of important industrial suspensions, such as coatings and nanocomposites, can be based on polymeric media; these are covered in Chapter 10.
- Type
- Chapter
- Information
- Colloidal Suspension Rheology , pp. 36 - 79Publisher: Cambridge University PressPrint publication year: 2011
References
Transport characteristics of suspensions: VIII. A note on the the viscosity of Newtonian suspensions of uniform spherical particlesJ Colloid Sci 20 1965 267CrossRefGoogle Scholar
Prediction of the viscosity of multimodal suspensions from unimodal viscosity dataTrans Soc Rheol 12 1968 281CrossRefGoogle Scholar
The characterization of the total stress of concentrated suspensions of noncolloidal spheres in Newtonian fluidsJ Rheol 44 2000 185CrossRefGoogle Scholar
Particle motions in sheared suspensions: XXV. Streamlines around cylinders and spheresJ Colloid Interface Sci 27 1968 7CrossRefGoogle Scholar
The microrheology of dispersionsRheology: Theory and Applications, Vol. 4New YorkAcademic Press 1967 85CrossRefGoogle Scholar
Streamlines around single spheres and trajectories of pairs of spheres in two-dimensional creeping flowsChem Eng Sci 32 1977 1505CrossRefGoogle Scholar
Berichtigung zu meiner Arbeit: “Eine neue Bestimmung der MoleküldimensionenAnn Physik 34 1911 591CrossRefGoogle Scholar
1911 1382
Ueber die Viskosität von Suspensionen un die Bestimmung der Avogradoschen ZahlKollolid-Z 9 1911 154Google Scholar
Rheological properties of monodisperse latex systems: I. Concentration dependence of relative viscosityJ Colloid Sci 16 1961 13CrossRefGoogle Scholar
The dependence of synthetic latex viscosity on particle size and size distributionJ Rheol 12 1968 357Google Scholar
Hard sphere colloidal dispersions: Viscosity as a function of shear rate and volume fractionJ Chem Phys 83 1986 4717CrossRefGoogle Scholar
Simple shear flow round a rigid sphere: Inertial effects and suspension rheologyJ Fluid Mech 44 1970 1CrossRefGoogle Scholar
The determination of the bulk stress in a suspension of spherical particles to order c2J Fluid Mech 56 1972 401CrossRefGoogle Scholar
The hydrodynamic interaction of two small freely-moving spheres in a linear flow fieldJ Fluid Mech 56 1972 375CrossRefGoogle Scholar
The microrheology of colloidal dispersions: XII. Trajectories of orthokinetic pair collisions of latex spheres in a simple electrolyteJ Colloid Interface Sci 82 1981 175CrossRefGoogle Scholar
The viscosity of bimodal and polydisperse suspensions of hard spheres in the dilute limitJ Fluid Mech 278 1994 267CrossRefGoogle Scholar
The non-Newtonian rheology of dilute colloidal suspensionsJ Fluid Mech 456 2002 239CrossRefGoogle Scholar
The viscosity of a dilute suspension of rough spheresJ Fluid Mech 421 2000 339CrossRefGoogle Scholar
An analytic form for the pair distribution function and rheology of a dilute suspension of rough spheres in plane strain flowJ Fluid Mech 534 2005 97CrossRefGoogle Scholar
Numerical simulations of particulate suspensions via a discretized Boltzmann equation: 2. Numerical resultsJ Fluid Mech 271 1994 311CrossRefGoogle Scholar
Study of a dissipative particle dynamics based approach for modeling suspensionsJ Rheol 49 2005 401CrossRefGoogle Scholar
Microhydrodynamics: Principles and Selected ApplicationsStoneham, MAButterworth-Heinemannn 1991Google Scholar
The pathological behaviour of sheared hard spheres with hydrodynamic interactionsEurophys Lett 32 1995 535CrossRefGoogle Scholar
Stokesian dynamics simulation of Brownian suspensionsJ Fluid Mech 313 1996 181CrossRefGoogle Scholar
Microstructure of strongly sheared suspensions and its impact on rheology and diffusionJ Fluid Mech 348 1997 103CrossRefGoogle Scholar
Lubrication breakdown in hydrodynamic simulations of concentrated colloidsAdv Colloid Interface Sci 59 1995 19CrossRefGoogle Scholar
Dynamic simulation of suspensions of non-Brownian hard spheresJ Fluid Mech 325 1996 53CrossRefGoogle Scholar
Fore-and-aft asymmetry in a concentrated suspension of solid spheresJ Rheol 31 1987 725CrossRefGoogle Scholar
Effects of surface roughness on a sphere sedimenting through a dilute suspension of neutrally buoyant spheresPhys Fluids A 4 1992 2607CrossRefGoogle Scholar
The kinetics of flowing dispersions: IX. Doublets of rigid spheres (experimental)J Colloid Interface Sci 61 1977 44CrossRefGoogle Scholar
Shear-induced particle diffusivities from numerical simulationsJ Fluid Mech 443 2001 101Google Scholar
Deterministic and stochastic behaviour of non-Brownian spheres in sheared suspensionsJ Fluid Mech 460 2002 307CrossRefGoogle Scholar
Chaos and threshold for irreversibility in sheared suspensionsNature 438 2005 997CrossRefGoogle ScholarPubMed
Rheology and microstructure in concentrated noncolloidal suspensionsJ Rheol 46 2002 1031CrossRefGoogle Scholar
Random packings of spheres and fluidity limits of monodisperse and bidisperse suspensionsPhys Rev Lett 68 1992 1422CrossRefGoogle ScholarPubMed
Is random close packing of spheres well defined?Phys Rev Lett 84 2000 2064CrossRefGoogle ScholarPubMed
Improving the density of jammed disordered packings using ellipsoidsScience 303 2004 990CrossRefGoogle ScholarPubMed
On the viscosity of a concentrated suspension of solid spheresChem Eng Sci 22 1967 847CrossRefGoogle Scholar
Hydrodynamic transport coefficients of random dispersions of hard spheresJ Chem Phys 93 1990CrossRefGoogle Scholar
Hard-sphere colloidal dispersions: The scaling of rheological properties with particle size, volume fraction, and shear rateJ Rheol 33 1989 421CrossRefGoogle Scholar
Nature of divergence in low shear viscosity of colloidal hard sphere dispersionsPhys Rev E 65 2002CrossRefGoogle ScholarPubMed
Die Abhängigkeit des Fliessverhaltens konzentrierter Kugelsuspensionen von der Strömungsform: Ein Vergleich der Viskosität in Scher- und Dehn-StrömungenRheol Acta 19 1980 322CrossRefGoogle Scholar
Experimental measurements of the normal stresses in sheared Stokesian suspensionsJ Fluid Mech 490 2003 293CrossRefGoogle Scholar
Rheological properties of suspensions in Newtonian and non-Newtonian fluidsJ Polym Eng 5 1985 293CrossRefGoogle Scholar
Relative viscosity models and their application to capillary flow data of highly filled hard-metal carbide compoundsPolym Compos 26 2005 29CrossRefGoogle Scholar
A mechanism of non-Newtonian flow in suspensions of rigid spheresTrans Soc Rheol 3 1959Google Scholar
Rheology of concentrated disperse systems and minimum energy-dissipation principle: 1. Viscosity-concentration relationshipRheol Acta 16 1977 82CrossRefGoogle Scholar
Application of Ree-Eyring generalized flow theory to suspensions of spherical particlesJ Colloid Sci 11 1956 80CrossRefGoogle Scholar
Rheological behavior of filled polymeric systems: II. The effect of a bimodal size distribution of particulatesJ Rheol 32 1988 751CrossRefGoogle Scholar
Flow of suspensions containing particles of two different sizes through a capillary tubeJ Rheol 26 1982 387CrossRefGoogle Scholar
Numerical simulation of the dense random packing of a binary mixture of hard spheres: Amorphous metalsPhys Rev B 35 1987 7351CrossRefGoogle ScholarPubMed
Dynamic viscosity of macroscopic suspensions of bimodal sized spheresJ Rheol 41 1997 1261CrossRefGoogle Scholar
A generalized model to predict the viscosity of solutions with suspended particles: 3. Effects of particle interaction and particle-size distributionJ Appl Polym Sci 50 1993 123CrossRefGoogle Scholar
An empirical model predicting the viscosity of highly concentrated, bimodal dispersions with colloidal interactionRheol Acta 40 2001 434CrossRefGoogle Scholar
Dynamic simulation of bimodal suspensions of hydrodynamically interacting spherical particlesJ Fluid Mech 253 1993 1CrossRefGoogle Scholar
Shear-induced structure in a concentrated suspension of solid spheresJ Rheol 24 1980 799CrossRefGoogle Scholar
Transient response of concentrated suspensions after shear reversalJ Rheol 46 2002 295CrossRefGoogle Scholar
Transient normal stress response in a concentrated suspension of spherical particlesJ Rheol 46 2002 321CrossRefGoogle Scholar
The rheology of concentrated suspensions of non-colloidal particlesParticulate Two-phase FlowBostonButterworth-Heinemann, 1993 169Google Scholar
Viscous resuspension in a tube: The impact of secondary flows resulting from second normal stress differencesPhys Fluids 19 2007CrossRefGoogle Scholar
Self-diffusion of particles in shear-flow of a suspensionJ Fluid Mech 79 1977 191CrossRefGoogle Scholar
The shear-induced migration of particles in concentrated suspensionsJ Fluid Mech 181 1987 415CrossRefGoogle Scholar
Measuring shear-induced self-diffusion in a counter-rotating geometryPhys Rev E 63 2001 1403CrossRefGoogle Scholar
Measurements of the full shear-induced self-diffusion tensor of noncolloidal suspensionsJ Chem Phys 116 2002 10529CrossRefGoogle Scholar
Shear-induced self-diffusion in non-colloidal suspensionsJ Fluid Mech 506 2004 285CrossRefGoogle Scholar
Dynamic structure factor study of diffusion in strongly sheared suspensionsJ Fluid Mech 527 2005 141CrossRefGoogle Scholar
NMR flow imaging of fluids and solid suspensions in Poiseuille flowJ Rheol 35 1991 735CrossRefGoogle Scholar
Migration of particles undergoing pressure-driven flow in a circular conduitJ Rheol 41 1997 621CrossRefGoogle Scholar
Imaging of particle shear migration with electrical impedance tomographyPhys Fluids 11 1999 2865CrossRefGoogle Scholar
An experimental study of the motion of concentrated suspensions in two-dimensional channel flow: 1. Monodisperse systemsJ Fluid Mech 363 1998 25CrossRefGoogle Scholar
Shear-induced particle migration in Couette and parallel-plate viscometers: NMR imaging an stress measurementsPhys Fluids 6 1994 2561CrossRefGoogle Scholar
Particle migration in a Couette apparatus: Experiment and modelingJ Rheol 42 1998 307CrossRefGoogle Scholar
Laser Doppler velocimetry measurements of particle velocity fluctuations in a concentrated suspensionJ Rheol 46 2002 241CrossRefGoogle Scholar
Local determination of the constitutive law of a dense suspension of noncolloidal particles through magnetic resonance imagingJ Rheol 50 2006 259CrossRefGoogle Scholar
A constitutive equation for concentrated suspensions that accounts for shear-induced particle migrationPhys Fluids A 4 1992 30CrossRefGoogle Scholar
Pressure-driven flow of suspensions: Simulation and theoryJ Fluid Mech 275 1994 157CrossRefGoogle Scholar
Rheology and structure of concentrated suspensions of hard spheres: Shear induced migrationJ Phys II 5 1995 1597Google Scholar
Curvilinear flows of noncolloidal suspensions: The role of normal stressesJ Rheol 43 1999 1213CrossRefGoogle Scholar
The influence of secondary flows induced by normal stress differences on the shear-induced migration of particles in concentrated suspensionsJ Fluid Mech 603 2008 207CrossRefGoogle Scholar
Flow-aligned tensor models for suspension flowsInt J Multiphase Flow 28 2002 137CrossRefGoogle Scholar
Evaluation of particle migration models based on laser Doppler velocimetry measurements in concentrated suspensionsJ Rheol 48 2004 255CrossRefGoogle Scholar
Hydrodynamic particle migration in a concentrated suspension undergoing flow between rotating eccentric cylindersInd Eng Chem Res 34 1995 3187CrossRefGoogle Scholar
Migration of particles undergoing pressure-driven flow in a circular conduitJ Rheol 41 1997 621CrossRefGoogle Scholar
Behaviour of macroscopic rigid spheres in Poiseuille flow: 2. Experimental results and interpretationJ Fluid Mech 14 1962 136CrossRefGoogle Scholar
Inertial migration of rigid spheres in two-dimensonal unidirectional flowsJ Fluid Mech 65 1974 365CrossRefGoogle Scholar
Inertial migration of rigid spherical particles in Poiseuille flowJ Fluid Mech 515 2004 171CrossRefGoogle Scholar
Trajectory analysis for non-Brownian inertial suspensions in simple shear flowJ Fluid Mech 559 2006 151CrossRefGoogle Scholar
Sedimentation of hard-sphere suspensions at low Reynolds numberJ Fluid Mech 525 2005 73CrossRefGoogle Scholar
Viscous resuspension of a sediment within a laminar and stratified flowInt J Multiphase Flow 16 1990 567CrossRefGoogle Scholar
Migration of buoyant particles in low-Reynolds-number pressure-driven flowsJ Fluid Mech 523 2005 1CrossRefGoogle Scholar
The stress system in a suspension of force-free particlesJ Fluid Mech 41 1970 545CrossRefGoogle Scholar
The viscosity of a concentrated suspension of spherical particlesJ Colloid Sci 6 1951 162CrossRefGoogle Scholar
- 1
- Cited by