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1 - Introduction to Colloidal Suspension Rheology

Published online by Cambridge University Press:  07 April 2021

By
Norman J. Wagner  and
Jan Mewis
Edited by
Norman J. Wagner  and
Jan Mewis
Norman J. Wagner
Affiliation:
University of Delaware
Jan Mewis
Affiliation:
KU Leuven, Belgium
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Summary

The content of this chapter provides a brief overview of the basic concepts of colloid science that will be used in this book. Foundational knowledge is provided by reviewing our understanding of the simplest case of suspensions of hard spheres. First, the characteristic properties of Brownian hard spheres are presented. This includes a discussion of the relevant forces on and between particles in fluids at rest or during flow. On this basis, the microstructure and the phase behavior of the suspensions under consideration are evaluated. The basic rheology of hard sphere suspensions is reviewed in some detail, covering linear and nonlinear shear behavior, oscillatory flow, and also normal stress differences and shear thickening. The rheology is discussed in relation to the effect of flow on microstructure. As a foundation for understanding more complex suspensions, some basic colloidal interaction potentials are introduced along with their resulting, rich phase behavior. A special section of this chapter is dedicated to thixotropy, as this phenomenon occurs in several of the real life systems discussed in subsequent chapters. An appendix reviews the basic rheological concepts as an aid to the reader.

Keywords

rheologycolloidssuspensionsoverviewbasicsBrownianhard spheres
Type
Chapter
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Theory and Applications of Colloidal Suspension Rheology , pp. 1 - 43
Publisher: Cambridge University Press
Print publication year: 2021

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References

Mewis, J, Wagner, NJ. Colloidal Suspension Rheology. Cambridge: Cambridge University Press; 2012. 393 p.Google Scholar
Hiemenz, PC, Rajagopalan, R. Principles of Colloid and Surface Chemistry. 3rd ed. Boca Raton, FL: CRC Press; 1997. 650 p.Google Scholar
Russel, WB, Saville, DA, Schowalter, WR. Colloidal Dispersions. Cambridge: Cambridge University Press; 1989. 525 p.Google Scholar
Berg, JC. An Introduction to Interfaces and Colloids. Hackensack, NJ: World Scientific Publishing Co. Pte Ltd.; 2010. 785 p.Google Scholar
Hunter, RJ, White, LR. Foundations of Colloid Science. Oxford: Clarendon Press; 1987. 673 p.Google Scholar
Macosko, CW. Rheology Principles, Measurements, and Applications. 1st ed. New York: VCH Publications; 1994. 549 p.Google Scholar
Laun, HM. Rheological properties of aqueous polymer dispersions. Angewandte Makromolekulare Chemie. 1984;123(1):335–359.Google Scholar
Shikata, T, Pearson, DS. Viscoelastic behavior of concentrated spherical suspensions. Journal of Rheology. 1994;38(3):601.Google Scholar
Stokes, GG. On the effect of internal friction of fluids on the motion of pendulums. Transactions of the Cambridge Philosophical Society. 1851;9(ii):8–106.Google Scholar
Sutherland, A. A dynamical theory of diffusion for non-electrolytes and the molecular mass of albumin. Philosophical Magazine. 1905;9:781–785.Google Scholar
Einstein, A. Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen. Annalen der Physik. 1905;17:549–560.Google Scholar
Smoluchowski, M. Zur kinetischen Theorie der Brownschen Molekularbewegung und der Suspensionen. Annalen der Physik. 1906;21:756–780.Google Scholar
Kulkarni, PM, Morris, JF. Suspension properties at finite Reynolds number from simulated shear flow. Physics of Fluids. 2008;20(4):040602.Google Scholar
Cheng, Z, Chaikin, PM, Russel, WB, Meyer, WV, Zhu, J, Rogers, RB, et al. Phase diagram of hard spheres. Materials & Design. 2001;22(7):529–534.Google Scholar
Pusey, PN, Vanmegen, W. Phase-behavior of concentrated auspensions of nearly hard colloidal spheres Nature. 1986;320(6060):340–342.Google Scholar
Torquato, S. Statistical description of microstructures. Annual Review of Materials Research. 2002;32:77–111.CrossRefGoogle Scholar
Torquato, S, Stillinger, FH. Jammed hard-particle packings: From Kepler to Bernal and beyond. Reviews of Modern Physics. 2010;82(3):2633–2672.Google Scholar
Pusey, PN, Vanmegen, W. Observation of a glass-transition in suspensions of spherical colloidal particles. Physical Review Letters. 1987;59(18):2083–2086.Google Scholar
Verlet, L, Weis, J. J. Equilibrium theory of simple liquids. Physical Review A. 1972;5(2):939–951.CrossRefGoogle Scholar
Silbert, LE, Ertaş, D, Grest, GS, Halsey, TC, Levine, D. Geometry of frictionless and frictional sphere packings. Physical Review E. 2002;65(3):031304.CrossRefGoogle ScholarPubMed
Yurkovetsky, Y, Morris, JF. Particle pressure in sheared Brownian suspensions. Journal of Rheology. 2008;52(1):141–164.Google Scholar
Banchio, AJ, Nagele, G, Bergenholtz, J. Viscoelasticity and generalized Stokes-Einstein relations of colloidal dispersions. Journal of Chemical Physics. 1999;111(18):8721–8740.Google Scholar
Russel, WB, Wagner, NJ, Mewis, J. Divergence in the low shear viscosity for Brownian hard-sphere dispersions: At random close packing or the glass transition? Journal of Rheology. 2013;57(6):1555–1567.CrossRefGoogle Scholar
Bergenholtz, J, Wagner, NJ. The Huggins coefficient for the square-well colloidal fluid. I&EC Research. 1994;33:2391–2397.Google Scholar
Einstein, A. Eine neue Bestimmung der Molekuldimensionen. Ann Physik. 1906;19:289-306.Google Scholar
Einstein, A. Berichtigung zu meiner Arbeit: “Eine neue Bestimmung der Moleküldimensionen”. Annalen der Physik. 1911;34:591–592.Google Scholar
Banchio, AJ, Brady, JF. Accelerated Stokesian dynamics: Brownian motion. Journal of Chemical Physics. 2003;118(22):10323–10332.Google Scholar
Phan, SE, Russel, WB, Zhu, JX, Chaikin, PM. Effects of polydispersity on hard sphere crystals. Journal of Chemical Physics. 1998;108(23):9789–9795.Google Scholar
Lionberger, RA, Russel, WB. High-frequency modulus of hard-sphere colloids. Journal of Rheology. 1994;38(6):1885–1908.Google Scholar
de Kruif, CG, van Lersel, EMF, Vrij, A, Russel, WB. Hard-sphere colloidal dispersions – viscosity as a function of shear rate and volume fraction Journal of Chemical Physics. 1985;83(9):4717–4725.CrossRefGoogle Scholar
Bergenholtz, J, Brady, JF, Vicic, M. The non-Newtonian rheology of dilute colloidal suspensions. Journal of Fluid Mechanics. 2002;456:239–275.Google Scholar
Batchelor, GK, Green, JT. The determination of the bulk stress in a suspension of spherical particles to order c². Journal of Fluid Mechanics. 1972;56:401–427.Google Scholar
Dai, SC, Tanner, R. Elongational flows of some non-colloidal suspensions. Rheologica Acta. 2017;56(1):63–71.Google Scholar
Brady, J, Khair, A, Swaroop, M. On the bulk viscosity of suspensions. Journal of Fluid Mechanics. 2006;554:109–123.Google Scholar
Foss, DR, Brady, JF. Structure, diffusion and rheology of Brownian suspensions by Stokesian dynamics simulation. Journal of Fluid Mechanics. 2000;407:167–200.Google Scholar
Wagner, NJ, Brady, JF. Shear thickening in colloidal dispersions. Physics Today. 2009;62(10):27–32.Google Scholar
Maranzano, BJ, Wagner, NJ. The effects of interparticle interactions and particle size on reversible shear thickening: Hard-sphere colloidal dispersions. Journal of Rheology. 2001;45(5):1205–1222.Google Scholar
Maranzano, BJ, Wagner, NJ. The effects of particle-size on reversible shear thickening of concentrated colloidal dispersions. Journal of Chemical Physics. 2001;114(23):10514–10527.CrossRefGoogle Scholar
Bender, JW, Wagner, NJ. Optical measurement of the contributions of colloidal forces to the rheology of concentrated suspensions. Journal of Colloid and Interface Science. 1995;172(1):171–184.Google Scholar
Krishnamurthy, LN, Wagner, NJ, Mewis, J. Shear thickening in polymer stabilized colloidal dispersions. Journal of Rheology. 2005;49(6):1347–1360.Google Scholar
Cheng, X, McCoy, JH, Israelachvili, JN, Cohen, I. Imaging the microscopic structure of shear thinning and thickening colloidal suspensions. Science. 2011;333(6047):1276–1279.Google Scholar
Morris, JF. Shear thickening of concentrated suspensions: Recent developments and relation to other phenomena. Annual Review of Fluid Mechanics. 2020;52(1):121–144.Google Scholar
Asakura, S, Oosawa, F. On interaction between two bodies immersed in a solution of macromolecules. Journal of Chemical Physics. 1954;22:1255–1256.Google Scholar
Toussaint, F, Roy, C, Jézéquel, P.-H. Reducing shear thickening of cement-based suspensions. Rheologia Acta. 2009;48(8):883–895.Google Scholar
Krishnamurthy, LN, Wagner, NJ. Letter to the editor: Comment on: “Effect of attractions on shear thickening in dense suspensions” Journal of Rheology 2004;4, 1321 (2004). Journal of Rheology. 2005;49(3):799–803.Google Scholar
Morris, JF, Boulay, F. Curvilinear flows of noncolloidal suspensions: The role of normal stresses. Journal of Rheology. 1999;43(5):1213–1237.CrossRefGoogle Scholar
Cwalina, CD, Wagner, NJ. Material properties of the shear-thickened state in concentrated near hard-sphere colloidal dispersions. Journal of Rheology. 2014;58(4):949–967.CrossRefGoogle Scholar
Dhaene, P, Mewis, J, Fuller, GG. Scattering dichroism measurements of flow-induced structure of a shear thickening suspension. Journal of Colloid and Interface Science. 1993;156(2):350–358.Google Scholar
Kalman, DP, Wagner, NJ. Microstructure of shear-thickening concentrated suspensions determined by flow-USANS. Rheologica Acta. 2009;48(8):897–908.Google Scholar
Gurnon, AK, Wagner, NJ. Microstructure and rheology relationships for shear thickening colloidal dispersions. Journal of Fluid Mechanics. 2015;769:242–276.Google Scholar
Silbert, LE, Melrose, JR. The rheology and microstructure of concentrated, aggregated colloids. Journal of Rheology. 1999;43(3):673–700.Google Scholar
Wagner, NJ, Bender, JW. The role of nanoscale forces in colloid dispersion rheology. MRS Bulletin. 2004;29(2):100–106.Google Scholar
Jamali, S, Boromand, A, Wagner, N, Maia, J. Microstructure and rheology of soft to rigid shear-thickening colloidal suspensions. Journal of Rheology. 2015;59(6):1377–1395.Google Scholar
Singh, A, Mari, R, Denn, MM, Morris, JF. A constitutive model for simple shear of dense frictional suspensions. Journal of Rheology. 2018;62(2):457–468.Google Scholar
Lee, Y-F, Luo, Y, Brown, SC, Wagner, NJ. Experimental test of a frictional contact model for shear thickening in concentrated colloidal suspensions. Journal of Rheology. 2020;64(2):267–282.CrossRefGoogle Scholar
Reynolds, O. On the dilatancy of media composed of rigid particles in contact, with experimental illustrations. Philosophical Magazine [5th Series]. 1885;20:469–481.Google Scholar
Metzner, AB, Whitlock, M. Flow behavior of concentrated (dilatant) suspensions. Transactions of the Society of Rheology. 1958;2:239–253.Google Scholar
O’Brien, VT, Mackay, ME. Stress components and shear thickening of concentrated hard sphere suspensions. Langmuir. 2000;16(21):7931–7938.Google Scholar
Brown, E, Jaeger, HM. The role of dilation and confining stresses in shear thickening of dense suspensions. Journal of Rheology. 2012;56(4):875–923.Google Scholar
Wang, M, Brady, JF. Constant stress and pressure rheology of suspensions. Physical Review Letters. 2015;115(15):158301.Google Scholar
Laun, HM, Bung, R, Schmidt, F. Rheology of extremely shear thickening polymer dispersions (passively viscosity switching fluids). Journal of Rheology. 1991;35(6):999–1034.Google Scholar
Farr, RS, Melrose, JR, Ball, RC. Kinetic theory of jamming in hard-sphere startup flows. Physical Review E. 1997;55(6):7203–7211.CrossRefGoogle Scholar
Mewis, J, Wagner, NJ. Thixotropy. Advances in Colloid and Interface Science. 2009;147–148:214–227.Google Scholar
Larson, RG, Wei, Y. A review of thixotropy and its rheological modeling. Journal of Rheology. 2019;63(3):477–501.Google Scholar
Geri, M, Venkatesan, R, Sambath, K, McKinley, GH. Thermokinematic memory and the thixotropic elasto-viscoplasticity of waxy crude oils. Journal of Rheology. 2017;61(3):427–454.Google Scholar
Hipp, JB, Richards, JJ, Wagner, NJ. Structure-property relationships of sheared carbon black suspensions determined by simultaneous rheological and neutron scattering measurements. Journal of Rheology. 2019;63(3):423–436.Google Scholar
Zia, RN, Landrum, BJ, Russel, WB. A micro-mechanical study of coarsening and rheology of colloidal gels: Cage building, cage hopping, and Smoluchowski’s ratchet. Journal of Rheology. 2014;58(5):1121–1157.Google Scholar
Mewis, J, Schoukens, G. Mechanical spectroscopy of colloidal dispersions. Faraday Discussions. 1978;65:58–64.Google Scholar
Goodeve, CF. A general theory of thixotropy and viscosity. Transactions of the Faraday Society. 1939;35:342–358.Google Scholar
Roussel, N, Le Roy, R, Coussot, P. Thixotropy modelling at local and macroscopic scales. Journal of Non-Newtonian Fluid Mechanics. 2004;117:85–95.Google Scholar
Armstrong, MJ, Beris, AN, Rogers, SA, Wagner, NJ. Dynamic shear rheology of a thixotropic suspension: Comparison of an improved structure-based model with large amplitude oscillatory shear experiments. Journal of Rheology. 2016;60(3):433–450.Google Scholar
Mendes, PRD, Thompson, RL. A unified approach to model elasto-viscoplastic thixotropic yield-stress materials and apparent yield-stress fluids. Rheologica Acta. 2013;52(7):673–694.Google Scholar
Stickel, JJ, Powell, RL. Fluid mechanics and rheology of dense suspensions. Annual Review of Fluid Mechanics. 2005;37(1):129–149.Google Scholar
Wei, YF, Solomon, MJ, Larson, RG. A multimode structural kinetics constitutive equation for the transient rheology of thixotropic elasto-viscoplastic fluids. Journal of Rheology. 2018;62(1):321–342.Google Scholar
Mendes, PRD, Thompson, RL. A critical overview of elasto-viscoplastic thixotropic modeling. Journal of Non-Newtonian Fluid Mechanics. 2012;187(4):8–15.Google Scholar
Dullaert, K, Mewis, J. A structural kinetics model for thixotropy. Journal of Non-Newtonian Fluid Mechanics. 2006;139(1–2):21–30.Google Scholar
Mewis, J, Spaull, AJB, Helsen, J. Structural hysteresis. Nature. 1975;253(5493):618–619.Google Scholar
Mwasame, PM, Beris, AN, Diemer, RB, Wagner, NJ. A constitutive equation for thixotropic suspensions with yield stress by coarse-graining a population balance model. AIChE Journal. 2017;63(2):517–531.Google Scholar
Stickel, JJ, Phillips, RJ, Powell, RL. A constitutive model for microstructure and total stress in particulate suspensions. Journal of Rheology. 2006;50(4):379–413.Google Scholar
Denn, MM, Bonn, D. Issues in the flow of yield-stress liquids. Rheologica Acta. 2011;50(4):307–315.Google Scholar
Dimitriou, CJ, McKinley, GH. A comprehensive constitutive law for waxy crude oil: A thixotropic yield stress fluid. Soft Matter. 2014;10(35):6619–6644.Google Scholar
Schalek, E, Szegvari, A. Ueber Eisenoxydgallerten. Kolloid-Z. 1923;32:318–319.Google Scholar
Weltmann, RN, inventor; Interchemical Corporation, assignee. Viscometer Recorder. US patent 2,497,919. 1950.Google Scholar
Green, H, Weltmann, RN. Analysis of the thixotropy of pigment-vehicle suspensions. Basic principles of the hysteresis loop. Industrial and Engineering Chemistry, Analytical Edition. 1943;15(3):201–206.Google Scholar
Weltmann, RN. Breakdown of thixotropic structure as a function of time. Journal of Applied Physics. 1943;14(7):343–350.Google Scholar

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