Abstract
We deal with scaling relations based on fractal theory and rheological properties of a colloidal suspension to determine a structure parameter of colloidal aggregates and thereby predict shear viscosity of the colloidal suspension using an effective-medium model. The parameter denoted by β is m(3-d f ), where m indicates shear rate (D) dependence of aggregate size R, i.e.R∝D−m, and d f is the fractal dimension for the aggregate. A scaling relation between yield stress and particle volume fraction φ is applied to a set of experimental data for colloidal suspensions consisting of 0.13 μm zinc oxide and hydroxyethyl acrylate at φ = 0.01-0.055 to determine β. Another scaling relation between intrinsic viscosity and shear rate is used at lower φ than the relation for the yield stress. It is found that the estimations of β from the two relations are in a good agreement. The parameter β is utilized in establishing rheological models to predict shear viscosity of aggregated suspension as a function of φ and D. An effective-medium (EM) model is employed to take hydrodynamic interaction between aggregates into account. Particle concentration dependence of the suspension viscosity which is given in terms of volume fraction of aggregates φ a instead of φ is incorporated to the EM model. It is found that the EM model combined with Quemada’s equation is quite successful in predicting shear viscosity of aggregated suspension.
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References
Batchelor, G.K. and J.T. Green, 1972, The determination of the bulk stress in a suspension of spherical particles to order c2, J. Fluid Mech. 56, 401–427.
Buscall, R., P.D. Mills, J.W. Goodwin, and D. Lawson, 1988, Scaling behaviour of the rheology of aggregate networks formed from colloidal particles, J. Chem. Soc., Faraday Trans. 1 84, 4249–4260.
Casson, N., 1959, A flow equation for pigment-oil suspensions of the printing ink type, In: Mill, C.C., eds., Rheology of Disperse Systems, Pergamon Press, Oxford, 84–104.
Cho, J. and S. Koo, 2015, Characterization of particle aggregation in a colloidal suspension of magnetite particles, J. Ind. Eng. Chem. 27, 218–222.
Eggersdorfer, M.I., D. Kadau, H.J. Herrmann, and S.E. Pratsinis, 2010, Fragmentation and restructuring of soft-agglomerates under shear, J. Colloid Interface Sci. 342, 261–268.
Einstein, A., 1906, A new determination of the molecular dimensions, Ann. Phys. 19, 289–306.
Jullien, R. and R. Botet, 1987, Aggregation and Fractal Aggregates, World Scientific, Singapore.
Krieger, I.M. and T.J. Dougherty, 1959, A mechanism for non Newtonian flow in suspensions of rigid spheres, Trans. Soc. Rheol. 3, 137–152.
Lee, B. and S. Koo, 2014, Estimation of microstructure of titania particulate dispersion through viscosity measurement, Powder Technol. 266, 16–21.
Lee, H. and S. Koo, 2016, Analysis of fractal aggregates in a colloidal suspension of carbon black from its sedimentation and viscosity, Korea-Aust. Rheol. J. 28, 267–273.
Lin, M.Y., H.M. Lindsay, D.A. Weitz, R.C. Ball, R. Klein, and P. Meakin, 1989, Universality in colloid aggregation, Nature 339, 360–362.
Meakin, P., 1987, Fractal aggregates, Adv. Colloid Interface Sci. 28, 249–331.
Mewis, J. and N.J. Wagner, 2012, Colloidal Suspension Rheology, Cambridge Press, Cambridge.
Patel, P.D. and W.B. Russel, 1988, A mean field theory for the rheology of phase separated or flocculated dispersions, Colloid Surf. 31, 355–383.
Potanin, A.A., 1992, On the model of colloid aggregates and aggregating colloids, J. Chem. Phys. 96, 9191–9200.
Potanin, A.A., 1993, On the computer simulation of the deformation and breakup of colloidal aggregates in shear flow, J. Colloid Interface Sci. 157, 399–410.
Potanin, A.A., R. De Rooij, D. van den Ende, and J. Mellema, 1995, Microrheological modeling of weakly aggregated dispersions, J. Chem. Phys. 102, 5845–5853.
Quemada, D., 1977, Rheology of concentrated disperse systems and minimum energy dissipation principle: 1. Viscosity-concentration relationship, Rheol. Acta 16, 82–94.
Quemada, D., 1998, Rheological modelling of complex fluids. I. The concept of effective volume fraction revisited, Eur. Phys. J. Appl. Phys. 1, 119–127.
Russel, W.B. and P.R. Sperry, 1994, Effect of microstructure on the viscosity of hard sphere dispersions and modulus of composites, Prog. Org. Coat. 23, 305–324.
Shih, W.H., W.Y. Shih, S.I. Kim, J. Liu, and I.A. Aksay, 1990, Scaling behavior of the elastic properties of colloidal gels, Phys. Rev. A. 42, 4772–4779.
Smith, T.L. and C.A. Bruce, 1979, Intrinsic viscosities and other rheological properties of flocculated suspensions of nonmagnetic and magnetic ferric oxides, J. Colloid Interface Sci. 72, 13–26.
Snabre, P. and P. Mills, 1996, I. Rheology of weakly flocculated suspensions of rigid particles, J. Phys. III France 6, 1811–1834.
Sonntag, R.C. and W.B. Russel, 1986, Structure and breakup of flocs subjected to fluid stresses: I. Shear experiments, J. Colloid Interface Sci. 113, 399–413.
Wessel, R. and R.C. Ball, 1992, Fractal aggregates and gels in shear flow, Phys. Rev. A. 46, R3008–R3011.
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Kim, D., Koo, S. Prediction of shear viscosity of a zinc oxide suspension with colloidal aggregation. Korea-Aust. Rheol. J. 30, 67–74 (2018). https://doi.org/10.1007/s13367-018-0008-8
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DOI: https://doi.org/10.1007/s13367-018-0008-8