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On the effective viscosity of fresh concrete: A homogenization approach

Tuan Nguyen-Sy, Duong Nguyen-The


Two new homogenization schemes together with the classical generalized self-consistent scheme (GSC) and its extension are proposed to deal with the effective viscosity of fresh concrete. All these models exploit the composite sphere morphology of suspension made of a viscous fluid and spherical particles. They differ from each other by the ways the extra fluid zone (EFZ) located in between the composite sphere are treated. The comparison with experimental data shows that the GSC provides very good result for a well arranged particle size scale that allows mapping the whole medium by composite spheres of different size scales. However, the GSC cannot be used for a suspension with a non negligible volume of the EFZ. For such a case, extensions of the GSC those take into account the contribution of the EFZ to the overall viscous behavior of the system is necessary to fit with experimental data. Two of them work very well for non-cohesive particles and the other can be employed for suspension with cohesive particles such as the case of fresh cement paste.


homogenization; viscosity; fresh concrete; coated morphology

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A. Leemann and F. Winnefeld. The effect of viscosity modifying agents on mortar and concrete. Cement and Concrete Composites, 29, (5), (2007), pp. 341–349.

H. Okamura and M. Ouchi. Self-compacting concrete. Journal of Advanced Concrete Technology, 1, (1), (2003), pp. 5–15.

A. Einstein. Effect of suspended rigid spheres on viscosity. Ann. Phys, 19, (1906), pp. 289–306.

M. Mooney. The viscosity of a concentrated suspension of spherical particles. Journal of Colloid Science, 6, (2), (1951), pp. 162–170.

I. M. Krieger and T. J. Dougherty. A mechanism for non Newtonian flow in suspensions of rigid spheres. Transactions of the Society of Rheology, 3, (1), (1959), pp. 137–152.

J. V. Robinson. The viscosity of suspensions of spheres. The Journal of Physical Chemistry, 53, (7), (1949), pp. 1042–1056.

G. F. Eveson, S. G. Ward, and R. L. Whitmore. Classical colloids. Theory of size distribution; paints, coals, greases, etc. Discussions of the Faraday Society, 11, (1951), pp. 11–14.

R. J. Farris. Prediction of the viscosity of multimodal suspensions from unimodal viscosity data. Transactions of the Society of Rheology, 12, (2), (1968), pp. 281–301.

D. H. Berry and W. B. Russel. The rheology of dilute suspensions of slender rods in weak flows. Journal of Fluid Mechanics, 180, (1987), pp. 475–494.

F. M. Van der Kooij, E. S. Boek, and A. P. Philipse. Rheology of dilute suspensions of hard platelike colloids. Journal of Colloid and Interface Science, 235, (2), (1987), pp. 344–349.

I. Marti, O. H¨ofler, P. Fischer, and E. J. Windhab. Rheology of concentrated suspensions containing mixtures of spheres and fibres. Rheologica Acta, 13, (4), (2005), pp. 474–480.

X.Wang, X. Xu, and S. U. Choi. Thermal conductivity of nanoparticle-fluid mixture. Journal of Thermophysics and Heat Transfer, 13, (4), (1999), pp. 474–480.

C. T. Nguyen, F. Desgranges, G. Roy, N. Galanis, T. Mar´e, S. Boucher, and H. A. Mintsa. Temperature and particle-size dependent viscosity data for water-based nanofluids–hysteresis phenomenon. International Journal of Heat and Fluid Flow, 28, (6), (2007), pp. 1942–1506.

J. H. Lee, K. S. Hwang, S. P. Jang, B. H. Lee, J. H. Kim, S. U. Choi, and C. J. Choi. Effective viscosities and thermal conductivities of aqueous nanofluids containing low volume concentrations of Al2O3 nanoparticles. International Journal of Heat and Mass Transfer, 51, (11), (2008), pp. 2651–2656.

Z. Hashin. Viscoelastic behavior of heterogeneous media. Journal of Applied Mechanics, 32, (3), (1965), pp. 630–636.

J. D. Eshelby and R. E. Peierls. The determination of the elastic field of an ellipsoidal inclusion, and related problems. Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 241, (1226), (1957), pp. 376–396.

T. Mori and K. Tanaka. Average stress in matrix and average elastic energy of materials with misfitting inclusions. Acta Metallurgica, 21, (5), (1973), pp. 571–574.

Y. Benveniste. A new approach to the application of Mori-Tanaka’s theory in composite materials. Mechanics of Materials, 6, (2), (1987), pp. 147–157.

R. M. Christensen and K. H. Lo. Solutions for effective shear properties in three phase sphere and cylinder model. Journal of the Mechanics and Physics of Solids, 27, (4), (1987), pp. 315–330.

E. Herve and A. Zaoui. N-layered inclusion-based micromechanical modelling. International Journal of Engineering Science, 31, (1), (1993), pp. 1–10.

E. Herve and A. Zaoui. Micromechanical modeling of packing and size effects in particulate composites. International Journal of Solids and Structures, 44, (25), (2007), pp. 8213–8228.

Z. Toutou, C. Lanos, Y. Mélinge, and N. Roussel. Modèle de viscosité multi-échelle: de la pâte de ciment au micro-béton. Rhéologie, 5, (2004), pp. 1–9.

Z. Toutou and N. Roussel. Multi scale experimental study of concrete rheology: from water scale to gravel scale. Materials and Structures, 39, (2), (2004), pp. 189–199.

D. J. Durian. Foam mechanics at the bubble scale. Physical Review Letters, 75, (Dec, 1995), pp. 4780–4783.

N. Phan-Thien and D. C. Pham. Differential multiphase models for polydispersed suspensions and particulate solids. Journal of Non-Newtonian Fluid Mechanics, 72, (2), (1997), pp. 305–318.

T.-S. Vu, G. Ovarlez, and X. Chateau. Macroscopic behavior of suspensions of noncolloidal particles in yield stress fluids. Journal of Rheology, 54, (06, 2010).

T. S. Vu. Rhéologie des suspensions non newtoniennes. PhD thesis, Université Paris-Est, (2010).

L. Struble and G.-K. Sun. Viscosity of Portland cement paste as a function of concentration. Advanced Cement Based Materials, 2, (2), (1995), pp. 62–69.

H. J. H. Brouwers. Viscosity of a concentrated suspension of rigid monosized particles. Physical Review E, 81, (5), (2010).

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