Abstract
This chapter deals with the rheological properties of viscoplastic suspensions. In Sect. 2, we discuss the theoretical behavior of suspensions of rigid particles in linear and nonlinear media. In Sect. 3, we present appropriate model systems, experimental setups and methods. The main experimental observations are presented in Sect. 4: we present the evolution of the elastic, plastic, and flow properties with the particle volume fraction, and we discuss the emergence of a shear-dependent microstructure. Finally, shear-induced migration and its link with normal stress differences are briefly discussed in Sect. 5.
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Notes
- 1.
We do not consider here the case of frictional materials.
- 2.
Some aspects of the linear and nonlinear behavior of polydisperse suspensions are discussed in Vu et al. (2010).
- 3.
For simplicity, we will use n to denote the index of both the suspending fluid and the suspension in the sequel.
References
Abbott, J. R., Tetlow, N., Graham, A. L., Altobelli, S. A., Fukushima, E., Mondy, L. A., et al. (1991). Experimental observations of particle migration in concentrated suspensions: Couette flow. Journal of Rheology, 35, 773–795.
Acrivos, A. (1995). Shear-induced particle diffusion in concentrated suspensions of non-colloidal particles? Bingham Award lecture, 1994. Journal of Rheology, 39, 813.
Altobelli, S. A., Givler, R. C., & Fukushima, E. (1991). Velocity and concentration measurements of suspensions by nuclear magnetic resonance imaging. Journal of Rheology, 35, 721–734.
Altobelli, S. A., Fukushima, E., & Mondy, L. A. (1997). Nuclear magnetic resonance imaging of particle migration in suspensions undergoing extrusion. Journal of Rheology, 41, 1105–1115.
Ancey, C., & Jorrot, H. (2001). Yield stress for particle suspensions within a clay dispersion. Journal of Rheology, 45, 297–319.
Blanc, F., Peters, F., & Lemaire, E. (2011a). Experimental signature of the pair trajectories of rough spheres in the shear-induced microstructure in noncolloidal suspensions. Physical Review Letters, 107, 208302.
Blanc, F., Peters, F., & Lemaire, E. (2011b). Local transient rheological behavior of concentrated suspensions. Journal of Rheology, 55, 835–854.
Blanc, F., Lemaire, E., Meunier, A., & Peters, F. (2013). Microstructure in sheared non-Brownian concentrated suspensions. Journal of Rheology, 57, 273–292.
Bonnoit, C., Darnige, T., Clement, E., & Lindner, A. (2010). Inclined plane rheometry of a dense granular suspension. Journal of Rheology, 54, 65–79.
Boyer, F., Pouliquen, O., & Guazzelli, É. (2011a). Dense suspensions in rotating-rod flows: Normal stresses and particle migration. Journal of Fluid Mechanics, 686, 5–25.
Boyer, F., Guazzelli, É., & Pouliquen, O. (2011b). Unifying suspension and granular rheology. Physical Review Letters, 107, 188301.
Brady, J. F., & Morris, J. F. (1997). Microstructure of strongly sheared suspensions and its impact on rheology and diffusion. Journal of Fluid Mechanics, 348, 103–139.
Callaghan, P. T. (1991). Principles of nuclear magnetic resonance spectroscopy. Oxford: Clarendon Press.
Callaghan, P. T. (1999). Rheo-NMR: Nuclear magnetic resonance and the rheology of complex fluids. Reports on Progress in Physics, 62, 599.
Chateau, X., Ovarlez, G., & Trung, K. L. (2008). Homogenization approach to the behavior of suspensions of noncolloidal particles in yield stress fluids. Journal of Rheology, 52, 489–506.
Cheddadi, I., Saramito, P., & Graner, F. (2012). Steady Couette flows of elastoviscoplastic fluids are nonunique. Journal of Rheology, 56, 213–239.
Coussot, P. (1997). Mudflow rheology and dynamics. Rotterdam: Balkema.
Couturier, É., Boyer, F., Pouliquen, O., & Guazzelli, É. (2011). Suspensions in a tilted trough: Second normal stress difference. Journal of Fluid Mechanics, 686, 26–39.
Dagois-Bohy, S., Hormozi, S., Guazzelli, É., & Pouliquen, O. (2015). Rheology of dense suspensions of non-colloidal spheres in yield-stress fluids. Journal of Fluid Mechanics, 776, R2.
Dai, S. C., Bertevas, E., Qi, F., & Tanner, R. I. (2013). Viscometric functions for noncolloidal sphere suspensions with Newtonian matrices. Journal of Rheology, 57, 493–510.
Dbouk, T., Lobry, L., & Lemaire, E. (2013). Normal stresses in concentrated non-Brownian suspensions. Journal of Fluid Mechanics, 715, 239–272.
Deboeuf, S., Lenoir, N., Hautemayou, D., Bornert, M., Blanc, F., & Ovarlez, G. (2018). Imaging non-Brownian particle suspensions with X-ray tomography: Application to the microstructure of Newtonian and visco-plastic suspensions. Journal of Rheology, 62, 643–663.
Denn, M. M., & Morris, J. F. (2014). Rheology of non-Brownian suspensions. Annual Review of Chemical and Biomolecular Engineering, 5, 203–228.
Dzuy, N. Q., & Boger, D. V. (1983). Yield stress measurement for concentrated suspensions. Journal of Rheology, 27, 321–349.
Erdoǧan, S. T., Martys, N. S., Ferraris, C. F., & Fowler, D. W. (2008). Influence of the shape and roughness of inclusions on the rheological properties of a cementitious suspension. Cement and Concrete Composites, 30, 393–402.
Fall, A., Lemaitre, A., Bertrand, F., Bonn, D., & Ovarlez, G. (2010). Shear thickening and migration in granular suspensions. Physical Review Letters, 105, 268303.
Fall, A., Bertrand, F., Hautemayou, D., Mézière, C., Moucheront, P., Lemaitre, A., et al. (2015). Macroscopic discontinuous shear thickening versus local shear jamming in cornstarch. Physical Review Letters, 114, 098301.
Frankel, N. A., & Acrivos, A. (1967). On the viscosity of a concentrated suspension of solid spheres. Chemical Engineering Science, 22, 847–853.
Gallier, S., Lemaire, E., Peters, F., & Lobry, L. (2014). Rheology of sheared suspensions of rough frictional particles. Journal of Fluid Mechanics, 757, 514–549.
Garland, S., Gauthier, G., Martin, J., & Morris, J. F. (2013). Normal stress measurements in sheared non-Brownian suspensions. Journal of Rheology, 57, 71–88.
Geiker, M. R., Brandl, M., Thrane, L. N., & Nielsen, L. F. (2002). On the effect of coarse aggregate fraction and shape on the rheological properties of self-compacting concrete. Cement, Concrete and Aggregates, 24, 3–6.
Hafid, H., Ovarlez, G., Toussaint, F., Jezequel, P. H., & Roussel, N. (2015). Assessment of potential concrete and mortar rheometry artifacts using magnetic resonance imaging. Cement and Concrete Research, 71, 29–35.
Hutton, J. F. (1972). Effect of changes of surface tension and contact angle on normal force measurement with the Weissenberg rheogoniometer. Rheologica Acta, 11, 70–72.
Jau, W. C., & Yang, C. T. (2010). Development of a modified concrete rheometer to measure the rheological behavior of conventional and self-consolidating concretes. Cement and Concrete Composites, 32, 450–460.
Keentok, M. (1982). The measurement of the yield stress of liquids. Rheologica Acta, 21, 325–332.
Koehler, E. P., Fowler, D. W., Ferraris, C. F., & Amziane, S. (2005). A new, portable rheometer for fresh self-consolidating concrete. ACI Special Publications, 233, 97.
Leighton, D., & Acrivos, A. (1987a). Measurement of shear-induced self-diffusion in concentrated suspensions of spheres. Journal of Fluid Mechanics, 177, 109–131.
Leighton, D., & Acrivos, A. (1987b). The shear-induced migration of particles in concentrated suspensions. Journal of Fluid Mechanics, 181, 415–439.
Lhuillier, D. (2009). Migration of rigid particles in non-Brownian viscous suspensions. Physics of Fluids, 21, 023302.
Liard, M., Martys, N. S., George, W. L., Lootens, D., & Hebraud, P. (2014). Scaling laws for the flow of generalized Newtonian suspensions. Journal of Rheology, 58, 1993–2015.
Maire, E., Buffiere, J. Y., Salvo, L., Blandin, J. J., Ludwig, W., & Letang, J. M. (2001). On the application of X-ray microtomography in the field of materials science. Advanced Engineering Materials, 3, 539–546.
Mahaut, F., Chateau, X., Coussot, P., & Ovarlez, G. (2008a). Yield stress and elastic modulus of suspensions of noncolloidal particles in yield stress fluids. Journal of Rheology, 52, 287–313.
Mahaut, F., Mokeddem, S., Chateau, X., Roussel, N., & Ovarlez, G. (2008b). Effect of coarse particle volume fraction on the yield stress and thixotropy of cementitious materials. Cement and Concrete Research, 38, 1276–1285.
Martínez-Padilla, L. P., & Rivera-Vargas, C. (2006). Flow behavior of Mexican sauces using a vane-in-a-large cup rheometer. Journal of Food Engineering, 72, 189–196.
Mewis, J., & Wagner, N. (2012). Colloidal suspension rheology. Cambridge: Cambridge University Press.
Mills, P., & Snabre, P. (1995). Rheology and structure of concentrated suspensions of hard spheres: Shear induced particle migration. Journal de Physique II, 5, 1597–1608.
Mohan, L., Cloitre, M., & Bonnecaze, R. T. (2015). Build-up and two-step relaxation of internal stress in jammed suspensions. Journal of Rheology, 59, 63–84.
Morris, J. F., & Boulay, F. (1999). Curvilinear flows of noncolloidal suspensions: The role of normal stresses. Journal of Rheology, 43, 1213–1237.
Morris, J. F. (2009). A review of microstructure in concentrated suspensions and its implications for rheology and bulk flow. Rheologica Acta, 48, 909–923.
Narumi, T., See, H., Honma, Y., Hasegawa, T., Takahashi, T., & Phan-Thien, N. (2002). Transient response of concentrated suspensions after shear reversal. Journal of Rheology, 46, 295–305.
Nott, P. R., & Brady, J. F. (1994). Pressure-driven flow of suspensions: Simulation and theory. Journal of Fluid Mechanics, 275, 157–199.
Nott, P. R., Guazzelli, E., & Pouliquen, O. (2011). The suspension balance model revisited. Physics of Fluids, 23, 043304.
Ovarlez, G., Bertrand, F., & Rodts, S. (2006). Local determination of the constitutive law of a dense suspension of noncolloidal particles through magnetic resonance imaging. Journal of Rheology, 50, 259–292.
Ovarlez, G., Rodts, S., Ragouilliaux, A., Coussot, P., Goyon, J., & Colin, A. (2008). Wide-gap Couette flows of dense emulsions: Local concentration measurements, and comparison between macroscopic and local constitutive law measurements through magnetic resonance imaging. Physical Review E, 78, 036307.
Ovarlez, G., Mahaut, F., Bertrand, F., & Chateau, X. (2011). Flows and heterogeneities with a vane tool: Magnetic resonance imaging measurements. Journal of Rheology, 55, 197–223.
Ovarlez, G., Cohen-Addad, S., Krishan, K., Goyon, J., & Coussot, P. (2013). On the existence of a simple yield stress fluid behavior. Journal of Non-Newtonian Fluid Mechanics, 193, 68–79.
Ovarlez, G., Mahaut, F., Deboeuf, S., Lenoir, N., Hormozi, S., & Chateau, X. (2015). Flows of suspensions of particles in yield stress fluids. Journal of Rheology, 59, 1449–1486.
Parsi, F., & Gadala-Maria, F. (1987). Fore-and-Aft asymmetry in a concentrated suspension of solid spheres. Journal of Rheology, 31, 725–732.
Phillips, R. J., Armstrong, R. C., Brown, R. A., Graham, A. L., & Abbott, J. R. (1992). A constitutive equation for concentrated suspensions that accounts for shear-induced particle migration. Physics of Fluids A: Fluid Dynamics, 4, 30–40.
Saak, A. W., Jennings, H. M., & Shah, S. P. (2001). The influence of wall slip on yield stress and viscoelastic measurements of cement paste. Cement and Concrete Research, 31, 205–212.
Seth, J. R., Mohan, L., Locatelli-Champagne, C., Cloitre, M., & Bonnecaze, R. T. (2011). A micromechanical model to predict the flow of soft particle glasses. Nature materials, 10, 838.
Shapley, N. C., Brown, R. A., & Armstrong, R. C. (2004). Evaluation of particle migration models based on laser doppler velocimetry measurements in concentrated suspensions. Journal of Rheology, 48, 255–279.
Sierou, A., & Brady, J. F. (2002). Rheology and microstructure in concentrated noncolloidal suspensions. Journal of Rheology, 46, 1031–1056.
Stickel, J. J., & Powell, R. L. (2005). Fluid mechanics and rheology of dense suspensions. Annual Review of Fluid Mechanics, 37, 129–149.
Suquet, P. (Ed.) (1997). Continuum micromechanics Wien: Springer.
Tetlow, N., Graham, A. L., Ingber, M. S., Subia, S. R., Mondy, L. A., & Altobelli, S. A. (1998). Particle migration in a Couette apparatus: experiment and modeling. Journal of Rheology, 42, 307–327.
Thomas, D. G. (1965). Transport characteristics of suspension: VIII A note on the viscosity of Newtonian suspensions of uniform spherical particles. Journal of Colloid Science, 20, 267–277.
Torquato, S. (2002). Random heterogeneous materials: Microstructure and macroscopic properties Heidelberg: Springer Science & Business Media.
Toutou, Z., & Roussel, N. (2006). Multi scale experimental study of concrete rheology: From water scale to gravel scale. Materials and Structures, 39, 189–199.
Vermant, J., Walker, L., Moldenaers, P., & Mewis, J. (1998). Orthogonal versus parallel superposition measurements. Journal of Non-Newtonian Fluid Mechanics, 79, 173–189.
Vu, T. S., Ovarlez, G., & Chateau, X. (2010). Macroscopic behavior of bidisperse suspensions of noncolloidal particles in yield stress fluids. Journal of Rheology, 54, 815–833.
Yammine, J., Chaouche, M., Guerinet, M., Moranville, M., & Roussel, N. (2008). From ordinary rhelogy concrete to self compacting concrete: A transition between frictional and hydrodynamic interactions. Cement and Concrete Research, 38, 890–896.
Zarraga, I. E., Hill, D. A., & Leighton, D. T, Jr. (2000). The characterization of the total stress of concentrated suspensions of noncolloidal spheres in Newtonian fluids. Journal of Rheology, 44, 185–220.
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Ovarlez, G. (2019). Rheology of Visco-Plastic Suspensions. In: Ovarlez, G., Hormozi, S. (eds) Lectures on Visco-Plastic Fluid Mechanics. CISM International Centre for Mechanical Sciences, vol 583. Springer, Cham. https://doi.org/10.1007/978-3-319-89438-6_5
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