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Rheometric Flows of Concentrated Suspensions of Solid Particles

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Journal of Applied Mechanics and Technical Physics Aims and scope

Abstract

Publications on experimental and theoretical studies of the rheological properties of concentrated suspensions of solid particles have been analyzed. According to modern concepts, the rheology of suspensions is considered as a result of contact interaction between their constituent particles due to external forces of formation and destruction of various-type conglomerate structures. A new rheological model of a highly concentrated suspension of solid particles in a Newtonian fluid is proposed, which describes both a continuous and discontinuous growth in the effective viscosity with a uniform increase in shear stress. Exact analytical formulas for the velocity profiles of suspension flows in “cone–plane” and “cylinder–cylinder” rotational viscometers, as well as a slit viscometer, are obtained. The proposed model is modified to take into account the non-Newtonian properties of a dispersion medium, which exhibits pseudoplastic and dilatant properties at low and high strain rates, respectively. The effective viscosity of such a suspension is presented as a sum of the contributions from the non-Newtonian dispersion medium and dispersed-phase solid particles. The rheology of the dispersed phase is described using the Ellis model. The velocity profiles in a pressure-driven flat channel are obtained numerically (by the finite-element method). It is shown that they can take various complex forms, depending on the model parameters.

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REFERENCES

  1. Verdier, C., Rheological properties of living materials. From cells to tissues, J. Theor. Med., 2003, vol. 5, no. 2, pp. 67–91. https://doi.org/10.1080/10273360410001678083

    Article  MATH  Google Scholar 

  2. Khodakov, G.S., Suspension rheology. The theory of phase flow and its experimental substantiation, Ros. Khim. Zh. (Zh. Ros. khim. ob-va Mendeleeva), 2003, vol. 47, no. 2, pp. 33–43.

  3. Guillou, S. and Makhloufi, R., Effect of a shear-thickening rheological behaviour on the friction coefficient in a plane channel flow: A study by direct numerical simulation, J. Non-Newton. Fluid Mech., 2007, vol. 144, pp. 73–86. https://doi.org/10.1016/j.jnnfm.2007.03.008

    Article  MATH  Google Scholar 

  4. Galindo-Rosales, F.J., Rubio-Hernandez, F.J., and Velazquez-Navarro, J.F., Shearthickening behavior of Aerosil® R816 nanoparticles suspensions in polar organic liquids, Rheol. Acta, 2009, vol. 48, pp. 699–708. https://doi.org/10.1007/s00397-009-0367-7

    Article  Google Scholar 

  5. Liu, A.J. and Nagel, S.R., The jamming transition and the marginally jammed solid, Ann. Rev. Condens. Matter Phys., 2010, vol. 1, pp. 347–369. https://doi.org/10.1146/annurev-conmatphys-070909-104045

    Article  ADS  Google Scholar 

  6. Seth, J.R., Mohan, L., Locatelli-Champagne, C., Cloitre, M., and Bonnecaze, R.T., A micromechanical model to predict the flow of soft particle glasses, Nat. Mater., 2011, vol. 10, pp. 838–843. https://doi.org/10.1038/nmat3119

    Article  ADS  Google Scholar 

  7. Galindo-Rosalesa, F.J., Rubio-Hernandez, F.J., and Sevilla, A., An apparent viscosity function for shear thickening fluids, J. Non-Newton. Fluid Mech., 2011, vol. 166, pp. 321–325. https://doi.org/10.1016/j.jnnfm.2011.01.001

    Article  MATH  Google Scholar 

  8. Boyer, F., Guazzell, E., and Pouliquen, O., Unifying suspension and granular rheology, Phys. Rev. Lett., 2011, vol. 107, p. 188301. https://doi.org/10.1103/PhysRevLett.107.188301

    Article  ADS  Google Scholar 

  9. Nakanishi, H., Nagahiro, S., and Mitarai, N., Fluid dynamics of dilatant fluids, Phys. Rev. E, 2012, vol. 85, p. 011401. https://doi.org/10.1103/PhysRevE.85.011401

    Article  ADS  Google Scholar 

  10. Fortier, A., Suspension Mechanics, Paris: Masson et Cie, 1967.

    Google Scholar 

  11. Ur’yev, N.B., Fiziko-khimicheskie osnovy tekhnologii dispersnykh system i materialov (Physicochemical Foundations of the Technology of Dispersed Systems and Materials), Moscow: Khimiya, 1988.

  12. Tanner, R.I., Engineering Rheology, Oxford: Oxford Univ. Press, 2000.

    MATH  Google Scholar 

  13. Brown, E. and Jaeger, H.M., Shear thickening in concentrated suspensions: Phenomenology, mechanisms and relations to jamming, Rep. Prog. Phys., 2014, vol. 77, p. 046602. http://iopscience.iop.org/0034-4885/77/4/046602

    Article  ADS  Google Scholar 

  14. Denn, M.M. and Morris, J.F., Rheology of non-Brownian suspensions, Ann. Rev. Chem. Biomol. Eng., 2014, vol. 5, pp. 203–228. https://doi.org/10.1146/annurev-chembioeng-060713-040221

    Article  Google Scholar 

  15. Ardakani, H.A., Mitsoulis, E., and Hatzikiriakos, S.G., Capillary flow of milk chocolate, J. Non-Newton. Fluid Mech., 2014, vol. 210, pp. 56–65. https://doi.org/10.1016/j.jnnfm.2014.06.001

    Article  Google Scholar 

  16. Mari, R., Seto, R., Morris, J.F., and Denn, M.M., Nonmonotonic flow curves of shear thickening suspensions, Phys. Rev. E, 2015, vol. 91, p. 052302. https://doi.org/10.1103/PhysRevE.91.052302

    Article  ADS  Google Scholar 

  17. Pan, Zh., de Cagny, H., Weber, B., and Bonn, D., S-shaped flow curves of shear thickening suspensions: Direct observation of frictional rheology, Phys. Rev. E, 2015, vol. 92, p. 032202. https://doi.org/10.1103/PhysRevE.92.032202

    Article  ADS  Google Scholar 

  18. Ness, C. and Sun, J., Shear thickening regimes of dense non-Brownian suspensions, Soft Matter, 2016, vol. 12, pp. 914–924. https://doi.org/10.1039/c5sm02326b

    Article  ADS  Google Scholar 

  19. Vázquez-Quesada, A. and Ellero, M., Rheology and microstructure of non-colloidal suspensions under shear studied with Smoothed Particle Hydrodynamics, J. Non-Newton. Fluid Mech., 2016, vol. 233, pp. 37–47. https://doi.org/10.1016/j.jnnfm.2015.12.009

    Article  MathSciNet  Google Scholar 

  20. Nagahiro, S. and Nakanishi, H., Negative pressure in shear thickening bands of a dilatant fluid, Phys. Rev. E, 2016, vol. 94, p. 062614. https://doi.org/10.1103/PhysRevE.94.062614

    Article  ADS  Google Scholar 

  21. Vázquez-Quesada, A., Wagner, N.J., and Ellero, M., Planar channel flow of a discontinuous shear-thickening model fluid: Theory and simulation, Phys. Fluid., 2017, vol. 29, p. 103104. https://doi.org/10.1063/1.4997053

    Article  ADS  Google Scholar 

  22. Singh, A., Mari, R., Denn, M.M., and Morris, J.F., A constitutive model for simple shear of dense frictional suspensions, J. Rheol., 2018, vol. 62, pp. 457–468. https://doi.org/10.1122/1.4999237

    Article  ADS  Google Scholar 

  23. Singh, A., Pednekar, S., Chun, J., Denn, M.M., and Morris, J.F., From yielding to shear jamming in a cohesive frictional suspension, Phys. Rev. Lett., 2019, vol. 122, p. 098004. https://doi.org/10.1103/PhysRevLett.122.098004

    Article  ADS  Google Scholar 

  24. Egres, R.G. and Wagner, N.J., The rheology and microstructure of acicular precipitated calcium carbonate colloidal suspensions through the shear thickening transition, J. Rheol., 2005, vol. 49, pp. 719–746. https://doi.org/10.1122/1.1895800

    Article  ADS  Google Scholar 

  25. Skulskiy, O.I., Slavnov, E.V., and Shakirov, N.V., The hysteresis phenomenon in nonisothermal channel flow of a non-Newtonian liquid, J. Non-Newton. Fluid Mech., 1999, vol. 81, pp. 17–26. https://doi.org/10.1016/S0377-0257(98)00091-3

    Article  MATH  Google Scholar 

  26. Aristov, S.N. and Skul’skii, O.I., Exact solution of the problem on a six-constant Jeffrey’s model of fluid in a plane channel, J. Appl. Mech. Tech. Phys., 2002, vol. 43, pp. 817–822. https://doi.org/10.1023/A:1020752101539

    Article  ADS  MathSciNet  Google Scholar 

  27. Aristov, S.N. and Skul’skii, O.I., Exact solution of the problem of flow of a polymer solution in a plane channel, J. Eng. Phys. Thermophys., 2003, vol. 76, pp. 577–585. https://doi.org/10.1023/A:1024768930375

    Article  Google Scholar 

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  1. Institute of Continuous Media Mechanics, Ural Branch, Russian Academy of Sciences, Perm, Russia

    O. I. Skul’skiy

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  1. O. I. Skul’skiy
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Translated by A. Sin’kov

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Skul’skiy, O.I. Rheometric Flows of Concentrated Suspensions of Solid Particles. J Appl Mech Tech Phy 62, 1165–1175 (2021). https://doi.org/10.1134/S0021894421070166

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