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Interface-resolved simulations of particle suspensions in Newtonian, shear thinning and shear thickening carrier fluids

  • Dhiya Alghalibi (a1) (a2), Iman Lashgari (a1), Luca Brandt (a1) and Sarah Hormozi (a3)

Abstract

We present a numerical study of non-colloidal spherical and rigid particles suspended in Newtonian, shear thinning and shear thickening fluids employing an immersed boundary method. We consider a linear Couette configuration to explore a wide range of solid volume fractions ( $0.1\leqslant \unicode[STIX]{x1D6F7}\leqslant 0.4$ ) and particle Reynolds numbers ( $0.1\leqslant Re_{p}\leqslant 10$ ). We report the distribution of solid and fluid phase velocity and solid volume fraction and show that close to the boundaries inertial effects result in a significant slip velocity between the solid and fluid phase. The local solid volume fraction profiles indicate particle layering close to the walls, which increases with the nominal $\unicode[STIX]{x1D6F7}$ . This feature is associated with the confinement effects. We calculate the probability density function of local strain rates and compare the latter’s mean value with the values estimated from the homogenisation theory of Chateau et al. (J. Rheol., vol. 52, 2008, pp. 489–506), indicating a reasonable agreement in the Stokesian regime. Both the mean value and standard deviation of the local strain rates increase primarily with the solid volume fraction and secondarily with the $Re_{p}$ . The wide spectrum of the local shear rate and its dependency on $\unicode[STIX]{x1D6F7}$ and $Re_{p}$ point to the deficiencies of the mean value of the local shear rates in estimating the rheology of these non-colloidal complex suspensions. Finally, we show that in the presence of inertia, the effective viscosity of these non-colloidal suspensions deviates from that of Stokesian suspensions. We discuss how inertia affects the microstructure and provide a scaling argument to give a closure for the suspension shear stress for both Newtonian and power-law suspending fluids. The stress closure is valid for moderate particle Reynolds numbers, $O(Re_{p})\sim 10$ .

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Corresponding author

Email address for correspondence: hormozi@ohio.edu

References

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Amarsid, L., Delenne, J.-Y., Mutabaruka, P., Monerie, Y., Perales, F. & Radjai, F. 2017 Viscoinertial regime of immersed granular flows. Phys. Rev. E 96 (1), 012901.
Andreotti, B., Forterre, Y. & Pouliquen, O. 2013 Granular Media: Between Fluid and Solid. Cambridge University Press.
Bagnold, R. 1954 Experiments on a gravity-free dispersion of large solid spheres in a Newtonian fluid under shear. Proc. R. Soc. Lond. A 225, 4963.
Batchelor, G. K. 1970 The stress system in a suspension of force-free particles. J. Fluid Mech. 41, 545570.
Batchelor, G. K. 1977 The effect of Brownian motion on the bulk stress in a suspension of spherical particles. J. Fluid Mech. 83, 97117.
Bird, R. B., Armstrong, R. C. & Hassanger, O. 1987 Dynamics of Polymeric Liquids, 2nd edn, vol. 1. Wiley.
Bonnoit, C., Lanuza, J., Lindner, A. & Clement, E. 2010 Mesoscopic length scale controls the rheology of dense suspensions. Phys. Rev. Lett. 105 (10), 108302.
Bouzid, M., Trulsson, M., Claudin, P., Clément, E. & Andreotti, B. 2013 Nonlocal rheology of granular flows across yield conditions. Phys. Rev. Lett. 111 (23), 238301.
Boyer, F., Guazzelli, É. & Pouliquen, O. 2011 Unifying suspension and granular rheology. Phys. Rev. Lett. 107 (18), 188301.
Brady, J. F. & Bossis, G. 1988 Stokesian dynamics. Annu. Rev. Fluid Mech. 20 (1), 111157.
Brenner, H. 1961 The slow motion of a sphere through a viscous fluid towards a plane surface. Chem. Engng Sci. 16 (3), 242251.
Breugem, W.-P. 2012 A second-order accurate immersed boundary method for fully resolved simulations of particle-laden flows. J. Comput. Phys. 231, 44694498.
Cassar, C., Nicolas, M. & Pouliquen, O. 2005 Submarine granular flows down inclined planes. Phys. Fluids 17 (10), 103301.
Chateau, X., Ovarlez, G. & Trung, K. L. 2008 Homogenization approach to the behavior of suspensions of noncolloidal particles in yield stress fluids. J. Rheol. 52, 489506.
Costa, P., Boersma, B. J., Westerweel, J. & Breugem, W.-P. 2015 Collision model for fully resolved simulations of flows laden with finite-size particles. Phys. Rev. E 92, 053012.
Costa, P., Picano, F., Brandt, L. & Breugem, W.-P. 2016 Universal scaling laws for dense particle suspensions in turbulent wall-bounded flows. Phys. Rev. Lett. 117 (13), 134501.
Coussot, P., Tocquer, L., Lanos, C. & Ovarlez, G. 2009 Macroscopic versus local rheology of yield stress fluids. J. Non-Newtonian Fluid Mech. 158 (1), 8590.
Couturier, É., Boyer, F., Pouliquen, O. & Guazzelli, É. 2011 Suspensions in a tilted trough: second normal stress difference. J. Fluid Mech. 686, 2639.
Cwalina, C. D. & Wagner, N. J. 2014 Material properties of the shear-thickened state in concentrated near hard-sphere colloidal dispersions. J. Rheol. 58 (4), 949967.
Dagois-Bohy, S., Hormozi, S., Guazzelli, E. & Pouliquen, O. 2015 Rheology of dense suspensions of non-colloidal spheres in yield-stress fluids. J. Fluid Mech. 776, R2–1R2–11.
Dbouk, T., Lemaire, E., Lobry, L. & Moukalled, F. 2013a Shear-induced particle migration: Predictions from experimental evaluation of the particle stress tensor. J. Non-Newtonian Fluid Mech. 198, 7895.
Dbouk, T., Lobry, L. & Lemaire, E. 2013b Normal stresses in concentrated non-Brownian suspensions. J. Fluid Mech. 715, 239272.
Deboeuf, A., Gauthier, G., Martin, J., Yurkovetsky, Y. & Morris, J. F. 2009 Particle pressure in a sheared suspension: A bridge from osmosis to granular dilatancy. Phys. Rev. Lett. 102 (10), 108301.
DeGiuli, E., Düring, G., Lerner, E. & Wyart, M. 2015 Unified theory of inertial granular flows and non-Brownian suspensions. Phys. Rev. E 91 (6), 062206.
Dontsov, E. & Peirce, A. 2014 Slurry flow, gravitational settling, and a proppant transport model for hydraulic fractures. J. Fluid Mech. 760, 567590.
Einstein, A. 1906 A new determination of the molecular dimensions. Ann. Phys. 324 (2), 289306.
Einstein, A. 1911 Berichtigung zu meiner Arbeit: eine neue Bestimmung der Moleküldimensionen. Ann. Phys. 339 (3), 591592.
Firouznia, M., Metzger, B., Ovarlez, G. & Hormozi, S. 2018 The interaction of two spheres in simple shear flows of yield stress fluids. J. Non-Newtonian Fluid Mech. 255, 1938.
Fornari, W., Brandt, L., Chaudhuri, P., Lopez, C. U., Mitra, D. & Picano, F. 2016 Rheology of confined non-Brownian suspensions. Phys. Rev. Lett. 116 (1), 018301.
Henann, D. L. & Kamrin, K. 2014 Continuum modeling of secondary rheology in dense granular materials. Phys. Rev. Lett. 113 (17), 178001.
Hormozi, S. & Frigaard, I. 2017 Dispersion of solids in fracturing flows of yield stress fluids. J. Fluid Mech. 830, 93137.
Kamrin, K. & Henann, D. L. 2015 Nonlocal modeling of granular flows down inclines. Soft Matt. 11 (1), 179185.
Konijn, B., Sanderink, O. & Kruyt, N. 2014 Experimental study of the viscosity of suspensions: Effect of solid fraction, particle size and suspending liquid. Powder Technol. 266, 6169.
Krieger, I. M. & Dougherty, T. J. 1959 A mechanism for non-Newtonian flow in suspensions of rigid spheres. Trans. Soc. Rheol. 3 (1), 137152.
Kulkarni, P. M. & Morris, J. F. 2008 Suspension properties at finite Reynolds number from simulated shear flow. Phys. Fluids 20, 040602.
Lambert, R., Picano, F., Breugem, W. P. & Brandt, L. 2013 Active suspensions in thin films: nutrient uptake and swimmer motion. J. Fluid Mech. 733, 528557.
Larson, R. G. 1999 The Structure and Rheology of Complex Fluids, vol. 150. Oxford University Press.
Lashgari, I., Picano, F., Breugem, W.-P. & Brandt, L. 2014 Laminar, turbulent and inertial shear-thickening regimes in channel flow of neutrally buoyant particle suspensions. Phys. Rev. Lett. 113, 254502.
Lashgari, I., Picano, F., Breugem, W. P. & Brandt, L. 2016 Channel flow of rigid sphere suspensions: particle dynamics in the inertial regime. Intl J. Multiphase Flow 78, 1224.
Liard, M., Martys, N. S., George, W. L., Lootens, D. & Hebraud, P. 2014 Scaling laws for the flow of generalized Newtonian suspensions. J. Rheol. 58, 19932015.
Linares-Guerrero, E., Hunt, M. L. & Zenit, R. 2017 Effects of inertia and turbulence on rheological measurements of neutrally buoyant suspensions. J. Fluid Mech. 811, 525543.
Madraki, Y., Hormozi, S., Ovarlez, G., Guazzelli, E. & Pouliquen, O. 2017 Enhancing shear thickening. Phys. Rev. Fluids 2 (3), 033301.
Mahaut, F., Chateau, X., Coussot, P. & Ovarlez, G. 2008 Yield stress and elastic modulus of suspensions of noncolloidal particles in yield stress fluids. J. Rheol. 52 (1), 287313.
Maron, S. H. & Pierce, P. E. 1956 Application of ree-eyring generalized flow theory to suspensions of spherical particles. J. Colloid Sci. 11, 8095.
Mendoza, C. I. & Santamaria-Holek, I. 2009 The rheology of hard sphere suspensions at arbitrary volume fractions: an improved differential viscosity model. J. Chem. Phys. 130, 044904.
Morrison, F. 2001 Understanding Rheology, 1st edn. Oxford University Press.
Nouar, C., Bottaro, A. & Brancher, J. P. 2007 Delaying transition to turbulence in channel flow: revisiting the stability of shear-thinning fluids. J. Fluid Mech. 592, 177194.
Ovarlez, G., Bertrand, F., Coussot, P. & Chateau, X. 2012 Shear-induced sedimentation in yield stress fluids. J. Non-Newtonian Fluid Mech. 177, 1928.
Ovarlez, G., Bertrand, F. & Rodts, S. 2006 Local determination of the constitutive law of a dense suspension of noncolloidal particles through magnetic resonance imaging. J. Rheol. 50 (3), 259292.
Ovarlez, G., Mahaut, F., Deboeufg, S., Lenoir, N., Hormozi, S. & Chateau, X. 2015 Flows of suspensions of particles in yield stress fluids. J. Rheol. 59, 14491486.
Picano, F., Breugem, W.-P. & Brandt, L. 2015 Turbulent channel flow of dense suspensions of neutrally buoyant spheres. J. Fluid Mech. 764, 463487.
Picano, F., Breugem, W.-P., Mitra, D. & Brandt, L. 2013 Shear thickening in non-Brownian suspensions: an excluded volume effect. Phys. Rev. Lett. 111 (9), 098302.
Poslinski, A. J., Ryan, M. E., Gupta, R. K., Seshadri, S. G. & Frechette, F. J. 1988 Rheological behavior of filled polymeric systems i. Yield stress and shear-thinning effects. J. Rheol. 32 (7), 703735.
Pouliquen, O. & Forterre, Y. 2009 A non-local rheology for dense granular flows. Phil. Trans. R. Soc. Lond. A 367 (1909), 50915107.
Prosperetti, A. 2015 Life and death by boundary conditions. J. Fluid Mech. 768, 14.
Quemada, D. 1977 Rheology of concentrated disperse systems and minimum energy dissipation principle. i. viscosity-concentration relationship. Rheol. Acta 16, 8294.
Shewan, H. & Stokes, J. 2015 Analytically predicting the viscosity of hard sphere suspensions from the particle size distribution. J. Non-Newtonian Fluid Mech. 222, 7281.
Sierou, A. & Brady, J. F. 2002 Rheology and microstructure in concentrated noncolloidal suspensions. J. Rheol. 46 (5), 10311056.
Singh, A. & Nott, P. 2003 Experimental measurements of the normal stresses in sheared Stokesian suspensions. J. Fluid Mech. 490, 293320.
Stickel, J. & Powell, R. 2005 Fluid mechanics and rheology of dense suspensions. Annu. Rev. Fluid Mech. 37, 129149.
Trulsson, M., Andreotti, B. & Claudin, P. 2012 Transition from the viscous to inertial regime in dense suspensions. Phys. Rev. Lett. 109 (11), 118305.
Vu, T., Ovarlez, G. & Chateau, X. 2010 Macroscopic behavior of bidisperse suspensions of noncolloidal particles in yield stress fluids. J. Rheol. 54 (4), 815833.
Yeo, K. & Maxey, M. R. 2010 Dynamics of concentrated suspensions of non-colloidal particles in Couette flow. J . Fluid Mech. 649, 205231.
Yeo, K. & Maxey, M. R. 2011 Numerical simulations of concentrated suspensions of monodisperse particles in a Poiseuille flow. J. Fluid Mech. 682, 491518.
Yeo, K. & Maxey, M. R. 2013 Dynamics and rheology of concentrated, finite-Reynolds-number suspensions in a homogeneous shear flow. Phys. Fluids 25 (5), 053303.
Yurkovetsky, Y. & Morris, J. F. 2008 Particle pressure in sheared Brownian suspensions. J. Rheol. 52 (1), 141164.
Zarraga, I., Hill, D. & Leighton, D. 2000 The characterization of the total stress of concentrated suspensions of noncolloidal spheres in Newtonian fluids. J. Rheol. 44, 185220.
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Interface-resolved simulations of particle suspensions in Newtonian, shear thinning and shear thickening carrier fluids

  • Dhiya Alghalibi (a1) (a2), Iman Lashgari (a1), Luca Brandt (a1) and Sarah Hormozi (a3)

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