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

Published online by Cambridge University Press:  06 August 2018

Dhiya Alghalibi ,
Iman Lashgari Open the ORCID record for Iman Lashgari [Opens in a new window] ,
Luca Brandt Open the ORCID record for Luca Brandt [Opens in a new window]  and
Sarah Hormozi Open the ORCID record for Sarah Hormozi [Opens in a new window]
Dhiya Alghalibi
Affiliation:
Linné Flow Centre and SeRC (Swedish e-Science Research Centre), KTH Mechanics, S-100 44 Stockholm, Sweden College of Engineering, Kufa University, Al Najaf, Iraq
Iman Lashgari
Affiliation:
Linné Flow Centre and SeRC (Swedish e-Science Research Centre), KTH Mechanics, S-100 44 Stockholm, Sweden
Luca Brandt
Affiliation:
Linné Flow Centre and SeRC (Swedish e-Science Research Centre), KTH Mechanics, S-100 44 Stockholm, Sweden
Sarah Hormozi*
Affiliation:
Department of Mechanical Engineering, Ohio University, Athens, OH 45701-2979, USA
*
†Email address for correspondence: hormozi@ohio.edu
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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, $O(Re_{p})\sim 10$.

JFM classification

Multiphase and Particle-laden Flows: Particle/fluid flow Non-Newtonian Flows: Rheology Complex Fluids: Suspensions
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 852 , 10 October 2018 , pp. 329 - 357
Copyright
© 2018 Cambridge University Press 

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References

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.Google Scholar
Andreotti, B., Forterre, Y. & Pouliquen, O. 2013 Granular Media: Between Fluid and Solid. Cambridge University Press.Google Scholar
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, 49–63.Google Scholar
Batchelor, G. K. 1970 The stress system in a suspension of force-free particles. J. Fluid Mech. 41, 545–570.Google Scholar
Batchelor, G. K. 1977 The effect of Brownian motion on the bulk stress in a suspension of spherical particles. J. Fluid Mech. 83, 97–117.Google Scholar
Bird, R. B., Armstrong, R. C. & Hassanger, O. 1987 Dynamics of Polymeric Liquids, 2nd edn, vol. 1. Wiley.Google Scholar
Bonnoit, C., Lanuza, J., Lindner, A. & Clement, E. 2010 Mesoscopic length scale controls the rheology of dense suspensions. Phys. Rev. Lett. 105 (10), 108302.Google Scholar
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.Google Scholar
Boyer, F., Guazzelli, É. & Pouliquen, O. 2011 Unifying suspension and granular rheology. Phys. Rev. Lett. 107 (18), 188301.Google Scholar
Brady, J. F. & Bossis, G. 1988 Stokesian dynamics. Annu. Rev. Fluid Mech. 20 (1), 111–157.Google Scholar
Brenner, H. 1961 The slow motion of a sphere through a viscous fluid towards a plane surface. Chem. Engng Sci. 16 (3), 242–251.Google Scholar
Breugem, W.-P. 2012 A second-order accurate immersed boundary method for fully resolved simulations of particle-laden flows. J. Comput. Phys. 231, 4469–4498.Google Scholar
Cassar, C., Nicolas, M. & Pouliquen, O. 2005 Submarine granular flows down inclined planes. Phys. Fluids 17 (10), 103301.Google Scholar
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, 489–506.Google Scholar
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.Google Scholar
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.Google Scholar
Coussot, P., Tocquer, L., Lanos, C. & Ovarlez, G. 2009 Macroscopic versus local rheology of yield stress fluids. J. Non-Newtonian Fluid Mech. 158 (1), 85–90.Google Scholar
Couturier, É., Boyer, F., Pouliquen, O. & Guazzelli, É. 2011 Suspensions in a tilted trough: second normal stress difference. J. Fluid Mech. 686, 26–39.Google Scholar
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), 949–967.Google Scholar
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, R2–1–R2–11.Google Scholar
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, 78–95.Google Scholar
Dbouk, T., Lobry, L. & Lemaire, E. 2013b Normal stresses in concentrated non-Brownian suspensions. J. Fluid Mech. 715, 239–272.Google Scholar
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.Google Scholar
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.Google Scholar
Dontsov, E. & Peirce, A. 2014 Slurry flow, gravitational settling, and a proppant transport model for hydraulic fractures. J. Fluid Mech. 760, 567–590.Google Scholar
Einstein, A. 1906 A new determination of the molecular dimensions. Ann. Phys. 324 (2), 289–306.Google Scholar
Einstein, A. 1911 Berichtigung zu meiner Arbeit: eine neue Bestimmung der Moleküldimensionen. Ann. Phys. 339 (3), 591–592.Google Scholar
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, 19–38.Google Scholar
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.Google Scholar
Henann, D. L. & Kamrin, K. 2014 Continuum modeling of secondary rheology in dense granular materials. Phys. Rev. Lett. 113 (17), 178001.Google Scholar
Hormozi, S. & Frigaard, I. 2017 Dispersion of solids in fracturing flows of yield stress fluids. J. Fluid Mech. 830, 93–137.Google Scholar
Kamrin, K. & Henann, D. L. 2015 Nonlocal modeling of granular flows down inclines. Soft Matt. 11 (1), 179–185.Google Scholar
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, 61–69.Google Scholar
Krieger, I. M. & Dougherty, T. J. 1959 A mechanism for non-Newtonian flow in suspensions of rigid spheres. Trans. Soc. Rheol. 3 (1), 137–152.Google Scholar
Kulkarni, P. M. & Morris, J. F. 2008 Suspension properties at finite Reynolds number from simulated shear flow. Phys. Fluids 20, 040602.Google Scholar
Lambert, R., Picano, F., Breugem, W. P. & Brandt, L. 2013 Active suspensions in thin films: nutrient uptake and swimmer motion. J. Fluid Mech. 733, 528–557.Google Scholar
Larson, R. G. 1999 The Structure and Rheology of Complex Fluids, vol. 150. Oxford University Press.Google Scholar
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.Google Scholar
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, 12–24.Google Scholar
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, 1993–2015.Google Scholar
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, 525–543.Google Scholar
Madraki, Y., Hormozi, S., Ovarlez, G., Guazzelli, E. & Pouliquen, O. 2017 Enhancing shear thickening. Phys. Rev. Fluids 2 (3), 033301.Google Scholar
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), 287–313.Google Scholar
Maron, S. H. & Pierce, P. E. 1956 Application of ree-eyring generalized flow theory to suspensions of spherical particles. J. Colloid Sci. 11, 80–95.Google Scholar
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.Google Scholar
Morrison, F. 2001 Understanding Rheology, 1st edn. Oxford University Press.Google Scholar
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, 177–194.Google Scholar
Ovarlez, G., Bertrand, F., Coussot, P. & Chateau, X. 2012 Shear-induced sedimentation in yield stress fluids. J. Non-Newtonian Fluid Mech. 177, 19–28.Google Scholar
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), 259–292.Google Scholar
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, 1449–1486.Google Scholar
Picano, F., Breugem, W.-P. & Brandt, L. 2015 Turbulent channel flow of dense suspensions of neutrally buoyant spheres. J. Fluid Mech. 764, 463–487.Google Scholar
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.Google Scholar
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), 703–735.Google Scholar
Pouliquen, O. & Forterre, Y. 2009 A non-local rheology for dense granular flows. Phil. Trans. R. Soc. Lond. A 367 (1909), 5091–5107.Google Scholar
Prosperetti, A. 2015 Life and death by boundary conditions. J. Fluid Mech. 768, 1–4.Google Scholar
Quemada, D. 1977 Rheology of concentrated disperse systems and minimum energy dissipation principle. i. viscosity-concentration relationship. Rheol. Acta 16, 82–94.Google Scholar
Shewan, H. & Stokes, J. 2015 Analytically predicting the viscosity of hard sphere suspensions from the particle size distribution. J. Non-Newtonian Fluid Mech. 222, 72–81.Google Scholar
Sierou, A. & Brady, J. F. 2002 Rheology and microstructure in concentrated noncolloidal suspensions. J. Rheol. 46 (5), 1031–1056.Google Scholar
Singh, A. & Nott, P. 2003 Experimental measurements of the normal stresses in sheared Stokesian suspensions. J. Fluid Mech. 490, 293–320.Google Scholar
Stickel, J. & Powell, R. 2005 Fluid mechanics and rheology of dense suspensions. Annu. Rev. Fluid Mech. 37, 129–149.Google Scholar
Trulsson, M., Andreotti, B. & Claudin, P. 2012 Transition from the viscous to inertial regime in dense suspensions. Phys. Rev. Lett. 109 (11), 118305.Google Scholar
Vu, T., Ovarlez, G. & Chateau, X. 2010 Macroscopic behavior of bidisperse suspensions of noncolloidal particles in yield stress fluids. J. Rheol. 54 (4), 815–833.Google Scholar
Yeo, K. & Maxey, M. R. 2010 Dynamics of concentrated suspensions of non-colloidal particles in Couette flow. J . Fluid Mech. 649, 205–231.Google Scholar
Yeo, K. & Maxey, M. R. 2011 Numerical simulations of concentrated suspensions of monodisperse particles in a Poiseuille flow. J. Fluid Mech. 682, 491–518.Google Scholar
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.Google Scholar
Yurkovetsky, Y. & Morris, J. F. 2008 Particle pressure in sheared Brownian suspensions. J. Rheol. 52 (1), 141–164.Google Scholar
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, 185–220.Google Scholar