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Inertial effects in shear flow of a fluid-particle mixture: Resolved simulations

Gedi Zhou1,* and Andrea Prosperetti2,3,1,†

  • 1Department of Mechanical Engineering, Johns Hopkins University, Baltimore, Maryland 21218, USA
  • 2Department of Mechanical Engineering, University of Houston, 4726 Calhoun Rd, Houston, Texas 77204-4006, USA
  • 3Faculty of Science and Technology and J.M. Burgers Centre for Fluid Dynamics, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands

  • *gzhou4@jhu.edu
  • †aprosper@central.uh.edu
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Phys. Rev. Fluids 5, 084301 – Published 10 August, 2020

DOI: https://doi.org/10.1103/PhysRevFluids.5.084301

Abstract

This paper presents results of the resolved simulation of particles suspended in a fluid in shear flow. Unlike most of the existing work on this subject, the ratio of the particle density to that of the suspending fluid is not 1 but varies between 2.5 and 10, with a focus on inertial effects rather than gravity, which is not considered. Two particle Reynolds numbers are considered, 20 and 40, while the average particle volume fraction varies from 5% to 33%. The study focuses on the effects of inertia on this class of flows. It is shown that the memory of the particles' earlier state of motion associated with inertia is responsible for significant effects. Among others, the collision rate is increased and, with it, the rate of momentum transfer from the moving walls into the bulk of the fluid-particle mixture; normal stress differences become larger and the particle-rich layer near the walls becomes denser. Comparable effects are found by increasing the particle density and the particle Reynolds number. The two normal stress differences are found to be both negative and comparable in spite of their very different physical origin. Additional results concern the wall slip, the stresslet, the effects of a nonzero collisional tangential force, the wall stress, and others. The great importance of particle-particle and particle-wall collisions reveals itself in influencing the rheology of the mixture, the normal stress differences, and the transport of momentum.

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References (56)

  1. M. M. Denn and J. F. Morris, Rheology of non-Brownian suspensions, Annu. Rev. Chem. Biomol. Eng. 5, 203 (2014).
  2. E. Guazzelli and J. F. Morris, A Physical Introduction to Suspension Dynamics (Cambridge University Press, Cambridge, UK, 2012).
  3. M. Maxey, Simulation methods for particulate flows and concentrated suspensions, Annu. Rev. Fluid Mech. 49, 171 (2017).
  4. J. J. Stickel and R. L. Powell, Fluid mechanics and rheology of dense suspensions, Annu. Rev. Fluid Mech. 37, 129 (2005).
  5. J. F. Brady and J. F. Morris, Microstructure of strongly sheared suspensions and its impact on rheology and diffusion, J. Fluid Mech. 348, 103 (1997).
  6. A. Sierou and J. F. Brady, Rheology and microstructure in concentrated noncolloidal suspensions, J. Rheol. 46, 1031 (2002).
  7. F. Gadala-Maria and A. Acrivos, Shear-induced structure in a concentrated suspension of solid spheres, J. Rheol. 24, 799 (1980).
  8. R. Verberg and D. L. Koch, Rheology of particle suspensions with low to moderate fluid inertia at finite particle inertia, Phys. Fluids 18, 083303 (2006).
  9. P. M. Kulkarni and J. F. Morris, Suspension properties at finite Reynolds number from simulated shear flow, Phys. Fluids 20, 040602 (2008).
  10. K. Yeo and M. R. Maxey, Dynamics of concentrated suspensions of non-colloidal particles in Couette flow, J. Fluid Mech. 649, 205 (2010).
  11. K. Yeo and M. R. Maxey, Dynamics and rheology of concentrated, finite-Reynolds-number suspensions in a homogeneous shear flow, Phys. Fluids 25, 053303 (2013).
  12. H. Haddadi and J. F. Morris, Microstructure and rheology of finite inertia neutrally buoyant suspensions, J. Fluid Mech. 749, 431 (2014).
  13. S. Gallier, E. Lemaire, L. Lobry, and F. Peters, Effect of confinement in wall-bounded non-colloidal suspensions, J. Fluid Mech. 799, 100 (2016).
  14. W. Fornari, L. Brandt, P. Chaudhuri, C. U. Lopez, D. Mitra, and F. Picano, Rheology of Confined Non-Brownian Suspensions, Phys. Rev. Lett. 116, 018301 (2016).
  15. M. Rahmani, A. Hammouti, and A. Wachs, Momentum balance and stresses in a suspension of spherical particles in a plane Couette flow, Phys. Fluids 30, 043301 (2018).
  16. J. Kromkamp, D. van den Ende, D. Kandhai, R. van der Sman, and R. Boom, Lattice Boltzmann simulation of 2D and 3D non-Brownian suspensions in Couette flow, Chem. Eng. Sci. 61, 858 (2006).
  17. A. J. C. Ladd and R. Verberg, Lattice-Boltzmann simulations of particle-fluid suspensions, J. Stat. Phys. 104, 1191 (2001).
  18. X. Yin and D. L. Koch, Hindered settling velocity and microstructure in suspensions of solid spheres with moderate Reynolds numbers, Phys. Fluids 19, 093302 (2007).
  19. W. Fornari, A. Formenti, F. Picano, and L. Brandt, The effect of particle density in turbulent channel flow laden with finite size particles in semi-dilute conditions, Phys. Fluids 28, 033301 (2016).
  20. N. Nangia, N. A. Patankar, and A. P. S Bhalla, A DLM immersed boundary method based wave-structure interaction solver for high density ratio multiphase flows, J. Comput. Phys. 398, 108804 (2019).
  21. F. Picano, W.-P. Breugem, and L. Brandt, Turbulent channel flow of dense suspensions of neutrally buoyant spheres, J. Fluid Mech. 764, 463 (2015).
  22. M. E. Rosti, M. N. Ardekani, and L. Brandt, Effect of elastic walls on suspension flow, Phys. Rev. Fluids 4, 062301 (2019).
  23. M. E. Rosti and L. Brandt, Suspensions of deformable particles in a Couette flow, J. Non-Newtonian Fluid Mech. 262, 3 (2018).
  24. N. Sharma and N. A. Patankar, A fast computation technique for the direct numerical simulation of rigid particulate flows, J. Comput. Phys. 205, 439 (2005).
  25. M. Uhlmann, An immersed boundary method with direct forcing for the simulation of particulate flows, J. Comput. Phys. 209, 448 (2005).
  26. M. Uhlmann and T. Doychev, Sedimentation of a dilute suspension of rigid spheres at intermediate Galileo numbers: The effect of clustering upon the particle motion, J. Fluid Mech. 752, 310 (2014).
  27. E. Climent and M. R. Maxey, Numerical simulations of random suspensions at finite Reynolds number, Int. J. Multiphase Flow 29, 579 (2003).
  28. A. A. Howard, M. R. Maxey, and K. Yeo, Settling of heavy particles in concentrated suspensions of neutrally buoyant particles under uniform shear, Fluid Dyn. Res. 50, 041401 (2018).
  29. K. Gudmundsson and A. Prosperetti, Improved procedure for the computation of Lamb's coefficients in the Physalis method for particle simulation, J. Comput. Phys. 234, 44 (2013).
  30. A. J. Sierakowski and A. Prosperetti, Resolved-particle simulation by the physalis method: Enhancements and new capabilities, J. Comput. Phys. 309, 164 (2016).
  31. Y. Wang, A. Sierakowski, and A. Prosperetti, Fully resolved simulation of particulate flows with particles-fluid heat transfer, J. Comput. Phys. 350, 638 (2017).
  32. D. Willen and A. Prosperetti, Resolved simulations of sedimenting suspensions of spheres, Phys. Rev. Fluids 4, 014304 (2019).
  33. S. Kim and S. J. Karrila, Microhydrodynamics: Principles and Selected Applications (Butterworth-Heinemann, Boston, MA, 1991; reprinted by Dover, New York).
  34. H. Lamb, Hydrodynamics, 6th ed. (Cambridge University Press, Cambridge, UK, 1932; reprinted by Dover, New York).
  35. A. J. Sierakowski, Numerical simulation of disperse particle flows on a graphics processing unit, Ph.D. thesis, Johns Hopkins University, 2016.
  36. J. A. Simeonov and J. Calantoni, Modeling mechanical contact and lubrication in direct numerical simulations of colliding particles, Int. J. Multiphase Flow 46, 38 (2012).
  37. C. T. Crowe, J. D. Schwarzkopf, M. Sommerfeld, and Y. Tsuji, Multiphase Flows with Droplets and Particles, 2nd ed. (CRC Press, Boca Raton, FL, 2012).
  38. D. Willen, A. J. Sierakowski, G. Zhou, and A. Prosperetti, Continuity waves in resolved-particle simulations of fluidized beds, Phys. Rev. Fluids 2, 114305 (2017).
  39. N. V. Brillantov and T. Pöschel, Kinetic Theory of Granular Gases (Oxford University Press, Oxford, UK, 2004).
  40. T. P. C. van Noije and M. H. Ernst, Velocity distributions in homogeneous granular fluids: The free and the heated case, Granular Matter 1, 57 (1998).
  41. D. M. Kalyon, Apparent slip and viscoplasticity of concentrated suspensions, J. Rheol. 49, 621 (2005).
  42. M. N. Ardekani, O. Abouali, F. Picano, and L. Brandt, Heat transfer in laminar Couette flow laden with rigid spherical particles, J. Fluid Mech. 834, 308 (2018).
  43. G. Drazer, J. Koplik, B. Khusid, and A. Acrivos, Deterministic and stochastic behavior of non-Brownian spheres in sheared suspensions, J. Fluid Mech. 460, 307 (2002).
  44. G. Zhou and A. Prosperetti, Lamb's solution and the stress moments for a sphere in Stokes flow, Eur. J. Mech. B/Fluids 79, 270 (2019).
  45. G. K. Batchelor, The stress system in a suspension of force-free particles, J. Fluid Mech. 41, 545 (1970).
  46. S. Gallier, E. Lemaire, F. Peters, and L. Lobry, Rheology of sheared suspensions of rough frictional particles, J. Fluid Mech. 757, 514 (2014).
  47. E. Guazzelli, and O. Pouliquen, Rheology of dense granular suspensions, J. Fluid Mech. 852, P1 (2018).
  48. I. M. Krieger, Rheology of monodisperse lattices, Adv. Colloid Interface Sci. 2, 111 (1972).
  49. F. Picano, W.-P. Breugem, D. Mitra, and L. Brandt, Shear Thickening in Non-Brownian Suspensions: An Excluded Volume Effect, Phys. Rev. Lett. 111, 098302 (2013).
  50. C. Gamonpilas, J. F. Morris, and M. M. Denn, Shear and normal stress measurements in non-Brownian monodisperse and bidisperse suspensions, J. Rheol. 60, 289 (2016).
  51. C. Gamonpilas, J. F. Morris, and M. M. Denn, Erratum: “Shear and normal stress measurements in non-Brownian monodisperse and bidisperse suspensions” [J. Rheol. 60(2), 289-296 (2016)], J. Rheol. 62, 665 (2018).
  52. R. Seto and G. G. Giusteri, Normal stress differences in dense suspensions, J. Fluid Mech. 857, 200 (2018).
  53. R. Mari, R. Seto, J. F. Morris, and M. M. Denn, Shear thickening, frictionless and frictional rheologies in non-Brownian suspensions, J. Rheol. 58, 1693 (2014).
  54. I. R. Peters, S. Majumdar, and H. M. Jaeger, Direct observation of dynamic shear jamming in dense suspensions, Nature 532, 214 (2016).
  55. Q. Xu, S. Majumdar, E. Brown, and H. M. Jaeger, Shear thickening of highly viscous granular suspensions, Europhys. Lett. 107, 68004 (2014).
  56. G. Drazer, J. Koplik, B. Khusid, and A. Acrivos, Microstructure and velocity fluctuations in sheared suspensions, J. Fluid Mech. 511, 237 (2004).

Outline

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Phys. Rev. Fluids 5, 084301– Published 10 August, 2020
  • Received 14 February 2020
  • Accepted 26 June 2020
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