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Importance of fluid inertia for the orientation of spheroids settling in turbulent flow

  • Muhammad Zubair Sheikh (a1) (a2), Kristian Gustavsson (a3), Diego Lopez (a4), Emmanuel Lévêque (a4), Bernhard Mehlig (a3), Alain Pumir (a1) and Aurore Naso (a4)...

Abstract

How non-spherical particles orient as they settle in a flow has important practical implications in a number of scientific and engineering problems. In a quiescent fluid, a slowly settling particle orients so that it settles with its broad side first. This is an effect of the torque due to convective inertia of the fluid that is set in motion by the settling particle, which maximises the drag experienced by the particle. Turbulent fluid-velocity gradients, on the other hand, tend to randomise the particle orientation. Recently the settling of non-spherical particles in turbulence was analysed neglecting the effect of convective fluid inertia, but taking into account the effect of the turbulent fluid-velocity gradients on the particle orientation. These studies reached the opposite conclusion, namely that the particle tends to settle with its narrow edge first, therefore minimising the drag on the particle. Here, we consider both effects, the convective inertial torque as well as the torque due to fluctuating fluid-velocity gradients. We ask under which circumstances either one or the other dominates. To this end we estimate the ratio of the magnitudes of the two torques. Our estimates suggest that the fluid-inertia torque prevails in high-Reynolds-number flows. In this case non-spherical particles tend to settle with orientations maximising drag. But when the Reynolds number is small, then the torque due to fluid-velocity gradients may dominate, causing the particle to settle with its narrow edge first, minimising the drag.

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Corresponding author

Email address for correspondence: Aurore.Naso@ec-lyon.fr

References

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Almondo, G., Einarsson, J., Angilella, J. R. & Mehlig, B. 2018 Intrinsic viscosity of a suspension of weakly Brownian ellipsoids in shear. Phys. Rev. Fluids 3, 064307.
Anand, P., Ray, S. S. & Subramanian, G.2019 Theory for the effect of fluid inertia on the orientation of a small particle settling in turbulence, Preprint, arXiv:1907.02857.
Bagheri, G. & Bonadonna, C. 2016 On the drag of freely falling non-spherical particles. Powder Technol. 301, 526544.
Bec, J., Homann, H. & Ray, S. S. 2014 Gravity-driven enhancement of heavy particle clustering in turbulent flow. Phys. Rev. Lett. 112, 184501.
Borgnino, M., Gustavsson, K., Lillo, F. D., Boffetta, G., Cencini, M. & Mehlig, B. 2019 Alignment of spheroidal self-propelled particles swimming in turbulent flows. Phys. Rev. Lett. 123, 138003.
Brenner, H. 1961 The Oseen resistance of a particle of arbitrary shape. J. Fluid Mech. 11, 604610.
Byron, M., Einarsson, J., Gustavsson, K., Voth, G., Mehlig, B. & Variano, E. 2015 Shape-dependence of particle rotation in isotropic turbulence. Phys. Fluids 27 (3), 035101.
Candelier, F., Einarsson, J. & Mehlig, B. 2016 Rotation of a small particle in turbulence. Phys. Rev. Lett. 117, 204501.
Candelier, F., Mehlig, B. & Magnaudet, J. 2019 Time-dependent lift and drag on a rigid body in a viscous steady linear flow. J. Fluid Mech. 864, 554595.
Chen, J. P. & Lamb, D. 1994 The theoretical basis for the parametrization of ice crystal habits: growth by vapor deposition. J. Atmos. Sci. 51, 12061221.
Chevillard, L. & Meneveau, L. 2013 Orientation dynamics of small, tiaxial-ellipsoidal particles in isotropic turbulence. J. Fluid Mech. 737, 571596.
Cox, R. G. 1965 The steady motion of a particle of arbitrary shape at small Reynolds numbers. J. Fluid Mech. 23, 625643.
Dabade, V., Marath, N. K. & Subramanian, G. 2015 Effects of inertia and viscoelasticity on sedimenting anisotropic particles. J. Fluid Mech. 778, 133188.
Ducasse, L. & Pumir, A. 2010 Inertial particle collisions in turbulent synthetic flows: quantifying the sling effect. Phys. Rev. E 80, 066312.
Durham, W. M., Climent, E., Barry, M., Lillo, F. D., Boffetta, G., Cencini, M. & Stocker, R. 2013 Turbulence drives microscale patches of motile phytoplankton. Nat. Commun. 4, 2148.
Frisch, U. 1995 Turbulence: The Legacy of A. N. Kolmogorov. Cambridge University Press.
Fung, J. C. H., Hunt, J. C. R., Malik, N. A. & Perkins, R. J. 1992 Kinematic simulation of homogeneous turbulence by unsteady random fourier modes. J. Fluid Mech. 236, 281318.
Good, G. H., Ireland, P. J., Bewley, G., Bodenschatz, E., Collins, L. R. & Warhaft, Z. 2014 Settling regimes of inertial particles in isotropic turbulence. J. Fluid Mech. 759, R3.
Gustavsson, K., Berglund, F., Johnsson, P. R. & Mehlig, B. 2016 Preferential sampling and small-scale clustering of gyrotactic microswimmers in turbulence. Phys. Rev. Lett. 116, 108104.
Gustavsson, K., Einarsson, J. & Mehlig, B. 2014a Tumbling of Small Axisymmetric Particles in Random and Turbulent Flows. Phys. Rev. Lett. 112, 014501.
Gustavsson, K., Jucha, J., Naso, A., Lévêque, E., Pumir, A. & Mehlig, B. 2017 Statistical Model for the Orientation of Nonspherical Particles Settling in Turbulence. Phys. Rev. Lett. 119, 254501.
Gustavsson, K., Sheikh, M. Z., Lopez, D., Naso, A., Pumir, A. & Mehlig, B. 2019 Effect of fluid inertia on the orientation of a small prolate spheroid settling in turbulence. New J. Phys. 21, 083008.
Gustavsson, K., Vajedi, S. & Mehlig, B. 2014b Clustering of particles falling in a turbulent flow. Phys. Rev. Lett. 112, 214501.
Happel, J. & Brenner, H. 1983 Low Reynolds Number Hydrodynamics: with Special Applications to Particulate Media. Kluwer.
Homann, H. & Bec, J. 2010 Finite-size effects in the dynamics of neutrally buoyant particles in turbulent flows. J. Fluid Mech. 651, 8191.
Jeffery, G. B. 1922 The motion of ellipsoidal particles immersed in a viscous fluid. Proc. R. Soc. Lond. A 102 (715), 161179.
Jucha, J., Naso, A., Lévêque, E. & Pumir, A. 2018 Settling and collision between small ice crystals in turbulent flows. Phys. Rev. Fluids 3, 014604.
Khayat, R. E. & Cox, R. G. 1989 Inertia effects on the motion of long slender bodies. J. Fluid Mech. 209, 435462.
Kim, S. & Karrila, S. 1991 Microhydrodynamics: Principles and Selected Applications. Butterworth-Heinemann.
Kiørboe, T. 2001 Formation and fate of marine snow: small-scale processes with large-scale implications. Sci. Mar. 65, 5771.
Klett, J. D. 1995 Orientation model for particles in turbulence. J. Atmos. Sci. 52, 22762285.
Kramel, S.2017 Non-spherical particle dynamics in turbulence. PhD thesis, Wesleyan University.
Landau, L. D. & Lifschitz, E. M. 1976 Mechanics. Buttlerworth-Heinemann.
Lopez, D. & Guazzelli, E. 2017 Inertial effects on fibers settling in a vortical flow. Phys. Rev. Fluids 2, 024306.
Marchioli, C., Fantoni, M. & Soldati, A. 2010 Orientation, distribution, and deposition of elongated, inertial fibers in turbulent channel flow. Phys. Fluids 22 (3), 033301.
Maxey, M. R. 1983 The gravitational settling of aerosol particles in homogeneous turbulence and random flow fields. J. Fluid Mech. 174, 441.
Naso, A., Jucha, J., Lévêque, E. & Pumir, A. 2018 Collision rate of ice crystals with water droplets in turbulent flows. J. Fluid Mech. 845, 615641.
Naso, A. & Prosperetti, A. 2010 The interaction between a solid particle and a turbulent flow. New J. Phys. 12, 033040.
Nielsen, P. 1993 Turbulence effects on the settling of suspended particles. J. Sedim. Petrol. 63, 835838.
Parsa, S., Calzavarini, E., Toschi, F. & Voth, G. 2012 Rotation rate of rods in turbulent fluid flows. Phys. Rev. Lett. 109, 134501.
Pruppacher, H. R. & Klett, J. D. 1997 Microphysics of Clouds and Precipitation, 2nd edn. Kluwer Academic.
Pumir, A. & Wilkinson, M. 2011 Orientation statistics of small particles in turbulence. New J. Phys. 13, 093030.
Ruiz, J., Macias, D. & Peters, F. 2004 Turbulence increases the average settling velocity of phytoplankton cells. Proc. Natl Acad. Sci. USA 101, 1772017724.
Shin, M. & Koch, D. L. 2005 Rotational and translational dispersion of fibers in isotropic turbulent flows. J. Fluid Mech. 540, 143173.
Siewert, C., Kunnen, R. P. J., Meinke, M. & Schröder, W. 2014a Orientation statistics and settling velocity if ellipsoids in decaying turbulence. Atmos. Res. 142, 4556.
Siewert, C., Kunnen, R. P. J. & Schröder, W. 2014b Collision rates of small ellipsoids settling in turbulence. J. Fluid Mech. 758, 686701.
Voth, G. A. & Soldati, A. 2017 Anisotropic particles in turbulence. Annu. Rev. Fluid Mech. 49, 249276.
Yang, P., Liou, K.-N., Bi, L., Liu, C., Yi, B. & Baum, B. A. 2015 On the radiative properties of ice clouds: light scattering, remote sensing, and radiation parametrization. Adv. Atmos. Sci. 32, 3263.
Zhan, C., Sardina, G., Lushi, E. & Brandt, L. 2014 Accumulation of motile elongated micro-organisms in turbulence. J. Fluid Mech. 739, 2236.
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Importance of fluid inertia for the orientation of spheroids settling in turbulent flow

  • Muhammad Zubair Sheikh (a1) (a2), Kristian Gustavsson (a3), Diego Lopez (a4), Emmanuel Lévêque (a4), Bernhard Mehlig (a3), Alain Pumir (a1) and Aurore Naso (a4)...

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