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Angular dynamics of small crystals in viscous flow
Phys. Rev. Fluids 2, 014302 – Published 30 January, 2017
DOI: https://doi.org/10.1103/PhysRevFluids.2.014302
Abstract
The angular dynamics of a very small ellipsoidal particle in a viscous flow decouples from its translational dynamics and the particle angular velocity is given by Jeffery's theory. It is known that cuboid particles share these properties. In the literature a special case is most frequently discussed, namely that of axisymmetric particles with a continuous rotation symmetry. Here we compute the angular dynamics of crystals that possess a discrete rotation symmetry and certain mirror symmetries but do not have a continuous rotation symmetry. We give examples of such particles that nevertheless obey Jeffery's theory. However, there are other examples where the angular dynamics is determined by a more general equation of motion.
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References (38)
- J. Happel and H. Brenner, Low Reynolds Number Hydrodynamics: With Special Applications to Particulate Media (Springer Science & Business Media, New York, 1983), Vol. 1.
- S. Kim and S. J. Karrila, Microhydrodynamics: Principles and Selected Applications (Dover, New York, 2005).
- G. B. Jeffery, The motion of ellipsoidal particles immersed in a viscous fluid, Proc. R. Soc. London Ser. A 102, 161 (1922).
- S. Parsa, E. Calzavarini, F. Toschi, and G. A. Voth, Rotation Rate of Rods in Turbulent Fluid Flow, Phys. Rev. Lett. 109, 134501 (2012).
- K. Gustavsson, J. Einarsson, and B. Mehlig, Tumbling of Small Axisymmetric Particles in Random and Turbulent Flows, Phys. Rev. Lett. 112, 014501 (2014).
- R. Ni, N. T. Ouelette, and G. A. Voth, Alignment of vorticity and rods with Lagrangian fluid stretching in turbulence, J. Fluid Mech. 743, R3 (2014).
- L. Chevillard and C. Meneveau, Orientation dynamics of small, triaxial-ellipsoidal particles in isotropic turbulence, J. Fluid Mech. 737, 571 (2013).
- M. Byron, J. Einarsson, K. Gustavsson, G. Voth, B. Mehlig, and E. Variano, Shape-dependence of particle rotation in isotropic turbulence, Phys. Fluids 27, 035101 (2015).
- L. Zhao, N. R. Challabotla, H. I. Andersson, and E. A. Variano, Rotation of Nonspherical Particles in Turbulent Channel Flow, Phys. Rev. Lett. 115, 244501 (2015).
- G. A. Voth and A. Soldati, Anisotropic particles in turbulence, Annu. Rev. Fluid Mech. 49, 249 (2017).
- E. J. Hinch and L. G. Leal, The effect of Brownian motion on the rheological properties of a suspension of non-spherical particles, J. Fluid Mech. 52, 683 (1972).
- G. Subramanian and D. L. Koch, Inertial effects on fibre motion in simple shear flow, J. Fluid Mech. 535, 383 (2005).
- J. Einarsson, J. R. Angilella, and B. Mehlig, Orientational dynamics of weakly inertial axisymmetric particles in steady viscous flows, Physica D 278-279, 79 (2014).
- J. Einarsson, F. Candelier, F. Lundell, J. R. Angilella, and B. Mehlig, Effect of weak fluid inertia upon Jeffery orbits, Phys. Rev. E 91, 041002(R) (2015).
- F. Candelier, J. Einarsson, F. Lundell, B. Mehlig, and J. R. Angilella, Role of inertia for the rotation of a nearly spherical particle in a general linear flow, Phys. Rev. E 91, 053023 (2015).
- T. Rosén, J. Einarsson, A. Nordmark, C. K. Aidun, F. Lundell, and B. Mehlig, Numerical analysis of the angular motion of a neutrally buoyant spheroid in shear flow at small Reynolds numbers, Phys. Rev. E 92, 063022 (2015).
- J. Meibohm, F. Candelier, T. Rosen, J. Einarsson, F. Lundell, and B. Mehlig, Angular velocity of a spheroid log rolling in a simple shear at small Reynolds number, Phys. Rev. Fluids 1, 084203 (2016).
- F. P. Bretherton, The motion of rigid particles in a shear flow at low Reynolds number, J. Fluid Mech. 14, 284 (1962).
- J. B. Harris, M. Nawaz, and J. F. T. Pittman, Low-Reynolds-number motion of particles with two or three perpendicular planes of symmetry, J. Fluid Mech. 95, 415 (1979).
- U. Nakaya, Snow Crystals: Natural and Artificial (Harvard University Press, Cambridge, 1954).
- B. Mason, The Physics of Clouds (Oxford University Press, Oxford, 1971).
- H. R. Pruppacher and J. D. Klett, Microphysics of Clouds and Precipitation, 2nd ed. (Kluwer Academic, Dordrecht, 1997).
- J. S. Guasto, R. Rusconi, and R. Stocker, Fluid mechanics of planktonic microorganisms, Annu. Rev. Fluid Mech. 44, 373 (2012).
- J. O. Kessler, Hydrodynamic focusing of motile algal cells, Nature (London) 313, 218 (1985).
- W. M. Durham, E. Climent, M. Barry, F. de Lillo, G. Boffetta, M. Cencini, and R. Stocker, Turbulence drives microscale patches of motile phytoplankton, Nat. Commun. 4, 2148 (2013).
- C. Zhan, G. Sardina, E. Lushi, and L. Brandt, Accumulation of motile elongated micro-organisms in turbulence, J. Fluid Mech. 739, 22 (2014).
- K. Gustavsson, F. Berglund, P. R. Jonsson, and B. Mehlig, Preferential Sampling and Small-Scale Clustering of Gyrotactic Microswimmers in Turbulence, Phys. Rev. Lett. 116, 108104 (2016).
- M. D. Guiry and G. M. Guiry, AlgaeBase, www.algaebase.org, accessed 19 July 2016.
- G. G. Marcus, S. Parsa, S. Kramel, R. Ni, and G. A. Voth, Measurements of the solid-body rotation of anisotropic particles in 3D turbulence, New J. Phys. 16, 102001 (2014).
- S. Meinhardt, J. Smiatek, R. Eichhorn, and F. Schmid, Separation of Chiral Particles in Micro- or Nanofluidic Channels, Phys. Rev. Lett. 108, 214504 (2012).
- S. Kramel, G. A. Voth, S. Tympel, and F. Toschi, Preferential Rotation of Chiral Dipoles in Isotropic Turbulence, Phys. Rev. Lett. 117, 154501 (2016).
- K. Gustavsson and L. Biferale, Preferential sampling of helicity by isotropic helicoids, Phys. Rev. Fluids 1, 054201 (2016).
- A. Pumir and M. Wilkinson, Orientation statistics of small particles in turbulence, New J. Phys. 13, 093030 (2011).
- R. Ni, S. Kramel, N. T. Ouelette, and G. A. Voth, Measurements of the coupling between the tumbling of rods and the velocity gradient tensor in turbulence, J. Fluid Mech. 766, 202 (2015).
- E. J. Hinch and L. G. Leal, Rotation of small non-axisymmetric particles in a simple shear flow, J. Fluid Mech. 92, 591 (1979).
- A. L. Yarin, O. Gottlieb, and I. V. Roisman, Chaotic rotation of triaxial ellipsoids in simple shear flow, J. Fluid Mech. 340, 83 (1997).
- J. Einarsson, B. M. Mihiretie, A. Laas, S. Ankardal, J. R. Angilella, D. Hanstorp, and B. Mehlig, Tumbling of asymmetric microrods in a microchannel flow, Phys. Fluids 28, 013302 (2016).
- S. H. Strogatz, Nonlinear Dynamics and Chaos (Westview, Boulder, 1994).