Hostname: page-component-5d59c44645-zlj4b Total loading time: 0 Render date: 2024-02-26T12:35:22.163Z Has data issue: false hasContentIssue false

Transport of anisotropic particles under waves

Published online by Cambridge University Press:  21 December 2017

Michelle H. DiBenedetto*
The Bob and Norma Street Environmental Fluid Mechanics Laboratory, Department of Civil and Environmental Engineering, Stanford University, Stanford, CA 94305, USA
Nicholas T. Ouellette
The Bob and Norma Street Environmental Fluid Mechanics Laboratory, Department of Civil and Environmental Engineering, Stanford University, Stanford, CA 94305, USA
Jeffrey R. Koseff
The Bob and Norma Street Environmental Fluid Mechanics Laboratory, Department of Civil and Environmental Engineering, Stanford University, Stanford, CA 94305, USA
Email address for correspondence:


Using a numerical model, we analyse the effects of shape on both the orientation and transport of anisotropic particles in wavy flows. The particles are idealized as prolate and oblate spheroids, and we consider the regime of small Stokes and particle Reynolds numbers. We find that the particles preferentially align into the shear plane with a mean orientation that is solely a function of their aspect ratio. This alignment, however, differs from the Jeffery orbits that occur in the residual shear flow (that is, the Stokes drift velocity field) in the absence of waves. Since the drag on an anisotropic particle depends on its alignment with the flow, this preferred orientation determines the effective drag on the particles, which in turn impacts their net downstream transport. We also find that the rate of alignment of the particles is not constant and depends strongly on their initial orientation; thus, variations in initial particle orientation result in dispersion of anisotropic-particle plumes. We show that this dispersion is a function of the particle’s eccentricity and the ratio of the settling and wave time scales. Due to this preferential alignment, we find that a plume of anisotropic particles in waves is on average transported farther but dispersed less than it would be if the particles were randomly oriented. Our results demonstrate that accurate prediction of the transport of anisotropic particles in wavy environments, such as microplastic particles in the ocean, requires the consideration of these preferential alignment effects.

JFM Papers
© 2017 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)


Andersson, H. I. & Soldati, A. 2013 Anisotropic particles in turbulence: status and outlook. Acta Mechanica 224, 22192223.Google Scholar
Bakhoday-Paskyabi, M. 2015 Particle motions beneath irrotational water waves. Ocean Dyn. 65, 10631078.Google Scholar
Beron-Vera, F. J., Olascoaga, M. J. & Lumpkin, R. 2016 Inertia-induced accumulation of flotsam in the subtropical gyres. Geophys. Res. Lett. 43, 1222812233.Google Scholar
Brenner, H. 1964 The Stokes resistance of an arbitrary particle II: an extension. Chem. Engng Sci. 19, 599629.Google Scholar
Bretherton, F. P. 1962 The motion of rigid particles in a shear flow at low Reynolds number. J. Fluid Mech. 14, 284304.Google Scholar
Broday, D., Fichman, M., Shapiro, M. & Gutfinger, C. 1997 Motion of diffusionless particles in vertical stagnation flows II. Deposition efficiency of elongated particles. J. Aero. Sci. 28, 3552.Google Scholar
Byron, M., Einarsson, J., Gustavsson, K., Voth, G., Mehlig, B. & Variano, E. 2015 Shape-dependence of particle rotation in isotropic turbulence. Phys. Fluids 27, 035101.Google Scholar
Challabotla, N. R., Zhao, L. & Andersson, H. I. 2015a Orientation and rotation of inertial disk particles in wall turbulence. J. Fluid Mech. 766, R2.Google Scholar
Challabotla, N. R., Zhao, L. & Andersson, H. I. 2015b Shape effects on dynamics of inertia-free spheroids in wall turbulence. Phys. Fluids 27, 061703.Google Scholar
Chubarenko, I., Bagaev, A., Zobkov, M. & Esiukova, E. 2016 On some physical and dynamical properties of microplastic particles in marine environment. Mar. Pollut. Bull. 108, 105112.Google Scholar
Eames, I. 2008 Settling of particles beneath water waves. J. Phys. Oceanogr. 38, 28462853.Google Scholar
Einarsson, J., Angilella, J. R. & Mehlig, B. 2014 Orientational dynamics of weakly inertial axisymmetric particles in steady viscous flows. Physica D 278, 7985.Google Scholar
Gallily, I. & Cohen, A. H. 1979 On the orderly nature of the motion of nonspherical aerosol particles. ii. inertial collision between a spherical large droplet and an axially symmetrical elongated particle. J. Colloid Interface Sci. 68, 338356.Google Scholar
Grinshpun, S. A., Redcoborody, Y. N., Kravchuk, S. G., Zadorozhnii, V. I. & Zhdanov, V. I. 2000 Particle drift in the field of internal gravity wave. Intl J. Multiphase Flow 26, 13051324.Google Scholar
Guha, A. 2008 Transport and deposition of particles in turbulent and laminar flow. Annu. Rev. Fluid Mech. 40, 311341.Google Scholar
Hasselmann, K. 1970 Wave driven inertial oscillations. Geophys. Fluid Dyn. 1, 463502.Google Scholar
Isobe, A., Kubo, K., Tamura, Y., Kako, S., Nakashima, E. & Fujii, N. 2014 Selective transport of microplastics and mesoplastics by drifting in coastal waters. Mar. Pollut. Bull. 89, 324330.Google Scholar
Jansons, K. M. & Lythe, G. D. 1998 Stochastic Stokes drift. Phys. Rev. Lett. 81, 31363139.Google Scholar
Jeffery, G. B. 1922 The motion of ellipsoidal particles imnmersed in a viscous fluid. Proc. R. Soc. Lond. A 102, 161179.Google Scholar
Klett, J. D. 1995 Orientation model for particles in turbulence. J. Atmos. Sci. 52, 22762285.Google Scholar
Kukulka, T., Proskurowski, G., Morét-Ferguson, S., Meyer, D. W. & Law, K. L. 2012 The effect of wind mixing on the vertical distribution of buoyant plastic debris. Geophys. Res. Lett. 39, L07601.Google Scholar
Lamb, H. 1945 Hydrodynamics, 6th edn. Dover.Google Scholar
Leal, L. G. 1980 Particle motions in a viscous fluid. Annu. Rev. Fluid Mech. 12, 435476.Google Scholar
Leibovich, S. 1983 The form and dynamics of Langmuir circulations. Annu. Rev. Fluid Mech. 15, 391427.Google Scholar
Ling, Y., Parmar, M. & Balachandar, S. 2013 A scaling analysis of added-mass and history forces and their coupling in dispersed multiphase flows. Intl J. Multiphase Flow 57, 102114.Google Scholar
Loth, E. 2008 Drag of non-spherical solid particles of regular and irregular shape. Powder Technol. 182, 342353.Google Scholar
Maxey, M. R. & Riley, J. J. 1983 Equation of motion for a small rigid sphere in a nonuniform flow. Phys. Fluids 26, 883889.Google Scholar
Maximenko, N., Hafner, J. & Niiler, P. 2012 Pathways of marine debris derived from trajectories of Lagrangian drifters. Mar. Pollut. Bull. 65, 5162.Google Scholar
McWilliams, J. C., Sullivan, P. P. & Moeng, C. 1997 Langmuir turbulence in the ocean. J. Fluid Mech. 334, 130.Google Scholar
Mortensen, P. H., Andersson, H. I., Gillissen, J. J. J. & Boersma, B. J. 2008 Dynamics of prolate ellipsoidal particles in a turbulent channel flow. Phys. Fluids 20, 093302.Google Scholar
Ni, R., Ouellette, N. T. & Voth, G. A. 2014 Alignment of vorticity and rods with Lagrangian fluid stretching in turbulence. J. Fluid Mech. 743, R3.Google Scholar
Oberbeck, A. 1876 Über stationäre Flüssigkeitsbewegungen mit Berücksichtigung der inneren Reibung. J. Reine Angew. Math. 81, 6280.Google Scholar
Ouchene, R., Khalij, M., Arcen, B. & Tanière, A. 2016 A new set of correlations of drag, lift and torque coefficients for non-spherical particles and large Reynolds numbers. Powder Technol. 303, 3343.Google Scholar
Ouellette, N. T., O’Malley, P. J. J. & Gollub, J. P. 2008 Transport of finite-sized particles in chaotic flow. Phys. Rev. Lett. 101, 174504.Google Scholar
Parsa, S., Calzavarini, E., Toschi, F. & Voth, G. A. 2012 Rotation rate of rods in turbulent fluid flow. Phys. Rev. Lett. 109, 134501.Google Scholar
Pumir, A. & Wilkinson, M. 2011 Orientation statistics of small particles in turbulence. New J. Phys. 13, 093030.Google Scholar
Ryan, P. G., Moore, C. J., van Franeker, J. A. & Moloney, C. L. 2009 Monitoring the abundance of plastic debris in the marine environment. Phil. Trans. R. Soc. Lond. B 364, 19992012.Google Scholar
Santamaria, F., Boffetta, G., Afonso, M. M., Mazzino, A., Onorato, M. & Pugliese, D. 2013 Stokes drift for inertial particles transported by water waves. Europhys. Lett. 102, 14003.Google Scholar
Shapiro, M. & Goldenberg, M. 1993 Deposition of glass fiber particles from turbulent air flow in a pipe. J. Aero. Sci. 24, 6587.Google Scholar
Shin, M. & Koch, D. L. 2005 Rotational and translational dispersion of fibres in isotropic turbulent flows. J. Fluid Mech. 540, 143173.Google Scholar
Siewert, C., Kunnen, R. P. J., Meinke, M. & Schröder, W. 2014 Orientation statistics and settling velocity of ellipsoids in decaying turbulence. Atmos. Res. 142, 4556.Google Scholar
Stokes, G. G. 1851 On the effect of the internal friction of fluids on the motion of pendulums. Trans. Camb. Phil. Soc. 9, 8106.Google Scholar
Van Sebille, E., Wilcox, C., Lebreton, L., Maximenko, N., Hardesty, B. D., Van Franeker, J. A., Eriksen, M., Siegel, D., Galgani, F. & Law, K. L. 2015 A global inventory of small floating plastic debris. Environ. Res. Lett. 10, 124006.Google Scholar
Voth, G. A. & Soldati, A. 2017 Anisotropic particles in turbulence. Annu. Rev. Fluid Mech. 49, 249276.Google Scholar
Zastawny, M., Mallouppas, G., Zhao, F. & Van Wachem, B. 2012 Derivation of drag and lift force and torque coefficients for non-spherical particles in flows. Intl J. Multiphase Flow 39, 227239.Google Scholar
Zhao, L., Challabotla, N. R., Andersson, H. I. & Variano, E. A. 2015 Rotation of nonspherical particles in turbulent channel flow. Phys. Rev. Lett. 115, 244501.Google Scholar