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Wake Field Flow of a Sphere Falling in a Finite Duct

Received: 18 February 2013     Published: 2 May 2013
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Abstract

We report on a simple study involving a single non-Brownian sphere settling under the influence of gravity in a quiescent viscous fluid housed in a finite square duct. Spheres are shown to achieve terminal velocity in a fraction of the time predicted by infinite fluid dynamics. Terminal velocities agree well with right cylinder equations for spheres with diame-ter-to-width ratios less than 0.45. The finite chamber length results a two-phase flow and interesting wake field dynamics for spheres with diameter-to-width ratios greater than 0.255.

Published in American Journal of Modern Physics (Volume 2, Issue 3)
DOI 10.11648/j.ajmp.20130203.11
Page(s) 98-103
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2013. Published by Science Publishing Group

Keywords

Finite Square Duct; Wake Field Flow; Terminal Velocity

References
[1] J. W. Swan & J. F. Brady, "Particle motion between parallel walls: Hydrodynamics and simulation" Phys. Fluids. 22, 103301 (2010)
[2] L. Zovatto & G. Pedrizzetti, "Flow about a circular cylinder between parallel walls" J. Fluid Mech. 440 (2001)
[3] P. Vasseur & R. G. Cox, "The lateral migration of spherical particles sedimenting in a stagnant bounded fluid" J. Fluid Mech. 80 (1977)
[4] T. Bohlin, "On the drag on a rigid sphere moving in a viscous liquid inside a cylindrical tube" Transactions of the Royal Institute of Technology 155 (1960)
[5] W. L. Haberman & R. M. Sayre, "Motion of rigid and fluid spheres in stationary and moving liquids inside cylindrical tubes" David Taylor Model Basin Report #1143, U. S. Department of the Navy (1958)
[6] J. Happel & E. Bart, "The settling of a sphere along the axis of a long square duct at low Reynolds’ number" Applied Scientific Research 29, 1 (1974)
[7] A. Miyamura, S. Iwasaki, & T. Ishii, "Experimental wall correction factors of single solid spheres in triangular and square cylinders, and parallel plates" International Journal of Multiphase Flow 7, 1 (1981)
[8] O. Pitois, C. Fritz, L. Pasol, & M. Vignes-Adler, "Sedimentation of a sphere in a fluid channel" Phys. Fluids 21 103304 (2009)
Cite This Article
  • APA Style

    J. Markiewicz, W. R. Matson. (2013). Wake Field Flow of a Sphere Falling in a Finite Duct. American Journal of Modern Physics, 2(3), 98-103. https://doi.org/10.11648/j.ajmp.20130203.11

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    ACS Style

    J. Markiewicz; W. R. Matson. Wake Field Flow of a Sphere Falling in a Finite Duct. Am. J. Mod. Phys. 2013, 2(3), 98-103. doi: 10.11648/j.ajmp.20130203.11

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    AMA Style

    J. Markiewicz, W. R. Matson. Wake Field Flow of a Sphere Falling in a Finite Duct. Am J Mod Phys. 2013;2(3):98-103. doi: 10.11648/j.ajmp.20130203.11

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  • @article{10.11648/j.ajmp.20130203.11,
      author = {J. Markiewicz and W. R. Matson},
      title = {Wake Field Flow of a Sphere Falling in a Finite Duct},
      journal = {American Journal of Modern Physics},
      volume = {2},
      number = {3},
      pages = {98-103},
      doi = {10.11648/j.ajmp.20130203.11},
      url = {https://doi.org/10.11648/j.ajmp.20130203.11},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajmp.20130203.11},
      abstract = {We report on a simple study involving a single non-Brownian sphere settling under the influence of gravity in a quiescent viscous fluid housed in a finite square duct. Spheres are shown to achieve terminal velocity in a fraction of the time predicted by infinite fluid dynamics. Terminal velocities agree well with right cylinder equations for spheres with diame-ter-to-width ratios less than 0.45. The finite chamber length results a two-phase flow and interesting wake field dynamics for spheres with diameter-to-width ratios greater than 0.255.},
     year = {2013}
    }
    

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  • TY  - JOUR
    T1  - Wake Field Flow of a Sphere Falling in a Finite Duct
    AU  - J. Markiewicz
    AU  - W. R. Matson
    Y1  - 2013/05/02
    PY  - 2013
    N1  - https://doi.org/10.11648/j.ajmp.20130203.11
    DO  - 10.11648/j.ajmp.20130203.11
    T2  - American Journal of Modern Physics
    JF  - American Journal of Modern Physics
    JO  - American Journal of Modern Physics
    SP  - 98
    EP  - 103
    PB  - Science Publishing Group
    SN  - 2326-8891
    UR  - https://doi.org/10.11648/j.ajmp.20130203.11
    AB  - We report on a simple study involving a single non-Brownian sphere settling under the influence of gravity in a quiescent viscous fluid housed in a finite square duct. Spheres are shown to achieve terminal velocity in a fraction of the time predicted by infinite fluid dynamics. Terminal velocities agree well with right cylinder equations for spheres with diame-ter-to-width ratios less than 0.45. The finite chamber length results a two-phase flow and interesting wake field dynamics for spheres with diameter-to-width ratios greater than 0.255.
    VL  - 2
    IS  - 3
    ER  - 

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Author Information
  • Department of Physics, DePaul University, Chicago, Illinois, U.S.A.

  • Department of Physics, DePaul University, Chicago, Illinois, U.S.A.

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