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A general solution for Stokes flow and its application to the problem of a rigid plate translating in a fluid

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Abstract

A general solution for 3D Stokes flow is given which is different from, and more compact than the existing ones and more compact than them in that it involves only two scalar harmonic functions. The general solution deduced is combined with the potential theory method to study the Stokes flow induced by a rigid plate of arbitrary shape translating along the direction normal to it in an unbounded fluid. The boundary integral equation governing this problem is derived. When the plate is elliptic, exact analytical results are obtained not only for the drag force but also for the velocity distributions. These results include and complete the ones available for a circular plate. Numerical examples are provided to illustrate the main results for circular and elliptic plates. In particular, the elliptic eccentricity of a plate is shown to exhibit significant influences.

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Authors and Affiliations

  1. School of Mechanics and Engineering, Southwest Jiaotong University, 610031, Chengdu, China

    Xiang-Yu Li

  2. School of Mechanical Engineering, Southwest Jiaotong University, 610031, Chengdu, China

    Si-Cong Ren & Qi-Chang He

  3. Laboratoire Modélisation et Simulation Multi Echelle UMR 8208 CNRS, Université Paris-Est, 5 Boulevard Descartes, 77454, Marne-la-Vallée, France

    Qi-Chang He

Authors
  1. Xiang-Yu Li
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  2. Si-Cong Ren
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  3. Qi-Chang He
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Corresponding authors

Correspondence to Xiang-Yu Li or Qi-Chang He.

Additional information

The project was supported by the National Natural Science Foundation of China (11102171) and by the Program for New Century Excellent Talents in University of Ministry of Education of China (NCET-13-0973).

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Li, XY., Ren, SC. & He, QC. A general solution for Stokes flow and its application to the problem of a rigid plate translating in a fluid. Acta Mech Sin 31, 32–44 (2015). https://doi.org/10.1007/s10409-015-0016-6

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  • DOI: https://doi.org/10.1007/s10409-015-0016-6

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