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Motion of a spherical solid particle in a nonuniform flow of a viscous incompressible liquid

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Abstract

The effect of a particle on the basic flow is studied, and the equations of motion of the particle are formulated. The problem is solved in the Stokes approximation with an accuracy up to the cube of the ratio of the radius of the sphere to the distance from the center of the sphere to peculiarities in the basic flow. An analogous problem concerning the motion of a sphere in a nonuniform flow of an ideal liquid has been discussed in [1]. We note that the solution is known in the case of flow around two spheres by a uniform flow of a viscous incompressible liquid [2], and we also note the papers [3, 4] on the motion of a small particle in a cylindrical tube.

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Literature cited

  1. 1.

    O. V. Voinov, “The force acting on a sphere in a nonuniform flow of an ideal incompressible liquid,” Zh. Prikl. Mekh. Tekh. Fiz., No. 4 (1973).

  2. 2.

    Shoichi Wakiya, “Slow motions of a viscous fluid around two spheres,” J. Phys. Soc. Japan,22, No. 4 (1967).

  3. 3.

    T. Greenstein and J. Happel., “Theoretical study of the slow motion of a sphere and a fluid in a cylindrical tube,” J. Fluid Mech.,34, No. 4 (1968).

  4. 4.

    H. Brenner, “Hydrodynamic resistance of particles at small Reynolds numbers,” in: Advances in Chemical Engineering, Vol. 6, Academic Press, New York (1966).

  5. 5.

    H. Lamb, Hydrodynamics, 6th ed., Dover (1932).

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Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 71–74, July–August, 1976.

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Kuptsov, V.S. Motion of a spherical solid particle in a nonuniform flow of a viscous incompressible liquid. J Appl Mech Tech Phys 17, 510–513 (1976). https://doi.org/10.1007/BF00852001

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Keywords

  • Mathematical Modeling
  • Mechanical Engineer
  • Small Particle
  • Industrial Mathematic
  • Solid Particle