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Distribution of the concentration in a diffusion wake with stokes flow around a particle

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Abstract

The problem of steady-state convective diffusion to a solid spherical particle located in a Stokes flow was discussed in [1] in the approximation of a diffusion boundary layer. The region of the rear critical point at which the boundarylayer solution is inacceptable was investigated in [2, 3]. With the investigation of the diffusional interaction of several particles in a stream of liquid (for example, two spheres with a common axis, directed along the flow), we must know the distribution of the concentration in a region of small angles behind the body, giving the flow for the following particle. In the present work a solution is given to the problem of the distribution of the concentration in the diffusional wake of a spherical particle. It is shown that the concentration rises proportionally to the square root of the distance to its surface.

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Literature cited

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    V. G. Levich, Physicochemical Hydrodynamics [in Russian], Fizmatgiz, Moscow (1959).

  2. 2.

    Sih Ping Huei and J. Newman, “Mass transfer to the rear of a sphere in Stokes flow,” J. Heat Mass Transfer,10, No. 12 (1967).

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    J. Newman, “Mass transfer to the rear of a cylinder at high Schmidt numbers,” J. Ind. Eng. Chem., Fund.,8, No. 3 (1969).

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    A. B. Voskanyan, A. M. Golovin, and V. V. Tolmachev, “Convective diffusion to a system of periodically arranged spheres at small Reynolds numbers,” Zh. Prikl. Mekh. Tekh. Fiz., No. 5 (1966).

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    H. Bateman and A. Erdelyi, Higher Transcendental Functions, Vol. 1, McGraw-Hill (1953).

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Additional information

Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 176–179, January–February, 1977.

The author thanks Yu. P. Gupalo and Yu. S. Ryazantsev for their useful observations.

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Polyanin, A.D. Distribution of the concentration in a diffusion wake with stokes flow around a particle. Fluid Dyn 12, 150–152 (1977). https://doi.org/10.1007/BF01074645

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Keywords

  • Boundary Layer
  • Spherical Particle
  • Small Angle
  • Diffusion Boundary
  • Stoke Flow