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Resistance Functions for Two Spheres in Axisymmetric Flow—Part I: Stream Function Theory

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  • Thanaa El Naqeeb
  • Rudi Schmitz

Abstract

We consider low‐Reynolds‐number axisymmetric flow about two spheres using a novel, biharmonic stream function. This enables us to calculate analytically not only the forces, but also the dipole moments (stresslets and pressure moments) and the associated resistance functions. In this paper the basics properties of axisymmetric flow and the stream function are discussed. Explicit series expansions, obtained by separation in bispherical coordinates, will be presented in a follow‐up paper.

Suggested Citation

  • Thanaa El Naqeeb & Rudi Schmitz, 2011. "Resistance Functions for Two Spheres in Axisymmetric Flow—Part I: Stream Function Theory," Journal of Applied Mathematics, John Wiley & Sons, vol. 2011(1).
    • Handle: RePEc:wly:jnljam:v:2011:y:2011:i:1:n:318907
    DOI: 10.1155/2011/318907
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    References listed on IDEAS

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    1. Schmitz, R. & Felderhof, B.U., 1982. "Friction matrix for two spherical particles with hydrodynamic interaction," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 113(1), pages 103-116.
    2. Felderhof, B.U., 1983. "The effect of Brownian motion on the transport properties of a suspension of spherical particles," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 118(1), pages 69-78.
    3. Felderhof, B.U. & Jones, R.B., 1987. "Linear response theory of the viscosity of suspensions of spherical brownian particles," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 146(3), pages 417-432.
    4. Wagner, Norman J. & Russel, William B., 1989. "Nonequilibrium statistical mechanics of concentrated colloidal dispersions: Hard spheres in weak flows with many-body thermodynamic interactions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 155(3), pages 475-518.
    5. Felderhof, B.U. & Jones, R.B., 1983. "Linear response theory of sedimentation and diffusion in a suspension of spherical particles," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 119(3), pages 591-608.
    6. Schmitz, R. & Felderhof, B.U., 1982. "Mobility matrix for two spherical particles with hydrodynamic interaction," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 116(1), pages 163-177.
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