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

Thanaa El- Naqeeb | Zendy; Rudi Schmitz | Zendy

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

Author(s) -

Thanaa El- Naqeeb,

Rudi Schmitz

Publication year - 2011

Publication title -

journal of applied mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.307

H-Index - 43

eISSN - 1687-0042

pISSN - 1110-757X

DOI - 10.1155/2011/318907

Subject(s) - biharmonic equation , rotational symmetry , stream function , spheres , flow (mathematics) , reynolds number , function (biology) , mathematics , mechanics , mathematical analysis , physics , classical mechanics , turbulence , vorticity , astronomy , evolutionary biology , vortex , biology , boundary value problem

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

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