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27 April 2004 Comparison of differential representations for radially symmetric Stokes flow
George Dassios, Panayiotis Vafeas
Abstr. Appl. Anal. 2004(4): 347-360 (27 April 2004). DOI: 10.1155/S1085337504306044


Papkovich and Neuber (PN), and Palaniappan, Nigam, Amaranath, and Usha (PNAU) proposed two different representations of the velocity and the pressure fields in Stokes flow, in terms of harmonic and biharmonic functions, which form a practical tool for many important physical applications. One is the particle-in-cell model for Stokes flow through a swarm of particles. Most of the analytical models in this realm consider spherical particles since for many interior and exterior flow problems involving small particles, spherical geometry provides a very good approximation. In the interest of producing ready-to-use basic functions for Stokes flow, we calculate the PNAU and the PN eigensolutions generated by the appropriate eigenfunctions, and the full series expansion is provided. We obtain connection formulae by which we can transform any solution of the Stokes system from the PN to the PNAU eigenform. This procedure shows that any PNAU eigenform corresponds to a combination of PN eigenfunctions, a fact that reflects the flexibility of the second representation. Hence, the advantage of the PN representation as it compares to the PNAU solution is obvious. An application is included, which solves the problem of the flow in a fluid cell filling the space between two concentric spherical surfaces with Kuwabara-type boundary conditions.


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George Dassios. Panayiotis Vafeas. "Comparison of differential representations for radially symmetric Stokes flow." Abstr. Appl. Anal. 2004 (4) 347 - 360, 27 April 2004.


Published: 27 April 2004
First available in Project Euclid: 4 May 2004

zbMATH: 1133.76309
MathSciNet: MR2064146
Digital Object Identifier: 10.1155/S1085337504306044

Primary: 35C10 , 76D07
Secondary: 35D99

Rights: Copyright © 2004 Hindawi

Vol.2004 • No. 4 • 27 April 2004
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