Abstract and Applied Analysis

Comparison of differential representations for radially symmetric Stokes flow

George Dassios and Panayiotis Vafeas

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Abstract

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.

Article information

Source
Abstr. Appl. Anal., Volume 2004, Number 4 (2004), 347-360.

Dates
First available in Project Euclid: 4 May 2004

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1083679183

Digital Object Identifier
doi:10.1155/S1085337504306044

Mathematical Reviews number (MathSciNet)
MR2064146

Zentralblatt MATH identifier
1133.76309

Subjects
Primary: 76D07: Stokes and related (Oseen, etc.) flows 35C10
Secondary: 35D99

Citation

Dassios, George; Vafeas, Panayiotis. Comparison of differential representations for radially symmetric Stokes flow. Abstr. Appl. Anal. 2004 (2004), no. 4, 347--360. doi:10.1155/S1085337504306044. https://projecteuclid.org/euclid.aaa/1083679183


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