On mass flux through a torus in Stokes flow
type: Item
instance of: scholarly article
title: On mass flux through a torus in Stokes flow
zbMATH Open document ID: 0545.76038
DOI: 10.1007/BF00944719
published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik
publication date: 1983-01-01T00:00:00Z
review text: This is the last already posthumous paper of Professor Keith Stewartson, a man of great mathematical knowledge and physical insight, and a close friend of many of us all over the world. The paper has all features of Professor Stewartsons style of writing: clarity of problem presentation, elegance and simplicity (to the possible extent) of solution, results verifiable either by comparison with experimental findings or already existing theories. The problem considered is the following: the torus is posed axisymmetrically in the Stokes flow; what is the flux of fluid that actually passes through the gap at the center of the torus? Using the solution already available [\textit{S. R. Majumdar}, \textit{M. E. O'Neill}, Z. Angew. Math. Phys. 28, 541-550 (1977; Zbl 0374.76030)] two limiting cases are considered: when \(b/a<<1\) (a being the crossectional radius of the torus, b the radius of the hole) and \(a/b<<1.\) The first problem is treated in the frames of the lubrication theory, the second using the slender body theory. Results are compared with a general formal solution which enables to compute the flux for moderate sizes of the hole to a given accuracy.
reviewed by: R.Herczynski
Mathematics Subject Classification ID: 76D07
zbMATH DE Number: 3868850
zbMATH Keywords: flow past a torus
zbMATH Keywords: torus is posed axisymmetrically in the Stokes flow
zbMATH Keywords: lubrication theory
zbMATH Keywords: slender body theory
author: Keith Stewartson
MaRDI profile type: Publication
cites work: On Stokes flow about a torus
cites work: A CLOSED TORUS IN STOKES FLOW
cites work: On axisymmetric Stokes flow past a torus
cites work: Asymmetric creeping motion of an open torus
cites work: Hydromechanics of low-Reynolds-number flow. Part 5. Motion of a slender torus
cites work: Slender-body theory for particles of arbitrary cross-section in Stokes flow
cites work: The motion of long slender bodies in a viscous fluid Part 1. General theory
full work available at URL: https://doi.org/10.1007/bf00944719
OpenAlex ID: W2059774495
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description: scientific article; zbMATH DE number 3868850