The motion of a sphere in an incompressible viscous fluid at Reynolds numbers considerably less than one

Authors
Citation
Er. Lindgren, The motion of a sphere in an incompressible viscous fluid at Reynolds numbers considerably less than one, PHYS SCR, 60(2), 1999, pp. 97-110
Citations number
19
Categorie Soggetti
Physics
Journal title
PHYSICA SCRIPTA
ISSN journal
02811847 → ACNP
Volume
60
Issue
2
Year of publication
1999
Pages
97 - 110
Database
ISI
SICI code
0281-1847(199908)60:2<97:TMOASI>2.0.ZU;2-N
Abstract
The analysis of the motion of a sphere in an incompressible, viscous fluid at low Reynolds numbers, and its experimental verification is a classical p roblem of utmost importance, both with respect to the fundamental principle s of the theory of fluid mechanics, and to a variety of applications, as fo r instance the viscometry of fluids. G. G. Stokes was the first one to addr ess this problem analytically (1845, 1851), followed by C.W Oseen, who poin ted out an inconsistency in Stokes' analysis, and presented a revised formu lation of this problem (1910), which was early recognized by Sir Horace Lam b and verified by him in an alternate approach (1911). These authors genera ted an extensive interest in this problem, resulting in a number of papers some few of which have not received recognition deserved. Reference is here made especially to Hilding Faxen, who was the first to obtain a rigorous a nalytical solution to the Stokes' Problem of the drag force for a sphere mo ving parallel with waifs bounding the fluid space (1921, 1923). His work as well has resolved some conflicting features of the Oseen-Lamb theory with regard to the Stokes' problem which still, seem to have escaped general kno wledge. This paper presents an effort to establish a reasonable interpretat ion of the theoretical models of the Stokes' Problem, complemented by some numerical evaluations, and experimental investigations, carried out over a number of years.