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
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.