A general theory for the motion of a body through a fluid at low Reynolds number. (English) Zbl 0703.76026

Chester, W.

Proc. R. Soc. Lond., Ser. A 430, No. 1878, 89-104 (1990).

Summary: The motion of a body through a viscous fluid at low Reynolds number is considered. The motion is steady relative to axes moving with a linear velocity, \(U_ a\), and rotating with an angular velocity, \(\Omega_ a\). The fluid motion depends on two (small) Reynolds numbers, R proportional to the linear velocity and T proportional to the angular velocity. The correction to the first approximation (Stokes flow) is a complicated function of R and T; it is O(R) for \(T^{1/2}\ll R\) and \(O(T^{1/2})\) for \(T^{1/2}\gg R\). General formulae are derived for the force and couple acting on a body of arbitrary shape. From them all the terms \(O(R+T)\) or larger can be calculated once the Stokes problem has been solved completely. Some special cases are considered in detail.

MSC:

76D07	Stokes and related (Oseen, etc.) flows
35Q30	Navier-Stokes equations

Keywords:

motion of a body; Stokes flow