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

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.


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