The leading effect of fluid inertia on the motion of rigid bodies at low Reynolds number

• Published in: Journal of fluid mechanics 2004-04, Vol.505, p.235-248
• Main Authors: LESHANSKY, A. M., LAVRENTEVA, O. M., NIR, A.
• Format: Article
• Language: English
• Subjects: Exact sciences and technology; Fluid dynamics; Fundamental areas of phenomenology (including applications); Laminar flows; Laminar flows in cavities; Laminar suspensions; Physics; Reynolds number; Uniform flow
• ISSN: 0022-1120; 1469-7645
• DOI: 10.1017/S0022112004008407

We investigate the influence of fluid inertia on the motion of a finite assemblage of solid spherical particles in slowly changing uniform flow at small Reynolds number, $Re$, and moderate Strouhal number, $\hbox{\it Sl}$. We show that the first effect of fluid inertia on particle velocities for times much larger than the viscous time scales as $\sqrt{\hbox{\it Sl\,Re}}$ given that the Stokeslet associated with the disturbance flow field changes with time. Our theory predicts that the correction to the particle motion from that predicted by the zero-$Re$ theory has the form of a Basset integral. As a particular example, we calculate the Basset integral for the case of two unequal particles approaching (receding) with a constant velocity along the line of their centres. On the other hand, when the Stokeslet strength is independent of time, the first effect of fluid inertia reduces to a higher order of magnitude and scales as $Re$. This condition is fulfilled, for example, in the classical problem of sedimentation of particles in a constant gravity field.