二次元的な曲がった流路の定常流れの中での微粒子の軌道

概要

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The motion of a small particle in a steady flow through a two-dimensional curved channel with a constant width is theoretically investigated. The relative motion of the viscous fluid to the small particle is taken to be a Stokes flow. The center line of the channel is curved periodically. The equations governing the motions of fluid and particle are formulated using curvilinear coordinates taken along the center line of the channel. A perturbation scheme is used for the case of small aspect ratio (the ratio of the width to the radius of curvature of the curved channel). The particle trajectory is analytically determined on the basis of the particle velocity with the precision of the first order of the aspect ratio. As a result, it is found that for small Reynolds numbers, there can exist only one trajectory along which the particle is carried without collision with the channel wall, and that trajectory is stable dynamically, while with increasing Reynolds number, there can exist two types of trajectories. One is unstable and the other is stable. The critical value mutually separating the two cases is found in an analytical form, and its value is independent of the aspect ratio and the period.
一般社団法人日本機械学会の論文
1991-02-25