抄録
In our previous experimental and numerical studies, we developed accurate submicron-particle classifiers using an almost rigidly rotating flow. In the present paper, with the final aim of improving the classification performance and devising new better classifiers on the numerical and theoretical bases of fluid and particle motions, we have ingeniouly performed a linear analysis of the steady and axisymmetric flow of attached and detached Stewartson layers developing at a step of a lower wall between rigidly rotating upper and lower walls shaped arbitrarily. We have used a singular perturbation method and boundary layer approximations, and have used, as boundary conditions, the theoretical linear solutions of Ekman layers and interior regions derived in our previous study. Consequently, we have derived theoretical linear solutions of E1/4- and E1/3-Stewartson layers and their Ekman extensions containing arbitrary additive constants that cannot be obtained by the conventional analysis following Van Heijst. The conventional solutions disagree with numerical solutions, but there is every possibility that the additive constants make the present solutions agree with numerical solutions qualitatively.
