The rotating flow of a separating mixture of particles and fluid in a finite straight axisymmetric container is considered. The analysis employs the ‘‘mixture’’ (‘‘diffusion’’) model under the assumptions that the Ekman numberE, the particle Taylor number &bgr;, and the relative density difference &egr; are small, and the volume fraction &agr; possesses initially a slight ‘‘stratification’’ aroundA0. It is shown that the Ekman layers on the endplates may considerably affect the azimuthal motion of the inviscid core via a spin‐up mechanism that has a relative importance reflected by &lgr;=E1/2/&egr;&bgr;H(His the dimensionless height of the container). When &lgr;≪1 a considerable retrograde motion, proportional to &egr;A0/&bgr;, shows up in agreement with previous infinitely ‘‘long cylinder’’ (i.e., endcaps neglected) solutions; this motion is substantially reduced when &lgr;∼1 and diminishes for &lgr;≫1. On the other hand, the radial motion in the core is insignificantly influenced by the Ekman layers; therefore, the main separation process is properly represented by the long cylinder solutions for a wide range ofH. In addition, it is shown that an initial radial stratification may induce a similar axial variation of &agr; in the Ekman layers.