Abstract
The flow of a centrifugally separating mixture of particles (droplets) and fluid is considered, with emphasis on the azimuthal no-slip requirement on the side wall of the cylindrical container. In the framework of the ‘‘mixture’’ averaged equations—when the Ekman number E, particle Taylor number β, and relative density difference ε are small—a single partial differential nonhomogeneous parabolic equation is obtained for the angular velocity ω(r,t) (relative to the rotating vessel). Analytical and numerical solutions are presented for the dilute limit and for the more general case, respectively. It is shown that, during the separation process, ω develops a quasisteady boundary layer of thickness δ(λ/(λ−1))1/2 on r=1, only if λ>1, where δ=H1/2E1/4 is the typical Stewartson layer scale, λ=E1/2/εβH, and H is the dimensionless height of the container. If λ≤1, however, the side wall affects ω in an unsteady, diffusing viscous domain. Correspondingly significant variations in the axial flux are induced by the Ekman layers. Comparisons to numerical results (produced by a code discussed elsewhere) of the full two-fluid equations display a favorable agreement.
Published Version
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