Steady Particulate Taylor-Couette Flow with Particle Migration

Steady Taylor-Couette flow of a particle-fluid suspension with non-neutrally buoyant particles between two coaxial rotating cylinders is studied with a novel two-fluid model. It is shown that steady particle distribution in particulate Taylor-Couette flow can exist in the case when the solid walls are permeable where the particles and the fluid can be sucked or injected with equal but opposite normal fluxes. With this assumption, an explicit formula is derived for the axisymmetric steady radial distribution of particles with particle migration in the dilute limit. Detailed results for several cases of major interest show that the local rate of particle migration depends largely on the local azimuthal speed, and the steady volume fraction of particles typically attains its maximum (or minimum) at the location of minimum (or maximum) local azimuthal speed. In particular, with a wider gap between two cylinders and a Stokes number of particles around the order of unity, the non-monotonic radial distribution of particle volume fraction with interior local maximum and/or minimum can occur when the inner cylinder rotates with the outer cylinder fixed or when the two cylinders counter-rotate with equal but opposite angular velocities.