On particulate Taylor-Couette flow driven by periodically oscillating cylinders

Oscillatory laminar Taylor-Couette flow of a particle-laden fluid between two periodically oscillating cylinders is studied under the assumption that the time-averaged value of particle volume fraction remain essentially constant with the time-periodic small-amplitude oscillation of particles around their initial positions. Unlike oscillatory Taylor-Couette flow of a clear fluid governed by a linear equation for the azimuthal velocity field alone, it is shown here that oscillatory particulate Taylor-Couette flow governed by coupled nonlinear equations for the azimuthal and radial velocity fields gives rise to the non-zero radial velocity field of dispersed particles which contains a non-periodic steady component. Explicit expressions are derived for the leading-order azimuthal and radial velocity fields of the suspension and dispersed particles. Assuming that the radii of cylinders are much larger than the thickness of Stokes boundary layer, detailed results are demonstrated for the case of a single oscillating cylinder and the case of oscillating inner cylinder with fixed outer cylinder. It is shown that the steady radial velocity of particles is vanishingly low except in a thin boundary layer of the oscillating cylinder, and the direction of steady radial velocity of particles is determined by whether the particles are heavier or lighter than the carrier fluid. Unlike known works on particulate Taylor-Couette flow driven by uniformly rotating cylinders, the results reported here could offer new insight to oscillatory particulate Taylor-Couette flow driven by periodically oscillating cylinders with non-neutrally buoyant particles.