Particulate Flow of a Viscous Fluid Driven by a Torsionally Oscillating Disk

A novel hydrodynamic model is used to study oscillatory flow of a particle-laden fluid driven by a torsionally oscillating disk. The present model is featured by a modified form of Navier-Stokes equations which is conceptually different than existing related models and enjoys relatively concise mathematical formulation. Explicit expressions are derived for the radial, azimuthal and axial velocities using the method of power series expansions of small amplitude parameter, and the derived solutions reduce to Rosenblat's earlier results for a clear fluid driven by a torsionally oscillating disk in the absence of suspended particles. The implications of the present results to dusty gases are discussed in detail with particular interest in the effects of suspended particles on the decay indexes and wavelengths of the induced oscillatory velocity fields. The results obtained in this work can be used to quantify the effects of suspended particles on particulate flow driven by a torsionally oscillating disk.