Rotational flow field of a particle-laden fluid on a co-rotating disk

The particle-modified velocity field of a rotating particulate fluid on a co-rotating disk is studied. Unlike a clear fluid, which admits pure rigid-body rotation with a zero radial velocity component, it is shown here that an unbounded particle-laden fluid does not admit pure rigid-body rotation. An exact solution is given for an unbounded rotating particle-laden fluid, which contains a non-zero radial velocity component and cannot meet the no-slip boundary conditions on a disk co-rotating at the same angular velocity. Explicit leading-order solutions are derived for the particle-modified velocity field of a rotating particulate fluid on a co-rotating disk. It is shown that the disturbed radial and azimuthal velocities due to the co-rotating disk are oscillatory and decay exponentially with the distance from the disk, while the disturbed axial velocity approaches a constant at infinity. The derived formula is used to discuss the radial, azimuthal, and axial velocities of dispersed particles and their effects on the rotational flow of the rotating particle-laden fluid.