Mixing and orientation behaviors of cylindrical particles in a mixing layer of an Oldroyd-B fluid

The effect of Stokes number, Weissenberg number, particle aspect ratio and particle-to-fluid density ratio on the mixing and orientation distributions of cylindrical particles in a mixing layer of an Oldroyd-B fluid is numerically studied using the pseudo-spectral method and Runge-Kutta method. The results show that the particles with annular orbit will rotate around the large vortex center and mix into the core of the vortex, while the particles with wavy orbit do not involve the mixing process. The particles with a small Stokes number are distributed homogenously and mixed thoroughly, whereas the particles with a large Stokes number are poorly mixed and centrifugalized to the edge of the vortex. The range of mixing area is decreased with increasing Stokes number. The initial orientation of the particles has a weak effect on its motion orbit. The roll-up of mixing layer drives the particles to the edge of the vortex, the particle mixing becomes worse with increasing Stokes number and particle aspect ratio, and with decreasing the Weissenberg number. When the Weissenberg number is small, and the Stokes number and particle aspect ratio are large, a little more particles orient towards the vorticity axis. With increasing the Weissenberg number, and decreasing the Stokes number and particle aspect ratio, more particles align themselves on the flow-gradient plane. The Stokes number has a stronger effect on the particle mixing than on the orientation distributions, whereas the particle aspect ratio and particle density have a stronger effect on the orientation distributions than on the particle mixing. The Weissenberg number has a stronger effect on the orientation distributions than the particle aspect ratio and Stokes number. The particles drift along the spanwise direction mostly take place at the initial stage, and both maximum and average drift distance finally reach a stable value.