Effect of particle shapes on diffusion and mixing in a cylindrical mixer with rotating paddles

Abstract

Numerical simulations were performed to study the particle shape effect on the particle-scale diffusion and mixing behavior in the mixer driven by the rotating paddles. Four shapes of particles, the sphere, the prolate spheroid, the oblate spheroid, and the cube, are simulated. Velocities, flow blockages, and diffusion of particles are analyzed. The mixing index is applied to quantitatively evaluate the mixing. Numerical results show that the circumferential velocity in the above-paddle region is much greater than in the paddle region. Compared to other shapes, the cubic particles have less movement in low velocity and more in high velocity. The cubic shape, rather than the ellipsoidal shape of different aspect ratios, plays a non-negligible role in flow blockage. For particle diffusion, the mean square displacement (MSD) varies linearly with time for the sphere, the prolate, and the oblate spheroids. The average diffusion coefficient is about 6.5 × 10^-5 m²/s. In contrast, the MSD of the cubes is greater than the other shapes, and a sub-diffusion phenomenon is observed. The mixing index increases with time and reaches approximately a steady value of 0.9 after 3.0 s. Because of the different particle–wall interactions, the mixing indices of the cube, the prolate, and the oblate spheroids in the mixer are less than those of the sphere. Finally, radial mixing and axial mixing are evaluated by the eight kinds of mixing functions. These mixing functions and their time-averaged values show that the cubic particle has significantly different features of mixing. Its radial mixing is stronger than other kinds of shapes. Also, the cube’ axial mixing upward is weaker whereas the mixing downward is the strongest.