Tumble mixers, such as the V-blender, are simple in concept and commonly used in industrial processes. They are employed to mix pharmaceuticals, chemicals, food, fertilizers, plastics and many other particulate materials.
V-blenders consist of two cylindrical sections joined at an angle of around 90o. The mixer is rotated about a horizontal axis, with mixing resulting from the tumbling motion of the particles. Internal baffles are sometimes used to improve mixing performance. V-blenders are designed for batch operation.
A numerical study of the mixing characteristics of a V-blender has been performed using DEM. The V-blender has 100 mm diameter sections separated by an angle of 85o, and is rotated at a speed of 30 rpm. A total of 50,000 identical particles of diameter 3 mm were considered, corresponding to a fill of approximately 50%.
Animations of the simulation results below show the time dependence of the particle positions. To obtain a qualitative indication of mixing, the particles are coloured according to their initial positions in the mixer.
time = 1 s
time = 15 s
A more quantitative assessment of the mixing properties of this V-blender can be obtained through the temporal dependence of an appropriate mixing measure. Here we consider the GMMI measure, defined by the relative position (in x, y or z direction) of the centroid of a chosen group of coloured particles.
The plot below shows the calculated values of the GMMI in the lateral (x) and axial (z) directions. In can be seen that during the first 20 s (corresponding to 10 rotations of the mixer) only a very slight mixing occurs in the lateral direction. The mixing in the axial direction is observed to be significantly slower, with almost no perceived mixing evident within this time period.
These quantitative results for the mixing rates confirm the observations from the above animations. Slow mixing rates are a feature generally observed for V-blenders.
Numerical simulations provides detailed insights into the mixing process that are difficult to obtain by other means. For examples, the oscillations present in the above plots result from the periodic motion of particles. While the axial motion is observed to have the same frequency as the driving motion (0.5 Hz), the frequency of the lateral motion is slightly higher (0.66 Hz).