270372 Axial Dispersion of Non-Spherical Particles in Horizontal, Rotating Cylinders
Rotating cylinders or kilns are widely employed in industry, ranging from the
pharmaceutical, food and agricultural to the chemical industry. Therefore, a
fundamental understanding of the underlying physics of such systems is not only
of academic interest, but also relevant for industrial applications. One specific
area that is currently only poorly understood, but at the same time particularly
relevant for industrial applications, is the axial dispersion of non-spherical
particles in horizontal, rotating cylinders. So far, most studies have only
concentrated on spherical particles in such systems (Zhu et al., 2008).
Granular materials are typically opaque, making the acquisition of experimental
measurements in such systems, e.g. using conventional high speed optical
imaging techniques, very challenging (Müller et al., 2010; Müller et al., 2011). As
an alternative, computational techniques, such as the discrete element method
(DEM), can be applied as a tool to investigate the underlying physics of particle
interactions and dynamics within a bed of grains (Third et al., 2010b; Third et al.,
2011). The DEM can provide both macroscopic and microscopic ‘measurements’
in granular system and, in addition, model non-spherical particles of various
shapes (Lu et al., 2012).
First, as a reference case we study the axial dispersion of monodisperse
spheres within a horizontal, rotating cylinder. Experiments using glass spheres
have shown that axial dispersion in rotating cylinders obeys Fick’s second law,
i.e. the mean square deviation of the particle positions is linearly proportional to
time (Hogg et al., 1966; Parker et al., 1997). These observations are in
agreement with previous DEM simulations (Third et al., 2010a; Taberlet and
Richard, 2006) and the results obtained here. However, the corresponding
information from non-spherical particle systems, e.g. beds composed of cubes,
is currently not available. In this work, non-spherical particles were modeled
using the super-quadric equation, viz. (x/a)^m + (y/b)^n + (z/c)^p =1 (a, b and c
are the lengths of the principle axes and m , n and p are indices controlling
the sharpness of the edges). In the simulations performed here 11220 particles
were placed in a horizontal, rotating cylinder. The aspect ratio of the
non-spherical particles was varied, but the volume of the non-spherical particles
was kept constant, and was equal to the volume of a sphere of diameter 3 mm,
leading to an approximately constant fill level of 26% in the DEM simulations. It
was found that the particle shape had a strong influence on the rate of axial
dispersion. For example, cubic particles of aspect ratio 1 were found to disperse
much faster than spherical particles of equal volume. Furthermore, the rate of
axial dispersion increased with increasing blockiness of the particles.
Hogg, R., Cahn, D.S., Healy, T.W., and Fuerstenau, D.W., 1966. Diffusional mixing in an
ideal system. Chemical Engineering Science, 21, 1025-1038.
Lu, G., Third, J.R., and Müller, C.R., 2012. Critical assessment of two approaches for
evaluating contacts between super-quadric shaped particles in DEM simulations. submitted
to Chemical Engineering Science.
Müller, C.R., Holland, D.J., Sederman, A.J., Dennis, J.S., and Gladden, L.F., 2010. Magnetic
resonance measurements of high-velocity particle motion in a three-dimensional gas-solid
spouted bed. Physical Review E, 82, 050302.
Müller, C.R., Holland, D.J., Third, J.R., Sederman, A.J., Dennis, J.S., and Gladden, L.F.,
2011. Multi-scale magnetic resonance measurements and validation of discrete element
model simulations. Particuology, 9, 330-341.
Parker, D.J., Dijkstra, A.E., Martin, T.W., and Seville, J.P.K., 1997. Positron emission particle
tracking studies of spherical particle motion in rotating drums. Chemical Engineering
Science, 52, 2011-2022.
Taberlet, N. and Richard, P., 2006. Diffusion of a granular pulse in a rotating drum. Physical
Review E, 73, 041301.
Third, J.R., Scott, D.M., and Müller, C.R., 2011. Axial transport within bi-disperse granular
media in horizontal rotating cylinders. Physical Review E, 84, 041301.
Third, J.R., Scott, D.M., and Scott, S.A., 2010a. Axial dispersion of granular material in
horizontal rotating cylinders. Powder Technology, 203, 510-517.
Third, J.R., Scott, D.M., Scott, S.A., and Müller, C.R., 2010b. Tangential velocity profiles of
granular material within horizontal rotating cylinders modeled using the DEM. Granular
Matter, 12, 587-595.
Zhu, H.P., Zhou, Z.Y., Yang, R.Y., and Yu, A.B., 2008. Discrete particle simulation of
particulate systems: A review of major applications and findings. Chemical Engineering
Science, 63, 5728-5770.