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Modelling Radial Mixing and Segregation in Rotating Drums: Effects of Process Parameters

Marleen M. H. D. Arntz1, Wouter. K. Den Otter2, Wim. J. Briels2, and Remko. M. Boom1. (1) Food and Bioprocess Engineering Group, Wageningen University, Bomenweg 2, Wageningen, 6703 HD, Netherlands, (2) Computational Biophysics, University of Twente, P.O. Box 217, Enschede, 7500 AE, Netherlands

Introduction: Mixing is the basis of more than 50% of the unit operations in the food industry. Examples are drying or sterilization of spices, the production of granulated products such as instant soups and the production of coated products such as candies and other snacks. However, the phenomena at the basis of the mixing process are poorly understood and therefore the effectiveness of a mixing process is difficult to predict a priori. Operations intended for mixing may even result in segregation instead of mixing, especially when the particles to be mixed have significantly different properties. Numerical simulations may help in finding guidelines for design of effective mixing operations, since they will yield the mixing behaviour as a function of process and material properties. This work reports on simulations with a strongly simplified system, excluding some of the segregation phenomena, by using a quasi-2D approach containing two types of particles that only differ in size. We have used a discrete-element modelling (DEM) approach, adopted from Schutyser et al. (2001). The mixing system studied is similar to that of Dury and Ristow, 1999 which is a horizontal rotating drum with a diameter of 0.07 m and a length of 0.025 m; the particles have a radius of 1.0 and 1.5 mm and a density of 2.5 kg/m3. The influence of the material properties of the particles and the drum are investigated. Focus is on the two process parameters that are most easily changed in practice, namely fill level and rotation speed of the drum. Studies on the influence of fill level on segregation conducted by, e.g., Dury and Ristow (1999) and Eskin and Kalman (2000) are complemented in this work by an investigation of the influence of the fill level on longer time scales, while the range of rotation speeds is increased compared to Dury and Ristow (1997). Entropy criterion: Our method of defining an order parameter, based on the definition of entropy (Schutyser et al., 2000) indicating the mixing performance of a rotating drum, is relatively straightforward in comparison to other methods mentioned in literature (e.g., Dury and Ristow, 1999). Moreover, the scattering in the values found is significantly smaller. Although, the focus in this work is not in the actual segregation pattern obtained, since we are more interested in the overall mixing performance, our approach is applicable for all segregation phenomena. The parameter is normalized, such that, 1 stands for perfect mixing and 0 for a perfectly segregated system. By comparison of the values of the order parameter with steady state snapshots of the system, we could conclude that the radial mixing can be considered good when the order parameter is higher than 0.9; while a value below app. 0.6 is indicative of segregation. Parametric study: The results of the simulations are not sigificantly dependent on the parameters related to the normal forces between particles and particles and drum. The parameters of the tangential forces in the system are however of great relevance. Especially the Coulomb fricton coefficient influences the dynamics strongly: low values lead to better mixing, implicating the importance of the smoothness of the drum wall and the particles for obtaining better mixing. Influence of the rotation speed of the drum: The rotation speed of the drum was varied from 0.57 rad/s to 25 rad/s, which covers the interval in which the Froude numbers are 0.0012 to 2.25. We found that the effect of the rotation speed on the final mixing state can be divided into five regimes: 1. Fr < 0.009: the final mixing intensity and speed are relatively low (segregation level 0.6 and nine revolutions needed to reach steady state) and are not affected by an increase of the rotation speed; 2. 0.009 ≤ Fr < 0.5: the mixing intensity and speed are increased (from segregation level 0.6 and nine revolutions to segregation level 0.9 and three revolutions needed to reach steady state); 3. 0.5 ≤ Fr < 1.1: increasing the rotation speed of the drum will not lead to any changes in the speed of mixing or in the final mixing state, which features an almost perfectly mixed core; 4. 1.1 ≤ Fr < 2.25: inverted segregation is observed; increasing the rotation speed in this region will lead to a decrease of mixing speed and mixing state; 5. Fr = 2.25: all particles stay at the wall of the drum (the centrifugal regime), leaving an empty space in the middle of the drum. These simulations were carried out with a fill level of 50%, other results (not shown here) seem to indicate that results with different fill levels are similar. Following Turner and Nakagawa (2000), two external forces act on a particle: the gravitational and the centrifugal force. For low values of the rotational speed, the centrifugal force is small, leading to dominance of the gravitational force. The combined gravitational force and the drag force exerted by the drumwall cause the particles to roll over the bulk particles as soon as they have reached a certain angle of respose, making the percolation mechanism possible (Eskin and Kaldman, 2000) and inducing radial segregation. This is what happens for regime one (Fr < 0.009). For higher rotation speeds, the centrifugal force becomes larger, but the gravitational force is still dominant (regime two). Bed expansion is observed in this regime. In regime three the centrifugal force has become so strong that the gravitational and centrifugal forces are comparable in size and an almost perfect mixed state is observed. In the fourth regime the centrifugal force dominates. Because smaller particles centrifuge first, they will go to the outside of the drum, leading to inverted segregation. According to Turner and Nakagawa (2000), the rotation speed at which the transition to this regime takes place is 17.15 rad/s for the smaller particles and 17.28 rad/s for the larger particles. These values coincide with the transition observed in our simulations. Influence of the fill level: Simulations with a rotation speed of 1.57 rad/s and fill levels varying from 8.5% to 90% have been conducted. A fill level of 23% leads to a final mixing intensity of 0.88, attained within three revolutions. Lower fill levels did not increase either the mixing performance or the speed. For fill levels from 23% to 56% the final mixing intensity decreases from 0.88 to 0.58, while three to nine revolutions are necessary. At a fill level of 63% a poorly mixed core is observed, giving rise to a higher value of the order parameter than at a fill level of 56%, based on the first eighteen rotations. In the simulation of a fill level of 79% an unmixed core is clearly visible but this core will slowly disappear through a diffusive mechanism; hence the unmixed core is not visible anymore after eighteen revolutions. The unmixed core present with a fill level of 90% is still present after thirty revolutions. We expect however that this core will also disappear when the rotating drum is rotated for longer times. All fill levels above 56% reach a final mixing intensity of 0.58; the rate of reaching this steady state decreases with higher fill levels. Dury and Ristow (1999) and Eskin and Kalman (2000) performed similar experiments. However, they only considered the first ten revolutions, assuming the final state was reached at that stage. Our results for the first ten revolutions agree well with their results, but it is clear that for higher fill levels the final state is not yet reached. During the ten revolutions convective transport causes the formation of a core of small particles and for high fill levels also the formation of an unmixed subcore. However, a much slower diffusional process to the slow reduction of this unmixed core, only noticeable for higher rotation times. Conclusions: The practical conclusions with respect to mixing particles in a rotating drum are: the mixing performance can be enhanced by reducing the roughness of the drum wall; if practically possible the same is true for the particle roughness reducing of the fill level below 23% will not increase the rate of mixing although the mixing rate for fill levels higher than 56% is lower, the same mixing intensity is reached finally increasing the rotation speed of the drum (Fr) only has a significant influence on the mixing performance when regime two or three can be attained By combining these results with further 3D studies, we think that the simulations carried out can indeed lead to establishing design guidelines for mixing systems, based on a reliable mapping of the occurrence of radial and axial segregation phenomena. C.M. Dury and G.H. Ristow, Physics of fluids, 11 (1999) 1387-1393 C.M. Dury and G.H. Ristow, J. Phys. I France, 7 (1997) 737-745 D. Eskin, H, Kalman, Chemical Engineering and Processing, 39 (2000) 539-545 J. L. Turner, M. Nakagawa, Powder Technology, 113 (2000), 119-123 M.A.I. Schutyser et al., Biotechnol Bioeng, 75 (2001), 666-675