In this work we examine the trajectory of particles within a continuous powder mixer using PEPT (Positron Emission Particle Tracking). Apart from experimental work examining mixing performance, no previous work exists investigating the particle trajectory from continuous powder mixing processes. The benefit of this approach is that the particle movement along the vessel can be measured non-invasively. PEPT has been reviewed in several existing papers and in this work we briefly summarize the method. A more detailed explanation of the technique can be found in Parker et al. [1] and in Jones et al. [2]. PEPT tracks a single radioactive tracer along a main flow of Lactose as a function of time. During radioactive decay, a high-energy positron is emitted, an electron nearby annihilates the positron, and two almost collinear gamma rays are generated. The PEPT camera consists of two symmetric plates that detect the gamma rays between them. If both gamma rays are absorbed by a detector element on each plate, then two lines can be drawn between the detector elements (one line for each gamma ray). After filtering scattered gamma rays, the intersection of the multiple pairs of lines gives the location of the tracer.

The continuous mixer examined in this work is manufactured by Buck Systems in Birmingham, England. The mixer is 0.31 meters long and the radius is 0.035 meters. The continuous mixer was inclined at an upward angle of 17„a. The mixer's rotation rate spans from 17 RPM to 200 RPM. The three agitator speeds examined in this work were 16, 75, and 170 rpm.

The effect of impeller rotation rate, powder flowrate, and powder cohesion on the particle trajectory, dispersive axial transport coefficient, and residence time are examined. It was found that the impeller rotation rate and powder hold-up affected the particle trajectory and residence time. Residence time is used to determine the strain and is an indirect indicator of the axial transport velocity the particle experiences within the vessel at varying processing conditions and bulk material properties. Several particle trajectories were recorded for each set of operating conditions (speed, powder, and flowrate). The average residence time was calculated using all trajectories. The findings were consistent with our previous experimental work (Portillo et al. [4]) using Danckwerts' RTD approach [3]. Experimental work already existed measuring residence time within a continuous mixer. However, the local residence time along the vessel axis had not been explored. We found that particles move along the axial length at fairly the same pace everywhere, even for the case that the vessel was inclined with a positive slope.

Cohesion is an important parameter affecting powder flow. The two materials examined were both common pharmaceutical ingredients that varied in cohesion: edible lactose (Dairy Crest) and free flowing lactose (Mallinckrodt). The effect of increasing cohesion (measured using the flow index, dilation, and the Hausner ratio) was longer average residence times. Interestingly, differences between the residence time profiles for the two materials, is greater at lower speeds and negligible at high speeds. Using the concepts of dispersion coefficient and Einstein's law, axial displacement was investigated. Experimentally the axial dispersion coefficient was related to residence time, consistent with theoretical derivations of the axial-dispersion model. Cohesion did not affect the axial dispersion coefficient significantly, but had considerable effects on the residence time and on the total particle path length.

Einstein [5] defined path length as the total distance covered by particles from the initial position (the entrance) to the final position. The path length is important for two reasons: (1) it provides a basis for measurement and prediction of the axial transport rate at the given fill level or powder hold-up; and (2) particle displacement is possibly impacted by electric charge which the particles may gain as they come in contact with other particles or the vessel. The time step interval is an important factor to consider, the work presented utilized an approximate time step of 0.017s, however we found that adjusting the time step altered the particle path length estimation. In particular a lower total length is obtained for longer time steps. Statistically it was found using an ANOVA that the total path length was shown to be affected by both cohesion and impeller rotation rate.

In summary, the effects of impeller rotation rate on the residence time, axial dispersion, and path length are complex. Therefore, in observations where the influence was questionable statistical analysis was applied in order to verify significance. We found that greater speeds resulted in lower residence times, higher axial dispersions, and lower total path length. The effect of powder hold-up was a bit more complicated since increasing the hold-up predominantly increased the residence time. Residence time showed an exponential trend with axial dispersion and a linear function with path length. In terms of the estimated particle total path length, longer path lengths occur at greater powder hold-ups. The effect of cohesion on the particles path length was highly significant. However, slightly higher axial dispersions were observed for less cohesive powders but this result was statistically not significant.

References:

[1] Parker D.J., Dijkstra A.E., Martin I.T.W., Seville J.P.K., 1997, Positron emission particle tracking studies of spherical particle motion in rotating drums, Chemical Engineering Science, 52, 13, 2011-2022.

[2] Jones J.R., Parker D.J., Bridgwater J., 2007, Axial mixing in a ploughshare mixer, Powder Technology, 178, 73-86.

[3] Danckwerts P.V., 1953, Continuous flow systems: Distribution of residence times, Chemical Engineering Science, 2, 1, 1-13.

[4] Portillo P.M., Ierapetritou M.G., and Muzzio F.J., 2008, Characterization of continuous Convective powder mixing processes, Powder Technology, 182, 368-378.

[5] Einstein, H.A., 1937. Bedload transport as a probability problem. Ph.D. Dissertation (English translation: In: H.W. Shen (Ed.), 1972. Sedimentation, Water Resources Publications, Fort Collins, CO, Appendix C. 105 pp.).