Figure 3. Random Forest out-of-bag permuted predictor importance estimates for local cluster characteristics. The left column corresponds to 1188 datasets from a fast fluidized bed 16,17,25, while the right column corresponds to 378 datasets from a turbulent fluidized bed20.
In an earlier study 26, the 1188 cluster datasets in the fast fluidized bed were found to be classifiable into two distinct data assemblies, with one composed of monodisperse particle systems (i.e., three narrow PSDs) and the other of non-monodisperse particle systems (i.e., two binary mixtures and one broad PSD), as shown in the cluster frequency versus duration plot in Figure 4. Clearly, the clusters from turbulent fluidization appear to be markedly different from that of fast fluidization, particularly in terms of much higher cluster frequency. Although the turbulent datasets consist of both monodisperse and non-monodisperse particle systems, the data points only overlap with the monodisperse data points of the fast fluidized bed. A closer look was taken at the data collected from turbulent fluidization to investigate if the data can be classified into distinct data assemblies based on the monodispersity versus non-monodispersity of the particle system, per that observed for fast fluidization (Figure 4). Figure 5 shows the plots of cluster frequency versus duration, with the data for the different particle systems represented by different symbols. Using different colors to represent all nine different particle systems, Figure 5a indicates no obvious demarcation into distinct data assemblies. Using three colors to represent the three particle systems (namely, narrow PSDs, binary mixtures, and broad PSDs), Figure 5b shows that, relative to the narrow PSDs, the maximum frequency of the binary mixtures was approximately half of that of the narrow PSDs or broad PSDs. Figure 5c presents data for the binary mixtures and the two constituents of narrow PSDs. Although the narrow PSD of polystyrene (PS) particles gave high-frequency clusters, the binary mixtures did not exhibit these, but instead gave clusters with larger durations than that of either constituent. As for the broad PSD mixtures, Figure 5d shows that the cluster frequencies were largely similar to that exhibited by the narrow PSD, and a few clusters had durations greater than that of the narrow PSD. Therefore, whereas the presence of particle mixtures (either binary mixtures or broader PSDs) gave significantly lower cluster durations in the fast fluidized bed (Figure 4), the effect is less marked in the turbulent fluidized bed (Figure 5). This again affirms that the underlying mechanisms governing cluster formation are different in the different regimes.