## 3 First Phase of Experimentation: Results and Discussion  
This phase aimed to study the BF regimes in order to find suitable process parameters for the considered charges. The evaluation of _Ba_ for several levels of the processing parameters allowed development of the contour maps shown in Figure 5. The red area is related to the macro-viscous behavior (_Ba_ less than 40), while the green one refers to _Ba_ greater than 450, corresponding to a grain-inertial flow; the transition between them is colored in yellow. The charge composed of only big media (Figure 5a) dissipated energy in the viscous fluid only at low rotational speed and for low filling percentage. At high barrel filling, it was easy to find an inertial flow regime; however, for higher rotation, the media particles were no longer in contact and were launched toward the barrel walls, according to the definition of cataracting motion. In this condition, the _Ba_ could not be evaluated, and a blank area is reported in the graph. For charge 2 (Figure 5b), a similar behavior was observed; the granular flow was maintained at higher rotational speed with respect to charge 1 but a slight decrease in the green area was present. When charge 3 was employed, the experiment on the laboratory BF machine showed that the grain-inertial flow was limited to a combination of high filling and high rotational speed (Figure 5c). Figure 4: Specim shape and dimensions. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Charge**} & \multirow{2}{*}{**Rotational Speed Range**} & \multicolumn{5}{c}{**Filling Percentage**} \\ \cline{3-6}  & & **30\%** & **40\%** & **50\%** & **60\%** \\ \hline
1 & 2–110 rpm & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) \\
2 & 2–110 rpm & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) \\
3 & 2–110 rpm & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Experiments for regime analysis. This implies that the particle kinetic energy was mainly dissipated in the viscous fluid rather than interparticle interactions. As mentioned above, rolling and cascading motions are required for BF operation. For this purpose, morphological analysis allowed the classification of flow behavior and the development of BB. In Figure 6, the yellow and green areas indicate the six possible motions and their transitions. At low rotational speed, it is evident that charge 3 was characterized by high fluidity, i.e., the capability to move as a fluid; thus, a slipping motion was observed for a wide range of the speed. This may indicate that the charge can be placed with ease in complex geometrical features, but it could suffer from a reduction in kinetic energy. Charge 1 was characterized by slumping for speed in the range 7-20 rpm and a maximum extension of the area at 45% filling. Conversely, charge 3 showed a narrow slumping domain, highlighting that this charge is unable to maintain the peculiar periodic behavior, i.e., the frequency of the avalanche. With regard to rolling, charge 1 and 2 had their lower limits at 50% and 40% respectively; this is in accordance with the best practice of approximately 50% filling percentage and a low Froude number, i.e., on the order of 0.1. The experiment with charge 3 shows that the minimum was observed at the smallest filling percentage, and it tended to increase with this variable. An extension of the rolling involved cascading where the charge-free surface was affected by the inertial forces and tended to be curved. The upper limit of charge 1 and 2 slightly decreased with filling percentage, while it was quite constant for charge 3; it can be assessed that the cascading/cataracting transition, characterized by the undesired launching of media, was avoided at a Froude number less than 0.5. The BB diagrams allowed selecting process parameter values for the investigated charges. The rolling regime was assured by adopting a 25-rpm rotational speed.