## 2 Results  
The physical properties of the raw materials used in this study were thoroughly evaluated, with results presented in Table 1. Sodium naproxen and dolomite (calcium carbonate) exhibited the most problematic flow characteristics, reflected in their high angles of repose (47.2\({}^{\circ}\) and 46.1\({}^{\circ}\), respectively) and large Hausner ratios (1.81 and 1.58). These values significantly exceed the acceptable thresholds for good powder flow and compressibility. In contrast, excipients such as polyvinylpyrrolidone (PVP) and cellulose demonstrated much lower compressibility indices (17.4% and 17.8%) and Hausner ratios close to 1.2, indicating favorable flow behavior. These initial properties influenced the subsequent choice of formulation strategy. Poor-flowing materials typically require granulation to ensure uniform die filling and consistent compression. Table 1 serves as a strong justification for exploring both direct compression and granulation routes in parallel, particularly considering the use of materials such as sodium naproxen and dolomite. Table 2 summarizes the experimental design, detailing the processing parameters for each batch. The reference batch (REF) was produced using a conventional V-type blender, which is widely used in the pharmaceutical industry. However, tablets from this batch showed the weakest performance across multiple quality criteria, including mass uniformity and mechanical strength. This highlights a key limitation of standard blending for challenging powders. \begin{table}
\begin{tabular}{l l l l l l l l} \hline \hline \multirow{2}{*}{**Sample**} & **Angle of** & **Angle of** & **Angle of** & **Aerated Bulk** & **Packed Bulk** & \multirow{2}{*}{**Compressibility**} & **Hausner** \\  & **Repose** & **Fall** & **Difference** & **Density** & **Density** & **Ratio** \\  & **[deg]** & **[deg]** & **[deg]** & **[g/cm\({}^{3}\)]** & **[g/cm\({}^{3}\)]** & **[\%]** & **[**]** \\ \hline Sodium naproxen & 47.2 & 21.1 & 26.1 & 0.382 & 0.693 & 44.9 & 1.81 \\ Polyvinylpyrrolidone (PVP) & 43.6 & 19.9 & 23.7 & 0.423 & 0.512 & 17.4 & 1.21 \\ Magnesium stearate & 42.7 & 17.2 & 25.5 & 0.383 & 0.586 & 34.6 & 1.53 \\ Cellulose & 45 & 24.8 & 20.2 & 0.403 & 0.49 & 17.8 & 1.22 \\ Dolomite & 46.1 & 22.7 & 23.4 & 0.979 & 1.544 & 36.6 & 1.58 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Characteristics of raw materials. \begin{table}
\begin{tabular}{l l} \hline \hline
**Batch** & **Symbol** \\ \hline Reference experiment & REF \\ Direct tableting, mixing time 2.5 min. & DT1 \\ Direct tableting, mixing time 5 min. & DT2 \\ Direct tableting, mixing time 10 min. & DT3 \\ Indirect tabletting, pan granulation, inclination angle 50\({}^{\circ}\) & IT1 \\ Indirect tabletting, pan granulation, inclination angle 30\({}^{\circ}\) & IT2 \\ Indirect tabletting, pan granulation, inclination angle 10\({}^{\circ}\) & IT3 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Experimental plan. In contrast, direct compression batches prepared using the vibratory ball mill (DT1-DT3) exhibited markedly improved outcomes. Increased mixing time resulted in better homogeneity, with DT4 (10 min) yielding tablets comparable to those obtained via indirect tableting. This result suggests that vibratory blending not only compensates for poor flow properties but also improves content uniformity without the need for granulation. The implications for industrial production are significant, as the vibratory approach reduces the number of process steps and eliminates solvent use. Indirect tableting (IT1-IT3), involving pan granulation at varying pan inclination angles (10\({}^{\circ}\), 30\({}^{\circ}\), and 50\({}^{\circ}\)), demonstrated how intermediate granule properties affect final tablet quality. At a 30\({}^{\circ}\) inclination (IT2), granules exhibited optimal flow and compaction behavior, leading to tablets with the best balance of mechanical and uniformity parameters.