## 3 Materials and Methods
### Experimental Procedure  
Experiments were performed for each distributor plate for a range of superficial air velocities to observe the minimum fluidization velocities and pressure drop across the bed for every initial bed height (bed aspect ratio, \(\mathrm{L}/\mathrm{D}_{\odot}\)). \(\mathrm{L}\) is the initial bed height, and \(\mathrm{D}_{\odot}\) is the diameter of the fluidization column. Due to the larger open area of distributor plates, a 100 \(\mathrm{\SIUnitSymbolMicro m}\) mesh was placed over each plate to prevent particles from falling into the plenum section. Before starting the fluidization experiments, the column was initially run without bed material to measure the pressure drop, which is purely the pressure drop for a specific plate. Afterward, bed material is introduced into the fluidization column up to different initial bed heights of 0.5, 0.833, and 1. Net pressure drop was calculated by subtracting the empty and distributor pressure drop from the total bed pressure drop for each bed aspect ratio.  
The airflow rate was controlled via a knob located at the rotameter. The flow rate was gradually increased, and the bed was carefully monitored to check for any bubbling of the static bed. The static bed vibrated slightly after attaining a specific flow rate, and tiny bubbles erupted through the bed surface. Such a condition was the initial minimum fluidization velocity (\(\mathrm{U}_{\mathrm{m}\mathrm{f}\mathrm{i}}\)). Further increasing the flow rate resulted in a more vigorous and larger eruption of bubbles, and the pressure drop did not increase further. This condition  
\begin{table}
\begin{tabular}{l c c c c} \hline \hline  & \multicolumn{4}{c}{**Number of Plates = 3**} \\  & **Perforated Plate, 45\({}^{\circ}\) Slotted Plate, Hybrid Plate (Perforated + Slotted)**} \\ \hline  & \multicolumn{4}{c}{**Operational Variables**} \\ \hline  & \multicolumn{4}{c}{**Input Variables**} & \multicolumn{4}{c}{**Output Variables**} \\ \hline
**Geometric Variables** & \begin{tabular}{c} Superficial Air Velocities \\ Three designs of Distributor Plates. \\ \end{tabular} & \begin{tabular}{c} 1.5\({}^{\circ}\)U\({}_{\mathrm{m}\mathrm{f}}\) \\ \end{tabular} & \begin{tabular}{c} 3.0\({}^{\circ}\)U\({}_{\mathrm{m}\mathrm{f}}\) \\ \end{tabular} & \
\begin{tabular}{c} 1. \\ 2. \\ \end{tabular} &
\begin{tabular}{c} Pressure drop across the bed (pa) \\ Bed height rise (m) \\ \end{tabular} \\
1. & Perforated distributor plate &
\begin{tabular}{c} Initial bed Height Ratio \\ (L/D)/bed aspect ratio \\ \end{tabular} & 0.5, 0.833, 1.16 & 0.5, 0.833, 1.16 & 3. \\
2. & 45\({}^{\circ}\) distributor plate & \begin{tabular}{c} Particle Size (\(\mathrm{\SIUnitSymbolMicro m}\)) \\ \end{tabular} & \begin{tabular}{c} Particle Size (\(\mathrm{\SIUnitSymbolMicro m}\)) \\ \end{tabular} & \
\begin{tabular}{c} Particle Size (\(\mathrm{\SIUnitSymbolMicro m}\)) \\ \end{tabular} &
\begin{tabular}{c} Particle Size (\(\mathrm{\SIUnitSymbolMicro m}\)) \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table}
Table 3: Experimental scheme for input and output operational parameters along with geometric parameter.  
Figure 2: Geometry of distributor plates.  
is the final minimum fluidization velocity (U\({}_{\text{mf,f}}\)) [10]. Further flow rate increment will remain constant and will not affect the pressure drop. All experiments were performed at room temperature of ~25 degrees centigrade and atmospheric pressure of 1 atm.