## 3 Results and Discussion  
First, we considered the fluidization of the calcium hydroxide by carrying out two runs, as shown in Figure 7. A linear increase in the pressure drop at small velocities was initially observed, owing to the fixed bed mode of contacting between the two phases. However, as the velocity was increased further, a prominent initial depression in the pressure drop profile before an increase sometimes existed. However, above 3 mm/s, the pressure drop tended to decrease with increased velocity. Moreover, the pressure drop profiles of the two runs had a significant difference, which can be attributed to bed non-homogeneities. Evidently, Run 2 showed better fluidization hydrodynamics as compared \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Particle Sample**} & \multirow{2}{*}{**Size**} & \multirow{2}{*}{**Density**} & \multirow{2}{*}{**Group**} & \multicolumn{2}{c}{**Theoretical**} \\ \cline{3-5}  & & (\(\mu\)m) & (kg/m\({}^{3}\)) & & **Re\({}_{\text{mf}}\) (-/-)** & **U\({}_{\text{mf}}\) (mm/s)** \\ \hline Activated carbon & 26.4 \(\pm\) 1.1 & 917 & C & 3.2 \(\times\) 10\({}^{-4}\) & 1.86 \(\times\) 10\({}^{-1}\) \\ Calcium hydroxide & 1.08 \(\pm\) 0.23 & 2211 & C & 5.6 \(\times\) 10\({}^{-8}\) & 7.80 \(\times\) 10\({}^{-4}\) \\ Inert sand & 256 & 2664 & B & 2.9 \(\times\) 10\({}^{-1}\) & 1.17 \(\times\) 10\({}^{1}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Main characteristics of the particle samples used. Figure 6: Particle mixing strategy based on the Geldart classification. with Run 1 because the fluidization carried out during Run 1 tended to partially eliminate the bed non-homogeneities. Therefore, Run 2 revealed improved fluidization behavior. The pressure drop in the initial portion of the pressure drop profile can be correlated with the Ergun equation to compute the effective hydrodynamic diameter of the resident solid particles. The Ergun equation is given as:  
\[\Delta p=\frac{150\mu U_{o}\Delta L}{d_{p}^{2}}\frac{(1-\varepsilon)^{2}}{ \varepsilon^{3}}+\frac{1.75\rho_{f}U_{o}^{2}\Delta L}{d_{p}}\frac{(1- \varepsilon)}{\varepsilon^{3}} \tag{2}\]  
where \(\Delta p\) is the pressure drop across the bed length \(\Delta L\), and \(U_{o}\) is the superficial velocity of the gas through the bed. For small velocities (laminar regime), the above equation yields a linear relationship between the pressure drop and the velocity. Therefore:  
\[\Delta p=\frac{150\mu\Delta L}{d_{p}^{2}}\frac{(1-\varepsilon)^{2}}{\varepsilon ^{3}}U_{o} \tag{3}\]  
The initial linear part of the pressure-drop profile in Figure 7 was used to compute the effective hydrodynamic diameter by evaluating the mean of both runs and with fitting Equation (3). It is clear from Figure 7 that the following equation:  
\[\Delta p=3670.4\times 10^{3}U_{o} \tag{4}\]  
yields a linear relationship between the pressure drop and the velocity such that the value of the coefficient of determination (R\({}^{2}\)) is 0.9979. Note that the location of lower port was accounted for in the evaluation of the \(\Delta L\) in Equation (3). Substituting the void fraction obtained from the experimental bed height data in Equation (3), and equating the slopes of Equations (3) and (4), it was possible to compute the effective average diameter of the particles present in the bed. Its value was found to be 3.72 \(\upmu\)m. The computed particle size is almost as much as four times higher than the average particle size obtained using the particle size analysis. This result can be attributed to the agglomeration phenomenon due to interparticle surface forces. Figure 7: Effect of velocity on the pressure drop profile of the bed of calcium hydroxide during fluidization at ambient conditions using nitrogen gas (the fit is for the initial linear portion of the pressure-drop profile). Next, we considered the case of particle mixing by adding 150 g of group B particles and carrying out the fluidization of the mixed bed.