## 3 Results and Discussion
The results are presented in Figure 8. At low velocities, Run 2 and the mixed bed due to partial elimination of bed non-homogeneity during the first fluidization run have not much difference. However, as the bed was fluidized, a substantial difference was observed between the pressure drop profiles. The mixed bed revealed a smooth pressure drop profile. This finding is a clear indication that the addition of external particles helped improve the fluidization behavior of the mixed bed. Next, we evaluated the quality of fluidization in terms of a dimensionless parameter, termed as the fluidization index (FI) [29]. For the case of the gas-solid fluidization, this is defined as the ratio of the pressure drop across the bed to the effective bed weight per unit cross-sectional area:  
\[FI=\frac{\Delta pA}{mg} \tag{5}\]  
where \(m\) is the amount of solid particles in the bed, \(\Delta p\) is the pressure drop across the bed, \(A\) is the area of the bed, and \(g\) is the gravitational acceleration. Once the incipient fluidization conditions are achieved, the FI should be unity as the pressure drop during fluidization should be equal to the effective weight per unit area of the bed. A low value of FI would indicate the gas channeling and bypassing without sufficiently coming into contact with solid particle present in the bed. This phenomenon is highly undesirable because it will lead to poor mixing. By contrast, a high value of FI would indicate hindrance to the gas flow aside from the usual drag due to the powder cohesiveness. Such kinds of bed non-homogeneities are also undesirable owing to the high energy cost associated with a high pressure drop. Moreover, FI, as a measure of the quality of the fluidization, is applicable only when the bed is fully fluidized. Figure 9 shows the fluidization indices for the monocomponent bed of calcium hydroxide and the binary-solid bed of calcium hydroxide and sand. We made necessary corrections to account for the location of the lower port in our experimental setup. For the monocomponent bed, FI was sometimes as high as 2.5, which means that the pressure drop was as much as 250% higher than the effective weight of the bed. By contrast, the mixed bed showed much better fluidization behavior as the FI is near unity once the bed becomes fully fluidized. Figure 8: Effect of the velocity and the particle-mixing on the pressure drop profiles of the bed of calcium hydroxide powder using nitrogen gas ambient conditions. To make a precise comparison, we have carried out chi-squared (\(\chi^{2}\)) test, which is a statistical method of assessing the goodness of fit between a set of observed values and those expected theoretically. More precisely, it is essentially the sum of the squares of the differences between the actual data and its expected value with each squared difference divided by the corresponding expected value. The value can be written as:  
\[\chi^{2}=\sum\frac{\left(FI_{actual}-FI_{expected}\right)^{2}}{FI_{expected}} \tag{6}\]  
where the \(FI_{expected}\) is taken as unity because the pressure drop during fluidization should ideally equal the effective weight of the bed. Considering the FI value for each individual velocity when the full fluidization was achieved (\(U_{o}>\)2.0 mm/s), we computed the sum required in Equation (6) for each run. We obtained \(\chi^{2}\) values to be 10.65, 3.86, and 0.27 for Run 1, Run 2, and the mixed bed case, respectively. A comparison clearly indicates a difference of more than 10 times between the mixed bed and the Run 2 while the same is almost 40 times when the Run 1 is considered. This is a clear indication of the improvement in the hydrodynamics of the fluidization of cohesive calcium hydroxide powder as a result of particle mixing. We also considered the fluidization of the monocomponent bed of activated carbon, as shown in Figure 6:0 When the gas velocity was very small, the pressure drop linearly increased with the velocity due to the fixed bed mode of contact of the gas with the resident solid particles.