## 4 Results and Discussion  
The dependence of the pressure drop on the superficial velocity is reported in Figure 3. The ordinate in the figure is the normalized pressure drop, which was computed by dividing the pressure drop by the effective weight of the bed. During the unassisted fluidization, a significant hysteresis is visible between the fluidization and defluidization. This is caused by initial non-homogeneities due to the presence of cracks, channels, and plugs, which leads to non-uniform flow of air through the bed. The bed is more homogenous during the defluidization. The difference in bed homogeneity usually results in hysteresis as discussed in detail by [PERSON] et al. [41]. The addition of even a small proportion of Geldart group A particles helps to mitigate the effect of hysteresis, which is further diminished when the flow is pulsed, as seen in Figure 4. The fluidization behavior is clearly further improved with the combination of assisted fluidization techniques of flow pulsation and particle mixing. Figure 3: Effect of velocity and particle mixing on the pressure drop behavior of the fluidized bed. Another interesting feature of Figure 3 is that the particle mixing causes a higher pressure drop at low velocities when the bed is not fluidized. The higher the fraction of external particles, the greater the pressure drop, because the addition of external particles lowers the bed void fraction due to the volume-contraction phenomenon, which is reflected in the increase of the pressure drop in the bed [28]. In fact, it was pointed out that a decrease in bed expansion during long-term fluidization of hydrophilic nano-titania at high velocities cannot be attributed to a reduction in the size of agglomerates [42]. Rather, it appears that since high velocities promote greater solid mixing in the bed, smaller agglomerates tend to occupy the interstitial spaces of their large counterparts, thus contributing to the bed volume contraction. The effect of the flow pulsation on the pressure drop profile is more pronounced for a fluidized bed containing a small amount of external particles (Figure 4a). At higher proportions of external particles, the pressure drop behavior is not affected so much by the flow pulsation (Figure 4b). It is clear from the pressure drop profiles shown in Figure 4 that hysteresis is present even with particle mixing, especially when higher amounts of external particles are added. The use of  
Figure 4: Effect of velocity on the pressure drop behavior of the fluidized bed subjected to the combined effect of flow pulsation and particle mixing; (**a**) 4.5 vol % particle mixing; and (**b**) 8.6 vol % particle mixing. flow pulsation, however, eliminates the hysteresis, which is a clear indication of the removal of bed non-homogeneities. The minimum fluidization velocity (\(U_{mf}\)) is an important parameter that characterizes the hydrodynamics of the fluidized bed. At incipient fluidization, the packed pressure drop is equal to the effective bed weight. Using this approach, we determined the minimum fluidization velocity as shown in Figure 5. The results are reported in Table 1. The void fraction at incipient fluidization was computed from the bed expansion data. Clearly, particle mixing lowered the \(U_{mf}\) by more than one-half of the corresponding value obtained using unassisted fluidization. When flow pulsation was introduced, a further substantial reduction in the \(U_{mf}\) was seen. Thus, the use of the combined assisted fluidization techniques of particle mixing and flow pulsation helped to reduce the \(U_{mf}\) from 118 to 25 mm/s, which is, indeed, a significant reduction. However, when the fraction of external particles was increased to 8.6 vol %, no reduction in the \(U_{mf}\) was noticed as compared to the case of 4.5 vol %. Instead, there was an increase, however small. Introducing flow pulsation to the mixed fluidized bed, nonetheless, once again significantly lowered the \(U_{mf}\) to 33 mm/s, which is, however, higher than the 25 mm/s achieved in the case of 4.6 vol %.