# Fluidization Dynamics of Hydrophobic Nanosilica with Velocity Step Changes
## 3 Results and Discussion
### Region-Wise Pressure Drop Behavior  
The dependence of the pressure drop on the velocity is shown in Figure 9a for the fluidized bed's upper region. Results of both cycles, i.e., gradual velocity increase (fluidization) and gradual velocity decrease (defluidization), are presented together in the figure. At low velocities, the velocity increase led to the pressure drop increase due to the fixed bed mode of gas-solid contact. When the velocity was increased above 2 mm/s, there was a significant decline in the pressure drop due to the onset of fluidization that caused motion of solids in the bed. Further increase in the velocity beyond 4 mm/s then led to a rise in the pressure drop due to the bed's expansion. As mentioned earlier, bed expansion caused the mass (solid materials) upward movement from lower bed sections to the upper region. This phenomenon was reflected in the pressure drop increase. Unlike the fluidization cycle, the velocity decrease led to a consistent pressure drop reduction during the defluidization cycle. As a result, there was a pronounced hysteresis effect observed in the upper region of the bed.  
Figure 9b shows the velocity dependence of the pressure drop in the middle region of the fluidized bed. The behavior at low velocities, in this case, was similar to the one observed for the upper region owing to the fixed bed mode of gas-solid contact. At the onset of the fluidization, the pressure drop dropped significantly due to the solid motion. As the velocity was raised above 4 mm/s, there was no noticeable change in the pressure drop profile. On the other hand, decreasing the velocity during the defluidization cycle led to a steady increase, albeit small, in the pressure drop behavior, due to the decrease in bed expansion, which caused the downward migration of the bed material upper region of the bed. A significant effect of hysteresis at low velocities was seen in this region. The pressure drop profiles in the lower region are shown in Figure 9c. The hysteresis effect, is at least in this case, compared to the middle and upper regions of the fluidized bed.  
The overall pressure drop profiles are presented in Figure 9d. These profiles represent the combined behavior of all the three regions shown before. The upper region behavior dominated  
Figure 9: Effect of velocity on the pressure drop in different regions of the fluidized bed during the fluidization and defluidization cycles (**a**) Upper (**b**) Middle (**c**) Lower (**d**) Overall.  
the overall behavior of the fluidized bed. Therefore, the hysteresis phenomenon was prominent in the overall pressure drop profiles as well. Another noteworthy feature in this figure was the overall pressure drop for the fully fluidized bed. In this case, the theoretical pressure drop can be defined as  
\[\left(\Delta P\right)_{theoretical}=(\rho_{b}-\rho)gL, \tag{2}\]  
where \(\rho_{b}\) and \(\rho\) are the bulk and fluid densities in kg\(\cdot\)m\({}^{-3}\), respectively. Notably, \(g\) is the acceleration due to gravity, and \(L\) is the height of the bed. Accounting for 83.2 g of the bed material and correcting for the height of the lowest pressure tap from the distributor plate, one obtains \(\left(\Delta P\right)_{theoretical}=\) 201 Pa. However, the experimental overall pressure drop for the fully fluidized bed obtained in this study was approximately 145 Pa, which was substantially lower than the actual value of 201 Pa, even though no instance of dead region or gas bypassing was observed. This reduction in the pressure drop can be attributed to the upward motion of solids, thereby lowering the upward moving fluidizing gas's relative velocity. This phenomenon reduced the gas-solid drag, resulting in a lower pressure drop.