Figure 8. Pressure overshoot of fluidized bed at different temperature.
By Eq. (17) the cohesive inter-particle forces at the incipient fluidization can be estimated. As can be seen in Figure 9(a), the estimated cohesive inter-particle force shows an almost linear increase with the increase in temperature. The Bond number (\(B_{O}\)) that is the ratio of cohesive inter-particle forces to particle weight, can be calculated as \(B_{O}\) = 0, 658, 1255, and 1540 for temperatureT = 20, 200, 400, and 600oC, respectively. Such high Bond number \(B_{O}\) at high temperature may be the reason for the fluidization transition of Geldart B to A for silica particles. Previous studies under ambient conditions show a typical range of \(B_{O}\) less than 1 for several Geldart A powders (e.g. FCC catalyst and Al2O3 powders)45. However, Valverde and Castellanos46 showed that for a modified 8.53 μm xerographic toner with \(B_{O}\) of 550, a fluidization transition from Geldart C to A was observed. The hydrodynamic force\(F_{N}\) can be calculated by44
\(F_{N}=\varepsilon_{\text{mf}}d_{p}^{2}\rho_{P}gH_{\text{mf}}\) (18)
It can be compared with the cohesive inter-particle force. Figure 9(b) shows that \(\frac{F_{C}}{F_{N}}\) increases with temperature.\(\frac{F_{C}}{F_{N}}\) is less than 7% at relatively low temperature (20 and 200oC), but increases to more than 12% at relatively high temperature (400 and 600oC). A level off of \(\frac{F_{C}}{F_{N}}\) at high temperature can also be identified, which is akin to the variation of\(\frac{U_{\text{mb}}}{U_{\text{mf}}}\), indicating that the level off of \(\frac{U_{\text{mb}}}{U_{\text{mf}}}\) at T = 400 and 600oC is closely related to that of\(\frac{F_{C}}{F_{N}}\).