Figure 7. Ratio of \(U_{\text{mb}}/U_{\text{mf}}\) at different temperature.
To further understand the mechanism underlying the fluidization transition for silica particles used in this work, we studied the pressure overshoot at the incipient fluidization, which is also shown closely related to the cohesive inter-particle forces.6, 24-26 Figure 8 shows pressure overshoot, which was obtained by subtracting the local minimum from the maximum of pressure drop over the superficial gas velocity, as shown in Figure 5. The pressure overshoot becomes higher with the increase in temperature, suggesting that the cohesive inter-particle forces are enhanced with the increase in temperature. It was reported that the existence of alkali metal elements in silica particles would cause the change in particle surface property at high temperature, and further increase the cohesive inter-particle forces.30 From Table 1, it can be seen that the silica particles is mainly composed of Si and O, together with some minor compositions of Al and K. Therefore, the fluidization transition of silica particles from Geldart B to A at elevated temperatures is mainly due to the enhanced cohesive inter-particle forces.
Castellanos et al.43 found that the pressure overshoot\(P_{t}\) can be directly related to the tensile yield strength\(\sigma_{t}\) of particles via
\(P_{t}=\left(\frac{\sigma_{t}}{\rho_{p}\left(1-\varepsilon_{\text{mf}}\right)gH_{\text{mf}}}+1\right)P_{c}\)(16)
where \(H_{\text{mf}}\) is the bed height at the minimum fluidization. The tensile yield strength \(\sigma_{t}\) can be further used to estimate the cohesive inter-particle forces following Molerus44:
\(F_{c}=\frac{\varepsilon_{\text{mf}}}{1-\varepsilon_{\text{mf}}}d_{p}^{2}\sigma_{t}\)(17)