Fig. 4.

Effects of scale-up on structured bubbling: (A) Resonant frequency for structure formation via vibration versus initial bed height, showing $h_{1,c}$, the critical bed height above which the resonant frequency becomes constant. (B) Correlation coefficient versus initial bed height for vibration, gas flow oscillation, the combination of vibration and gas flow oscillation, and free bubbling. (C) Horizontal and vertical separation distances (${\lambda }_H$ and ${\lambda }_V$) between bubbles for vibrated gas-fluidized beds with different widths. The fluidized particles in A and B are glass beads with ρ_p = 2,500 kg/m³ and d_p = 150–212 μm. The fluidized particles in C are glass beads with ρ_p = 2,500 kg/m³ and d_p = 212–300 μm. The initial bed height is 10 cm in C. The vibration frequency and amplitude are 5 Hz and 4.5 mm, respectively, for A–C. The U/U_mf is 1.44 in A and in the vibration and free bubbling cases in B. U/U_mf = $1.92+1.25\sin \left(2\pi 5t\right)$ in the gas flow oscillation and combination cases in B. U/U_mf = 1.42 in C.