Table 1.

Comparison between experiments and theoretical models for the bubble rise velocity, resonant frequency, and $h_{1,c}$, the bed height above which resonant frequency becomes constant with increasing bed height

Particle type	Particle size, μm	Particle density, kg/m3	Db, mm	$u_b$, m/s	$u_b^{\ast }$, m/s	$f_{r,c}$, Hz	$f_{r,c}^{\ast }$, Hz	$h_{1,c}$, mm	$h_{1,c}^{\ast }$, mm
Glass beads	150–212	2,500	17 ± 3	0.29 ± 0.04	0.29	5	5.05	43 ± 3	35
Glass beads	212–300	2,500	20 ± 3	0.31 ± 0.04	0.31	5	4.98	44 ± 4	41
Glass beads	400–600	2,500	20 ± 5	0.30 ± 0.06	0.31	5	5.17	41 ± 4	41
Ceramic beads	400–600	4,100	22 ± 5	0.32 ± 0.05	0.33	5	5.05	43 ± 3	45
Ceramic beads	400–600	6,000	23 ± 4	0.33 ± 0.05	0.34	5	4.88	46 ± 4	47

The symbols with and without * indicate the values obtained by theoretical models and experiments, respectively. $u_b^{\ast }$ is determined using Eq. 4, $f_{r,c}^{\ast }$ is determined using Eq. 2, and $h_{1,c}^{\ast }$ is determined using Eq. 6.