Criterion

Homogeneous

Bubbling

Reference

For estimation of fluidization state

$F{r}_{mf}=\frac{u_{mf}^2}{g{d}_p}$

Fr_mf < 0.13

Fr_mf > 1.3

Wilhelm and Kwauk [2]

$R=F{r}_{mf}R{e}_{mf}\left(\frac{{\rho }_p-{\rho }_f}{{\rho }_f}\right)\left(\frac{L_{mf}}{D_c}\right)$

R < 100

R > 100

Romero and Johanson [3]

$N_{tr}=\frac{Re}{F{r}^{0.5}}\left(\frac{{\rho }_p-{\rho }_f}{{\rho }_f}\right)$

N_tr < C₁

depending on ε and ε_mf

N_tr > C₁

Verloop and Heertjes [4]

$N_f=A{r}^m{\left(\frac{{\rho }_a}{{\rho }_f}\right)}^{0.5}$

ρ_a: average density of particulate phase

N_f < C₂

m and C₂ depend on range of operation

N_f > C₂

Doichev et al. [5]

$U_e=\frac{1}{F{r}_t^{0.5}}{\left(\frac{{\rho }_p-{\rho }_f}{{\rho }_p}\right)}^{0.5}$

$U_{\epsilon }=0.56n{\left(1-{\epsilon }_b\right)}^{0.5}{\epsilon }_b^{n-1}$

$F{r}_t=\frac{u_t}{\sqrt{g{d}_p}}$

U_e < U_e

U_e > U_e

Foscolo and Gibilaro [6]

$D_n=\left(\frac{Ar}{R{e}_{mf}}\right)\left(\frac{{\rho }_p-{\rho }_f}{{\rho }_f}\right)$

D_n < 10⁴

D_n > 10⁶

Liu et al. [7]

$F_G^{*}=\frac{Ar}{R{e}^2{\rho }^{*}}$

$F_G^{*}>11.3$

$F_G^{*}<11.3$

Kogane et al. [11]

For estimation of minimum bubbling fluidization velocity

$u_{mb}=100d_p$

u₀ < u_mb

u₀ > u_mb

Geldart [1]

$u_{mb}=\frac{2.07d_p{\rho }_f^{0.06}}{{\mu }_f^{0.347}}\exp \left(0.716F_{45}\right)$

F₄₅: mass fraction of particles having a diameter less than 45 μm

u₀ < u_mb

u₀ > u_mb

Abrahamsen and Geldart [8]

$R{e}_{mb}=0.263{\rho }^{\ast -0.553}A{r}^{0.612}$

Re < Re_mb

Re > Re_mb

Kuwagi et al. [9]

$R{e}_{mb}=0.297{\rho }^{\ast -0.5}A{r}^{0.5}$

Re < Re_mb

Re > Re_mb

Kogane et al. [11]