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Table 2 Summary of common overall mass transfer coefficient equation for bubble column

From: Mass transfer and flow characterization of novel algae-based nutrient removal system

Author Equation
Lewis (1924) [32] \({k}_{L}=\frac{{D}_{AB}}{{\updelta }_{\mathrm{L}}}\)
Higbie (1935) [25] \(\stackrel{-}{{k}_{L}}=2\sqrt{\frac{{D}_{V}}{\pi {t}_{T}}}=1.13\sqrt{\frac{{D}_{V}}{{t}_{T}}}\)
Danckwarts (1955) [17] \({k}_{L}={{(D}_{AB}s)}^{0.5}\)
Linek (2005) [33] \({k}_{L}=0.448{\left(\frac{P\rho }{V}\right)}^{0.25}{\left(\frac{{D}_{L}}{r}\right)}^{0.5}\)
Kawase and Moo Young (1991) [29] \({k}_{L}a=\frac{7CF\sqrt{{D}_{A}}{u}_{g}{\rho }_{L}^{0.85}\sqrt{g}}{{\mu }_{B}^{0.25}{\sigma }^{0.6}{d}_{c}^{0.17}}\)
Ferreira (2012) [20] \({k}_{L}a=3372\sqrt{\frac{{D}_{L}}{\pi }\sqrt{\frac{{u}_{G}^{1.87}g}{{\mu }_{l}{\mu }^{0.24}}}}\)
Calderbank (1958) [8] \({k}_{L}=0.422{N}_{\mathrm{SC}}^{-\frac{2}{3}}{\left(\frac{\Delta \rho {\mu }_{c}g}{{\rho }_{c}^{2}}\right)}^{1/3}\)
Levich (1962) [31] \({k}_{L}=\frac{{D}^{0.5}{\rho }^{0.5}}{{\sigma }^{0.5}{v}_{o}^{1.5}}\)
Godbole (1984) [21] \({k}_{L}=0.146{({j}_{g} }^{0.71}{)(v}^{-0.49})\)
Heijnen (1984) [24] \({k}_{L}a=0.32{j}_{g}^{0.7}\)
Kawase (1987) [28] \(\mathrm{Sh}=0.63*\frac{1}{\sqrt{\pi }}\sqrt{1.07}{\mathrm{Sc}}^\frac{1}{2}{\mathrm{Re}}^\frac{3}{4}{\mathrm{Fr}}^\frac{7}{60}{\mathrm{Bo}}^\frac{3}{5}\)
Nakanoh (1980) [37] \({k}_{L}=\frac{0.09{D}_{C}}{{d}_{\mathrm{pipe}}}{\mathrm{Sc}}^\frac{1}{2}{\mathrm{Bo}}^\frac{3}{4}{\mathrm{Ga}}^{0.39}\mathrm{Fr}\)