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Exp Fluids (2004) 37:631–644
Due to an oversight the following errors were overlooked in Eq. 10 and Eq. 12 on page 633. The correct equations are shown below.
$$ \begin{array}{*{20}l} {{{\left\langle {{\left\langle {V_{{gj}} } \right\rangle }} \right\rangle }} \hfill} & {{ = {\sqrt 2 }{\left\{ {\frac{{{\left( {\Delta \rho g_{z} + M_{{F\infty }} } \right)}\sigma }} {{\rho ^{2}_{f} }}} \right\}}^{{1 \mathord{\left/ {\vphantom {1 4}} \right. \kern-\nulldelimiterspace} 4}} } \hfill} \\ {{} \hfill} & {{ \times \frac{{18.67{\left( {1 - {\left\langle {\alpha _{g} } \right\rangle }} \right)}^{2} {\left\{ {\frac{{\Delta \rho g_{z} {\left( {1 - {\left\langle {\alpha _{g} } \right\rangle }} \right)} + M_{F} }} {{\Delta \rho g_{z} + M_{{{\text{F}}\infty }} }}} \right\}}}} {{1 + 17.67{\left( {1 - {\left\langle {\alpha _{g} } \right\rangle }} \right)}^{{6 \mathord{\left/ {\vphantom {6 7}} \right. \kern-\nulldelimiterspace} 7}} {\left\{ {\frac{{\Delta \rho g_{z} {\left( {1 - {\left\langle {\alpha _{g} } \right\rangle }} \right)} + M_{F} }} {{\Delta \rho g_{z} + M_{{F\infty }} }}} \right\}}^{{3 \mathord{\left/ {\vphantom {3 7}} \right. \kern-\nulldelimiterspace} 7}} }}} \hfill} \\ \end{array} $$
(10)
$$ {\left\langle {{\left\langle {V_{{gj}} } \right\rangle }} \right\rangle } = {\sqrt 2 }{\left( {\frac{{M_{{F\infty }} \sigma }} {{\rho ^{2}_{f} }}} \right)}^{{1 \mathord{\left/ {\vphantom {1 4}} \right. \kern-\nulldelimiterspace} 4}} \times \frac{{18.67{\left( {1 - {\left\langle {\alpha _{g} } \right\rangle }} \right)}^{2} {\left( {\frac{{M_{F} }} {{M_{{F\infty }} }}} \right)}}} {{1 + 17.67{\left( {1 - {\left\langle {\alpha _{g} } \right\rangle }} \right)}^{{6 \mathord{\left/ {\vphantom {6 7}} \right. \kern-\nulldelimiterspace} 7}} {\left( {\frac{{M_{F} }} {{M_{{F\infty }} }}} \right)}^{{3 \mathord{\left/ {\vphantom {3 7}} \right. \kern-\nulldelimiterspace} 7}} }} $$
(12)
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The online version of the original article can be found at http://dx.doi.org/10.1007/s00348-004-0844-9
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Takamasa, T., Hazuku, T., Fukamachi, N. et al. Effect of gravity on axial development of bubbly flow at low liquid Reynolds number. Exp Fluids 38, 700 (2005). https://doi.org/10.1007/s00348-005-0964-x
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DOI: https://doi.org/10.1007/s00348-005-0964-x