Gas absorption from rising bubbles for creeping flow

Input(s)

$D_{A B}$ :Diffusivity $\left(\mathrm{cm}^{2} / \mathrm{s}\right)$

$v_{t}$: Terminal Velocity $(\mathrm{cm} / \mathrm{s})$

D: Bubble Diameter $(\mathrm{cm})\left(\boldsymbol{N}_{\boldsymbol{A}}\right)$

$\boldsymbol{c}_{\boldsymbol{A} \boldsymbol{0}}$: Solubility $\left(\mathrm{g} / \mathrm{cm}^{3}\right)$

Output(s)

$N_{A}$: Average Molar Absorption Rate $\left(\mathrm{g} \mathrm{mol} / \mathrm{cm}^{2} \mathrm{~s}\right)$

Formula(s)

$$ \mathrm{N}_{\mathrm{A}}=\sqrt{\left(\frac{4 * \mathrm{D}_{\mathrm{AB}} * \mathrm{v}_{\mathrm{t}}}{3 * \pi * \mathrm{D}}\right)} * \mathrm{c}_{\mathrm{A} 0} $$

Reference(s)

Bird, R.B., Stewart, W.E. and Lightfoot, E.N. (2002). Transport Phenomena (Second Ed.). John Wiley \& Sons, Chapter: 18, Page: 561.