Example $1.$ Mass Transfer from Air

Bubbles in Fermentation

Calculate the maximum rate of absorption of $O_2$ in a fermenter from air

bubbles at $1$atm pressure having diameters of $100m$ at $37C$ into water

having a zero concentration of dissolved $O_2.$ The solubility of $O_2$ from air in

water at $37C$ is $2\mathrm{.}26{10}^{-7}$gmol$\frac{O_2}{c}{m}^3$ liquid or $2\mathrm{.}26{10}^{-4}$kgmol$\frac{O_2}{m^3}.$

The diffusivity of $O_2$ in water at $37C$ is $3\mathrm{.}25{10}^{-9}\frac{m^2}{s}.$ Agitation is used to

produce the air bubbles. ${}_c=994k\frac{g}{m^3},{}_c=6\mathrm{.}947{\mathrm{.}10}^{-4}$ Pa$.$s$,{}_p=1\mathrm{.}13k\frac{g}{m^3}$

$($air$)$