Calculate the maximum absorption rate of oxygen from air bubbles in a fermenter with a

pressure of $1$atm and $100m$ diameter into water at $37C.$ The initial dissolved oxygen in

water is denoted as $O.$ The solubility of oxygen in water at $37C$ is $2\mathrm{.}26{10}^{-7}$gmol $O_{2}c{m}^3.$

The diffusion coefficient of oxygen in water at $37C$ is $3\mathrm{.}25{10}^{-9}\frac{m^2}{s}.$ Assume the mass

transfer resistance from the inner surface of the bubble to the outside is negligible.

$k_L=2\frac{D_{AB}}{D}+0,31S{c}^{-\frac{2}{3}}(u_{c}gxP{c}^2{)}^{\frac{1}{3}}$

$D$ : is the diameter of the gas bubble $($m$),$

$u_c$ : is the viscosity of the solution $($Pa$.$s$),$

$g$ : is the acceleration due to gravity,

Sc: is the Schmidt number,

Pc: is the density of the continuous phase,

$Pp$ : is the density of the gas bubble $(1\mathrm{.}13\frac{kg}{m^3})$

$=P_c-P_p,>0$