1. The oxygen transfer process
The oxygen transfer model
Oxygen transfer coefficient (kL) and interfacial area (a)
Oxygen concentration at the gas-liquid interface(Co*)

2. The oxygen transfer process

3. The oxygen transfer model
CO is the concentration of oxygen dissolved in the bulk liquid kL is the mass transfer coefficient for the bubble boundary layer a is the interfacial area per unit volume CO* is the concentration of oxygen in the bubble boundary layer.

4. Oxygen transfer coefficient (kL) and interfacial area (a)
Because it not possible to accurately measure the total interfacial area of the gas bubbles (a) and kL.
The kL a represents the oxygen transfer rate per unit volume.

5. Oxygen concentration at the gas-liquid interface(Co*)
There is no probe small enough to directly measure.
the value of Co* can be approximated by indirect methods.

6. transfer coefficient (kL)
The mass transfer coefficient (kL) represents the rate at which oxygen molecules move through the boundary layer to the bulk liquid.
The value of kL can be increased by
reducing the size of the boundary layer
increasing the rate at which molecules travel through the boundary layer

7. previous chapter
the size of the boundary layer is determined by the level of mixing.
the diffusivity of the molecule through the boundary layer is determined by
Medium viscosity
Temperature

8. Oxygen uptake Oxygen as a growth limiting nutrient
Steady state analysis
Critical Oxygen Concentration
Integrating the oxygen uptake and oxygen transfer equations

9. Oxygen as a growth limiting nutrient
Monod model
The growth limiting substrate may be the carbon and energy source or it may be a nutrient such as a nitrogen compound.

10. In many fermentation systems, oxygen is often the growth limiting substrate.
The following figure shows a typical Monod relationship.