Dissolved Oxygen (DO) is an important substrate in aerobic fermentations. Oxygen molecules must overcome a series of transport resistances before being utilised by the cells.

Pauline Doran (Bioprocess Engineering Principles – 2013) describes eight mass transfer steps involved in transport of oxygen from the interior of the bubbles to the site of intracellular reaction:

1. Transfer from the interior of the bubble to the gas – liquid interface
2. Movement across the gas – liquid interface
3. Diffusion through the relatively stagnant liquid film surrounding the bubble
4. Transport through the bulk liquid
5. Diffusion through the relatively stagnant liquid film surrounding the cells
6. Movement across the liquid – cell interface
7. If the cells are in a floc, clump, or solid particle, diffusion though the solid to the individual cell
8. Transport through the cytoplasm to the site of reaction

The relative magnitudes of the various mass transfer resistances depend on the composition and rheological properties of the liquid, the type and mixing intensity, the size of the bubbles, the size of cell clumps, interfacial adsorption characteristics and a number of other factors.

Summarising the above:

1. The major resistance to oxygen transfer is the liquid film surrounding the gas bubbles
2. The most important property of air bubbles is their size

For optimum growth it is therefore important to maintain the dO₂ above this critical level by efficiently sparging (gas injection, bubbling gas through) the fermenter with air or mixed additional with pure oxygen. Of course, to be effective, the mass transfer rate from the gas bubbles to the liquid broth must equal or exceed the rate at which growing cells, bacteria take up the oxygen. In general terms the air or mixed gas volume required is ranging 1-2 litre/working volume/minute.

 The rate of transport is given by:

where k_L is the oxygen transport coefficient (cm/h), a is the gas-liquid interfacial area (cm²/cm³), k_La the volumetric oxygen transfer coefficient (h^-1), C* is saturated dO₂ concentration (mg/l) (approx. 8 mg/l at 25 deg. C and 1 atm.), C_L is the actual dO₂ concentration in the liquid (mg/l), and NO₂ is the rate of oxygen transfer (mg O₂/ l/h).

k_La values depends strongly on the  solution composition. Various solutes has a significant impact on the rate of oxygen transfer. During fermentation the coalescence properties vary and k_La can also be expected to vary accordingly.