A perfusion bioreactor consists of a layer of cells 1.5 mm thick that is supported between two very thin macroporous titanium meshes. A nutrient medium flows through the bioreactor in the direction of...

A perfusion bioreactor consists of a layer of cells 1.5 mm thick that is supported between two very thin macroporous titanium meshes. A nutrient medium flows through the bioreactor in the direction of the cell layer thickness. The cell volume fraction is 0.35 and the cells consume oxygen at a rate of 21 μM s⁻¹. The effective diffusivity of oxygen within the layer of cells has been estimated to be 2.05 × 10⁻⁵
cm²
s⁻¹. The oxygen concentration in the fluid that enters this bioreactor is equal to 200 μM. The exiting oxygen concentration of the fluid leaving this bioreactor cannot be less than 25 μM. Estimate the flow rate of the nutrient medium in cm3 min−1. The cross-sectional area of the cell layer normal to the flow of the nutrient medium is 64 cm2.