You wish to build a parallel-plate reactor to continuously perfuse cells in a monolayer of the bottom plate. The reactor has a height of 250mm (h), a...

You wish to build a parallel-plate reactor to continuously perfuse cells in a monolayer of the bottom plate. The reactor has a height of 250mm (h), a width of 2.5cm (w) and a length of 4cm (l). The tubing that exits the reactor encounters an open area for equilibration to the oxygen in the surrounding air and is then fed through a pump that circulates the culture medium at a flow rate of 0.3ml/s. This tubing has an outer diameter of 3mm, a wall thickness of 0.8mm, and a total length of 40cm (from the exit of the chamber to the entrance).

(a) What is general definition of time constant? Why are time constants important in tissue engineering applications?

(b) Calculate the time constant for diffusion, reaction and convention (residence time) of oxygen for this system. You may assume Michaelis-Menton kinetics, with a Km = 6nmol/ml, and a maximum consumption rate of 76nm/s.ml of cells. Also assume that the diffusion coefficient of oxygen through medium at 37oC is 2 X 10-5 cm/s2.

(c) If the cells were to proliferate so that there were twice as many cells a before in the same reactor, how would the system be affected (how does this affect the time constants)?

(d) List two examples of experimental parameters that can be changed to improve the oxygen delivery to the cells in this system.