The Southern California Florists Cooperative has contracted with us to design a system for control of insects in the event of sudden infestation in a greenhouse. The insecticide is available in the form of a liquid solution, which can be delivered with an initial concentration of the active agent of 5.6 X 10-4 mol/cm3. Our plan is to encapsulate this solution in hollow polysulfone fibers, with outside diameters of 310 micrometer and wall thicknesses of 20 micrometer.

The partition coefficient of the active agent between the solution, or within air, and the fiber wall is defined as cA(wall)/cA(mixture) = D, where D = 5 X 10-4. The diffusion coefficient of the active agent in solution is 10-5 cm2/s at 25 C, and the diffusion coefficient in the fiber wall is 10-7 cm2/s at 25 C. The active agent has a molecular weight of 100 g/mol. The air in the greenhouse is well-circulated by overhead fans and is kept at 25 C. The standard greenhouse contains 20,000 ft3 of air, and there is negligible exchange of air with the external environment. (The molecular weight of air is 29 g/mol.)

Good insect control requires an air concentration of the insecticide of at least 30 parts per million by weight (ppmw). The customer wants this level to be achieved within one day after activation of the product. Invoking a quasi-steady-state approximation, what is the minimum total volume of the liquid solution containing the active agent, possibly contained within several fibers, that must be employed for each infestation?