DSM – Catching Gas with Droplets #SWI2006

At DSM one is interested in the development of packaging materials that are not or little permeable for certain gases. Think of the packaging of meat in a polymer sheet, that should keep the meat free from oxygen. The idea to realize this is to include in the sheet of packaging material droplets that absorb the penetrating gas via a chemical reaction. Gas molecules diffusing through the sheet will hopefully encounter such a droplet and be adsorbed. However, a saturation of the droplets will cause the effectiveness of the absorption process to decrease in time.

Question:
Develop a mathematical model for this diffusion-reaction process. Determine from this model the dependence of the effectiveness of the method on a. the density of the absorbing droplets b. the shape of the absorbing droplets.