Modeling adsorption and reaction of contaminants by nanoparticle impregnated polymeric fibers

Fibers impregnated with nanoparticles have been used to remove contaminants present in water. We would like to develop mathematical models to incorporate water flow against such fibers in a small, packed cartridge, simultaneously allowing adsorption and reaction of contaminants by the nanoparticle surface. One would like to understand the optimum nanoparticle loading on fiber surface, as there may be issues of large pressure drop at high particle loading; the latter being desirable for rapid purification of water from the contaminants.