Alpha Geek
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A novel material based on the biopolymer polyglucosamine is cast into a homogeneous gel bead. The amine group on the biopolymer has a high affinity for transition metal ions at parts-per-million concentrations. When water containing metal ions contacts the gel, the metal ions selectively partition into the gel at the surface, and then diffuse through the gel. In essence, the gel acts as a second phase that extracts the metal ions from solution and concentrates them within the bead. Consequently, this material can be used to selectively remove toxic transition metal ions from wastewater. Although the real situation is somewhat more complicated, assume as a limiting case that the uptake rate of the metal ions is limited by the passive molecular diffusion of the metal ions through the gel. At relatively low metal ion concentrations in water below 1.0 mol/m3, the partition constant is defined by the relationship
where 
 is the molar concentration of the metal ion within the gel phase at the surface, cAs is the molar concentration of the metal in the aqueous phase at the surface, and K is a dimensionless partition constant, which is dependent on the concentration of biopolymer within the gel. In the present process, the bead diameter is 0.5 cm, and the biopolymer concentration within the gel sets K equal to 150. How long will it take for the cadmium concentration at the center of the gel bead to reach 12 mol/m3 if wastewater containing a constant concentration of 0.1 mol/m3 cadmium (11.2 ppm) rapidly flows over the gel bead? The diffusion coefficient of cadmium within the gel is approximately 2 × 10-6 cm2/s.
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