A novel metal ion adsorbent material based on the bio polymer poly glucosamine is cast into a gel bead. The amine groups on the bio polymer have a high affinity for transition metal ions at parts-per-million (mg/L) concentrations. When water containing metal ions contacts the gel, the metal ions selectively partition into the gel and then diffuse through the gel, which extracts the metal ions from solution and concentrates them within the bead. 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 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 linear relationship c'_A = Kc_As, where c'_A is the molar concentration of the metal ion within the gel phase at surface (r = R), c_AS is the molar concentration of the metal in the aqueous phase surrounding the surface, and K is partition constant, which is dependent on the amine concentration within the gel. In the present process, the bead diameter is 0.5 cm, and the amine concentration within the gel sets K equal to 150 m³ aqueous phase/m³ biopolymer phase. How long will it take for the cadmium concentration at the center of the gel bead to reach 12.0 mol/m³ if wastewater containing a constant concentration of 0.1 mol/m³ cadmium (11.2 mg/L) rapidly flows over the gel bead? The effective diffusion coefficient of cadmium within the gel, accounting for the absorption process, is approximately 2.0 × 10^-8 cm²/s.