A full factorial design-based desirability function approach to investigate the transport of Ni²⁺, Co²⁺, Cr³⁺ and Zn²⁺ through polymer inclusion membranes

In the present study, the full factorial design methodology was used to investigate and optimize the operating conditions of a membrane process involving polymer inclusion membranes (PIMs), for the competitive removal of Ni2+, Co2+, Cr3+ and Zn2+ from aqueous solutions. The effects of three parameters: initial concentration of metals (X-1), extractant content (X-2) and membrane thickness (X-3) were investigated on the matter fluxes crossing the PIMs (Ji), the amount of metal ions fixed within them (Tf), and transferred through them (Tt). The study revealed that: (1) the selectivity order of metal ions crossing the synthesized PIMs is: Zn > Ni > Cr > Co, (2) the order of significance of the effects is: X-1 > X-2 > X-3, (3) X(1 )and X-2 have positive effect on J, Tf and Tt while X-3 has a negative effect on J and Tt, and (4) the estimated models for the responses fit the experimental data adequately (determination coefficient: R-2 = 84.70%-99.99%; standard deviation: SD = 0.0021 - 1.58). The desirability function-based optimization indicated that: J(max) and T-tmax are obtained for X-1max (200 ppm), X-2max (60% w/w) and X-3min (50 mu m), for a desirability value of 0.93 and 0.81, respectively, while T-fmax is obtained for X-1max, X-2max and X-3max (65 mu m), for a desirability value of 0.93.