Understanding the Phenomenon of Copper Ions Release from Copper-Modified TFC Membranes: A Mathematical and Experimental Methodology Using Shrinking Core Model.

Type of metal and metal-oxide NPs added to modify Thin-Film Composites Reverse Osmosis Membranes (TFC-RO) can alter their anti-biofouling properties by changing the dissolution process. The development of a mathematical model can facilitate the selection of these NPs. This work consists of a mathematical and experimental methodology to understand copper-based NPs dissolution of three copper species incorporated into TFC-RO membranes: Cu-NPs, CuO-NPs and Cu-Oligomer complexes formed in situ during the polymerization process. Biocidal capacity of copper species into the membrane was evaluated using colony forming unit method (CFU) over E. coli. In addition, copper ion release kinetics for both NPs and modified membranes were determined. A model based on the shrinking core model (SCM) was validated and applied to determine the limiting rate step in the dissolution process and simulate the ion release kinetics. Fitted curves reached a good adjustment with the experimental data, demonstrating the SCM can be applied to predict ion release process for copper-based NPs in suspension and the modified membranes. All membranes reached similar inhibition rate >50%, however, differences in the dissolution level of copper-based NPs in membrane were noted, suggesting a dual-type effect that defined the copper toxicity into the membrane, associated to the dissolution capacity and ROS production.