Comparative mathematical modelling of a green approach for bioaccumulation of cobalt from wastewater

Cobalt is an essential element, but its wide use in industry generates important environmental and biological problems. The present study explores theoretical and empirical models of a green process for cobalt {Co²⁺} bioaccumulation from aqueous solutions. Two Gram-positive Bacillus subtilis species, strains CECT 4522 and LMM (the latter a former laboratory isolate from wastewater samples, which was phylogenetically characterized for the present work), were selected among others as the best Co²⁺ accumulation systems. Mathematical models representing kinetic and steady-state conditions for discrete and large amounts of bacterial biomass were expanded. In this way, it was possible to theoretically calculate the amount of Co²⁺ retained on the outer cell wall layer and incorporated inside the cell at any time. Theoretical and empirical hyperbolic-type models were suitable to fit the experimental bioaccumulation data for discrete amounts of bacteria biomass. In addition, kinetic relationships between the amount of Co²⁺ accumulated and the time before (or after) reaching steady state were established for large amounts of bacterial biomass. Other kinetic approaches were also satisfactorily tested. The two Gram-positive bacteria assayed are promising agents for developing heavy metal removal systems from industrial waste.