Mathematical modeling of heavy metal ions (Cd2+, Zn2+ and Pb2+) biosorption by chemically modified short hemp fibers

Biosorption, an innovative and low-cost effective method for removal of heavy metal ions from wastewaters, primarily depends on the diffusion of metal ions through the porous structure of sorbent and the resistance effects arise as the result of electrostatic repulsive interactions between ions within the sorbent. Herein, the biosorption of heavy metal ions (Pb2+, Cd2+ and Zn2+) from aqueous solution by lignocellulosic material (chemically modified hemp fibers) was investigated, in order to develop a mathematical model that would describe the phenomenon of different ions transport through porous fiber matrices. Obtained results show that the biosorption process is very fast at the beginning and mainly determined by diffusion of the ions through the porous fiber structure. However, over a period of time the biosorption slows down due to the increase of the resistance to the further transport of metal ions through the fibers (i.e. the electrostatic repulsive interactions between ions into the fibers increase with the increase of the ion concentration in the fibers). The effective diffusion coefficient of metal ions through the fibers, the profile of heavy metal ion concentration in the fibers and the effectiveness of sorption were determined by a mathematical model based on the second Fick's low. Proposed mathematical model is used to optimize the biosorption of heavy metal ions by connecting the model parameters with the fiber performances