Valorisation of banana peel waste for copper (II) and chromium (VI) biosorption from aqueous solution: classical and fractal-like kinetics and isotherms model analysis

Heavy metal contamination of aquatic systems poses significant environmental and public health risks, necessitating cost-effective remediation strategies. However, mechanistic understanding of metal uptake on heterogeneous bioolymeric surfaces remains limited. This study investigates the biosorption of chromium(VI) (Cr 6+ ) and copper(II) (Cu 2+ ) onto banana peel (BP)-derived biosorbent within a circular-economy framework. Batch biosorption experiments were conducted across a range of initial metal concentrations using BP-derived biosorbent. Classical and fractal-like pseudo-first-order (PFO) kinetic models, alongside Langmuir, Freundlich, and Langmuir-Freundlich isotherm models, were applied to experimental data to elucidate rate mechanisms and surface heterogeneity effects. PFO kinetics yielded strong fits for both metals (R 2 = 0.9930, Cr 6+ ; R 2 = 0.9776, Cu 2 + ; χ 2 < 0.1), with equilibrium adsorption capacities of 2.5664 mg/g and 12.053 mg/g, respectively. Fractal-like PFO models further improved predictions (R 2 = 0.9960, Cr 6+ ), with heterogeneity parameters h = 0.8483 (Cr 6+ ) and h = 0.1401 (Cu 2+ ), confirming diffusion-controlled pathways. The Langmuir-Freundlich model achieved the best overall isotherm fit (R 2 = 0.9817, Cr 6+ ; R 2 = 0.9212, Cu 2+ ), with Langmuir monolayer capacities of 11.3853 mg/g (Cr 6+ ) and 13.5136 mg/g (Cu 2+ ). The Freundlich parameter n F < 1 confirmed favourable, heterogeneous adsorption for both systems. The contrasting h values reveal mechanistically distinct sorption pathways for Cr 6+ and Cu 2+ on the heterogeneous BP surface. Integrating fractal kinetics with hybrid isotherm models provides deeper mechanistic insight than classical approaches alone, confirming BP waste as a promising, low-cost biosorbent for heavy-metal remediation.