Adsorption has become a competitive method in the field of wastewater and air treatment. Adsorption kinetics is one of the main factors that must be understood before the applicability of any adsorbent. In every adsorption process, linear or non-linear analysis of the kinetics is applied. The goodness of fit index (coefficient of correlation or sum of squares) is applied to access the best model. The usage of linear or non-linear from of the adsorption kinetics has an impact on the distribution of error function. Almost in every adsorption study, linear forms have been used to conclude the best kinetic model that influence the adsorption mechanism—which might be an error. Therefore, this review highlights the mistakes in the usage of linear and non-linear models. The applicability of the adsorption kinetics in wastewater treatment is also illuminated.

The use of adsorption using nanomaterials has become a very competitive method for removal of hazardous materials from wastewater. With increasing consumption of fossil fuels and development of energy storage systems, the levels of vanadium pollution are expected to increase. Utilizing natural shale and coal waste as adsorbents, batch adsorption, isotherms, and kinetics of vanadium was studied. The adsorption characteristics of shale and coal waste were studied using Fourier Transform Infrared spectroscope and Scanning Electron Microscopy. The effect of pH, the amount of adsorbent, vanadium concentration, temperature, and contact time between adsorbate and adsorbents were also studied to obtain optimum conditions for maximum adsorption of vanadium. The Fourier Transform Infrared results show little distortion in the vibration of bands, and hence the surface properties remain unchanged for both sorbents after adsorption. The adsorption kinetics are best described by pseudo-second order, while Langmuir model fits the adsorption isotherm for both adsorbents. Maximum sorption capacity is 67.57 mg/g for shale while that of coal is 59.88 mg/g at 298 K and pH 3. For both adsorbents, the adsorption process is spontaneous, endothermic, and chemisorption in nature. Both adsorbents can effectively be recycled twice.

This study examines the adsorption potential of activated carbons for vanadium (V) removal from aqueous solution. Activated carbons were produced via chemical activation of waste treatment sludge from the starch industry. Specific surface area and pore sizes of waste sludge samples were determined through chemical activation and pyrolysis. Experimental data indicated that sludge samples had micropore structure and specific surface area of up to 1196 m²/g. First-order and second-order models were applied to determine adsorption kinetics. Freundlich, Langmuir, and Dubinin–Radushkevich isotherms were used to analyze equilibrium data of adsorption. Equilibrium adsorption data showed the best fit to the Freundlich isotherm. Adsorption of vanadium (V) follows second-order kinetic models. Maximum adsorption was observed at pH 4.0. Langmuir adsorption capacity was found to be 37.17 mg/g. The results of the study indicated that activated carbon obtained from industrial sewage sludge was effective in removing vanadium from aqueous solutions, which creates a significant advantage for treatment of industrial wastewaters and management of solid wastes.