Development and validation of an adsorption kinetic model at solid-liquid interface using normalized Gudermannian function.

Abstract In this article, a brief outlook of different kinetic models employed in batch adsorption study has been discussed. As the adsorption kinetic modeling has so far been inadequately addressed in the literature, therefore the equilibrium kinetic profiles of adsorption study were portrayed into an innovative sigmoidal expression q t q e = 0.637 tan − 1 sinh 5.233 × t t e G n G , using the Gudermannian function with significant mathematical hypotheses. The kinetic data obtained from methylene blue and acridine orange dye adsorption studies using Abelmoschus esculentus seed powder were utilized to evaluate the adequacy of the proposed model. The extent of model compatibility was evaluated through six non-linear error functions represented as composite fractional error, residual root mean square error, Marquardt's percent standard deviation, average relative error, average percentage error and Chi-square error. This aforesaid three-parametric sigmoidal model was compared with pseudo-first-order, pseudo-second-order, intra-particle diffusion, Elovich, Bangham, modified-Freundlich and hyperbolic tangent model, which are known as the well-recognized kinetics. According to the comparison of different error functions and to the assessment of corrected Akaike information criterion, the developed model was ranked as the best fitting kinetic model illustrating the experimental data. It also demonstrated that the normalized Gudermannian kinetic equation has the ability to predict the equilibrium adsorption time at different initial dye concentrations, which can be exploited for configuring the large-scale industrial reactors. Graphical abstract Unlabelled Image Highlights • A three-parametric kinetic model was developed for batch adsorption at solid-liquid interface. • The normalized Gudermannian function was applied to describe the kinetic equilibrium data. • The proposed model can predict the exact equilibrium time of the adsorption process. • The model was employed to fit the experimental results for the adsorption of methylene blue and acridine orange dyes. • The feasibility of the kinetic model was verified using non-linear error functions and Akaike information criterion. [ABSTRACT FROM AUTHOR]