Liquid–solid adsorption processes interpreted by fractal-like kinetic models

The transport of an adsorbate molecule from the bulk of a fluid phase to the active centre of an adsorbent particle involves complex mechanisms. Mechanisms need to be described by accurate mathematical expressions for the proper design of a fluid–solid adsorption unit. Here we investigate adsorption from the liquid phase with a focus on interrelationships among pollutants and adsorbents characteristics, dynamic adsorption results, and fractal-like modelling of experimental data from the literature. Among all models, the fractal pseudo-first-order’s model was the most statistically accurate. The value of the hybrid fractional error function ranged between 3 × 10−4 and 1 × 10−2. This value was in general one order of magnitude lower than that obtained for a canonical pseudo-first-order model, which overestimate the values of the degree of surface coverage by 10–20%. The fractal model involves the presence of an instantaneous rate coefficient, which ranged between orders 10−3 and 1 min−1. Adsorbents showing different features have been analysed, for example with variations in particle size (order 100 μm), specific surface area (order 102 m2 g−1), and total pore volume (order 10−1 cm3 g−1). For short adsorption times, the instantaneous rate coefficient was positively affected by (1) decrease in particle size; (2) increase in specific surface area and total pore volume; (3) increase in specific mesopore volume; (4) increase in average pore size. The heterogeneity parameter of the fractal model influences the time decay rate of the former coefficient. This parameter ranged between 0.138 and 0.478, and it was higher when: (1) the pore space is more crowded by already adsorbed molecules; (2) a larger degree of surface chemical heterogeneity is determined; (3) the mean micropore size is smaller; (4) the specific volume of ultramicropores is larger; (5) the pore size distribution is more polydispersed.