Langmuir-derived model for diffusion- and reaction-limited adsorption of organic compounds on fractal aggregates

Natural colloids, aerosols, and aggregates generated in wastewater treatments have fractal geometries, and so not all the surface sites of these aggregates possess the same collision probability. II is this property that modifies the classical Langmuir adsorption isotherm, since it describes the equilibrium of the rare of collisions that adhere with the rate of desorption. In this paper, the growth site probability distribution is computed ?or aggregates with different fractal dimensions in the two- and three-dimensional models. These distributions are then used to find the adsorption isotherms depending on a model parameter eta. This parameter is related to the reactivity of the adsorbate, and its relationship to solubility and molecular size has tentatively been proposed and studied. The low concentration range of the adsorption isotherms can be fitted with the Freundlich isotherm for description purposes. When there is law affinity between adsorbate and matrix (reaction-limited adsorption), linear adsorption isotherms are obtained; conversely, isotherms are less linear when adsorbate reactivity increases. Furthermore, the increase of adsorbate solubility led to lower partition coefficients, in agreement with the results reported in the literature. Therefore, the isotherms obtained with the Langmuir-derived equation take into account the fractal geometry of aggregates and provide a good description of the linear and nonlinear isotherms of organic compounds in terms of their solubility, reactivity, and molecular size.