LANGMUIR-DERIVED MODEL FOR DIFFUSION-LIMITED AND REACTION-LIMITED ADSORPTION OF ORGANIC-COMPOUNDS ON FRACTAL AGGREGATES

Natural colloids, aerosols, and aggregates generated in wastewater tre atments have fractal geometries, and so not all the surface sites of t hese aggregates possess the same collision probability. II is this pro perty that modifies the classical Langmuir adsorption isotherm, since it describes the equilibrium of the rare of collisions that adhere wit h the rate of desorption. In this paper, the growth site probability d istribution is computed ?or aggregates with different fractal dimensio ns in the two- and three-dimensional models. These distributions are t hen used to find the adsorption isotherms depending on a model paramet er 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 adsorpti on isotherms can be fitted with the Freundlich isotherm for descriptio n purposes. When there is law affinity between adsorbate and matrix (r eaction-limited adsorption), linear adsorption isotherms are obtained; conversely, isotherms are less linear when adsorbate reactivity incre ases. Furthermore, the increase of adsorbate solubility led to lower p artition coefficients, in agreement with the results reported in the l iterature. Therefore, the isotherms obtained with the Langmuir-derived equation take into account the fractal geometry of aggregates and pro vide a good description of the linear and nonlinear isotherms of organ ic compounds in terms of their solubility, reactivity, and molecular s ize.