Modeling of mass transfer controlled adsorption rate based on the Langmuir adsorption isotherm

Adsorption techniques are extensively used in bulk separations, purifications, and physiochemical parameter determinations. Generally, the adsorption models are described for equilibrium conditions. This study investigates the development of a mathematical model which describes the rate of adsorption under the conditions when the dynamic mass transfer is the controlling step. The underlying assumption is that the equilibrium isotherms can be used to describe the adsorption phenomena. A mathematical model for the external mass transfer controlled adsorption rate based on the Langmuir adsorption isotherm was developed and validated using data reported in literature using different adsorbents and adsorbates. In addition, using Freundlich adsorption isotherm, mathematical models for zero, one-half, and first-order were obtained. The various relevant parameters, namely the adsorption capacity, the adsorption energy, and the mass transfer coefficients were evaluated and the extension of the model to energetically heterogeneous surfaces is discussed. In addition, the results obtained from the Langmuir isotherm-based model were compared against the results derived from the mass transfer controlled rate equation based on the Freundlich isotherm.