Modeling of adsorption dynamics at air–liquid interfaces using statistical rate theory (SRT)

Abstract

A large number of natural and technological processes involve mass transfer at interfaces. Interfacial properties, e.g., adsorption, play a key role in such applications as wetting, foaming, coating, and stabilizing of liquid films. The mechanistic understanding of surface adsorption often assumes molecular diffusion in the bulk liquid and subsequent adsorption at the interface. Diffusion is well described by Fick's law, while adsorption kinetics is less understood and is commonly described using Langmuir-type empirical equations. In this study, a general theoretical model for adsorption kinetics/dynamics at the air–liquid interface is developed; in particular, a new kinetic equation based on the statistical rate theory (SRT) is derived. Similar to many reported kinetic equations, the new kinetic equation also involves a number of parameters, but all these parameters are theoretically obtainable. In the present model, the adsorption dynamics is governed by three dimensionless numbers: ψ (ratio of adsorption thickness to diffusion length), λ (ratio of square of the adsorption thickness to the ratio of adsorption to desorption rate constant), and N k (ratio of the adsorption rate constant to the product of diffusion coefficient and bulk concentration). Numerical simulations for surface adsorption using the proposed model are carried out and verified. The difference in surface adsorption between the general and the diffusion controlled model is estimated and presented graphically as contours of deviation. Three different regions of adsorption dynamics are identified: diffusion controlled (deviation less than 10%), mixed diffusion and transfer controlled (deviation in the range of 10–90%), and transfer controlled (deviation more than 90%). These three different modes predominantly depend on the value of N k . The corresponding ranges of N k for the studied values of ψ ( 10 −2 < ψ < 10 4 ) and λ ( 10 −12 < λ < 10 8 ) are 10 1 < N k < 10 4 for the diffusion controlled, 10 −3 < N k < 10 1 for the mixed diffusion and transfer controlled, and 10 −4 < N k < 10 −3 for the transfer controlled, respectively. The study also shows that lower values of ψ and λ are favorable for maximum surface adsorption and consequently surface tension reduction.