The effect of bulk concentration on surfactant adsorption processes: The shift from diffusion-control to mixed kinetic diffusion control with bulk concentration

The surface tension relaxation at interfaces between surfactant solutions and immiscible fluids is calculated bg the rate that surfactant adsorbs in a two-step process: surfactant in the sublayer adsorbs, which, in turn, establishes a diffusive flux from the bulk. Therefore, both the adsorption and diffusion rates determine the behavior. These rates are commonly determined by minimizing the difference between experimental surface tension vs. time profiles and mass transfer model predictions. Usually, only a limited range of bulk concentrations C-0 is studied, and the profiles are found to he in agreement with a diffusion-control model, It is argued here that such apparent agreement is insufficient evidence to disregard the role of the adsorption/desorption kinetics in the adsorption process. In this paper, the concept of a shift in controlling mechanism from diffusion control at dilute concentration to mixed diffusion-kinetic control at more elevated bulk concentration is explored. This idea is illustrated theoretically for clean interface adsorption on a pendant bubble or drop using the Langmuir adsorption model in dimensionless form. It is further developed using the model constants for C(12)E(8).