A study on the asymptotic approximation for surfactant adsorption onto a spherical air-water interface

The asymptotic approximation equation was derived as a simple means for determining the adsorption mechanism and estimating surfactant diffusivity for surfactant adsorption onto a clean, spherical air-water interface (Makievski et al., 1999). However, the applicability of this approximation is yet to be examined. In this study, a theoretical simulation was conducted to better understand its applicability and validity. The diffusion-controlled adsorption of a nonionic surfactant onto a clean spherical interface (with radius = 0.03, 0.1, 0.5, and & INFIN; cm) was considered, and theoretical dynamic surface tension (gamma) profiles were generated using the Langmuir adsorption isotherm. The initial region of gamma(t(1/2)) profiles was best-fitted with asymptotic approximation with only one unknown parameter, the surfactant diffusivity. The initial region of the gamma(t(1/2)) profiles could be well-described by the asymptotic approximation (a parabolic equation), but a notable deviation was observed on the diffusivity obtained from the fitting. This deviation was dependent on the bulk concentration and the duration of the initial region fitted; whilst being only slightly dependent on bubble radius. Although the results demonstrated the viability of this approximation, there existed a possibility of obtaining multiple values of diffusivity by choosing different initial regions of a gamma(t(1/2)) profile.