A study on the method of short-time approximation–curvature effect

The short-time approximation method is known as a simple way to determine the adsorption mechanisms and to estimate the surfactant diffusivity. Three assumptions are needed in order to obtain the linear short-time approximation relationship between γ(t) and t^1/2 to fit the experimental dynamic surface tension data: the surfactant backward diffusion process is negligible, the forward adsorption contributed from the spherical geometry is much smaller than that to a planar surface, and surfactant follows Henry's equation of state. Recently, a general criterion, in terms of adsorption time and surface pressures for short-time approximation applicability on solution systems assuming a planar gas–liquid interface, has been explored by Casandra et al. (2015). How are the criteria applicable for spherical surfaces? Surface tension relaxes faster and reaches its equilibrium earlier for surfactant molecules mass-transporting onto a spherical interface than onto a planar interface due to the geometrical effect. Ignoring this geometrical effect may cause a serious error in estimating diffusivity and in determining the adsorption mechanism when applying the short-time approximation technique. In this study, a theoretical numerical simulation of the short-time approximation method was conducted, and the general criteria for accurately utilizing the short-time approximation were investigated.