Theoretical model in cylindrical coordinates to describe dynamic interfacial tension determination with spinning drop tensiometry

Highlights: • A theoretical model in cylindrical coordinates is presented. • The equation predicts that DIFT of surfactants is a function of time. • The exponential decay is observed in the calculated theoretical curves. • The experimental data are in agreement with the calculated theoretical curves. • The interphase diffusion coefficient K of three surfactants were calculated. -- Abstract: In this paper, a theoretical model in cylindrical coordinates is presented to describe the behavior of dynamic interfacial tension (DIFT) between the oil and water phases. The equation of DIFT is derived from mathematical derivation combined with Gibbs equation. The DIFTs of three sodium alkylbenzene sulfonates (p-S14-5, p-S16-5 and p-S18-5) were studied by the spinning drop technique. It is a function of time and exponential decay is observed. The experimental data are in agreement with the calculated theoretical curves. Meanwhile, the equation predicts that the computable variable $\left((\text{r}/2·\text{Ln}\left(1-exp\left(-\frac{\gamma -{\gamma }_{\infty }}{R·T·\Gamma }\right)\right)\right)$ should be linear with interphase diffusion time t and its slope depends on the interphase diffusion coefficient K if the assumptions involved in the derivation are valid. The average values and range of the interphase diffusion coefficient K of three surfactants were calculated by applying the slopes from the linear portions.