Diffusion-controlled adsorption dynamics of surface-active agents at fluid/fluid interfaces is described by the Ward Tordai equation which must be solved numerically when a nonlinear adsorption isotherm is involved [1]. These calculations are generally performed when knowing the composition of the surfactant solution and the adsorption behavior of its individual components (in terms of adsorption isotherm and equation of state as well as the associated parameters such as surface excess coverage and adsorption coefficient). However, for naturally occurring mixtures of surface active molecules (such as asphaltenes in crude oils [2], Arabic gum in food products [3], proteins in human biological fluids [4]) such information is often not available. This can also be the case for synthetic surfactants coming as mixtures of oligomers such as Tritons [5]. To alleviate this limitation, it is here reported a computational method for extracting the individual properties of pseudo-components within a surfactant mixture from its dynamic interfacial tension. The number of pseudo-components (
n) and their adsorption isotherm/equation of state are first chosen. The pseudo-components’ properties (concentration, adsorption coefficient, surface excess coverage) are then initialized at random values to solve numerically the
n corresponding Ward Tordai equations. The resulting evolution of surface coverage is subsequently converted into a dynamic interfacial tension curve, which can be compared to the experimental one by means of a weighted Sum of Squared Error (WSSE) accounting for the exponential decay form of most available data. During an iterative process using the quasi-Newton Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm, the pseudo-components’ properties can be optimized to minimize the WSSE. This method has been tested with the experimental dataset from Freer and Radke [6]. A ternary mixture model with 7 parameters (3 concentrations, 3 adsorption coefficients and 1 surface excess coverage) proved enough to capture the dynamic interfacial tension from a few seconds up to 24 hours adsorption. The sum of the pseudo-components’ concentrations is found very close to the nominal concentration of the asphaltenes solution used in experiments. Most asphaltenes appear to have a low surface activity while a tiny fraction (<1%) appears to have an extremely high one, in line with previous results obtained by fractionation or washout experiments. The accuracy of the method can further be checked by using the same calculations to predict the dilatational rheology of the same interface after 24 hours. The result compares very well with corresponding experiments over 7 frequency decades.
[1] Miller, R. (1981). Colloid and Polymer Science, 259(11), 1124-1128.
[2] Liu, F., Darjani, S., Akhmetkhanova, N., Maldarelli, C., Banerjee, S., & Pauchard, V. (2017) Langmuir, 33(8), 1927–1942.
[3] Castellani, O., Guibert, D., Al-Assaf, S., Axelos, M., Phillips, G. O., & Anton, M. (2010). Food hydrocolloids, 24(2), 193-199.
[4] Trukhin, D. V., Sinyachenko, O. V., Kazakov, V. N., Lylyk, S. V., Belokon, A. M., & Pison, U. (2001). Colloids and Surfaces B: Biointerfaces, 21(1), 231-238.
[5] Fainerman, V. B., Lylyk, S. V., Aksenenko, E. V., Makievski, A. V., Petkov, J. T., Yorke, J., & Miller, R. (2009). Colloids and Surfaces A: Physicochemical and Engineering Aspects, 334(1), 1-7.
[6] Freer, E. M., & Radke, C. J. (2004). Journal of Adhesion, 80(6), 481-496.
