Possible Existence of Convective Currents in Surfactant Bulk Solution in Experimental Pendant-Bubble Dynamic Surface Tension Measurements

Abstract

Traditionally, surfactant bulk solutions in which dynamic surface tension (DST) measurements are conducted using the pendant-bubble apparatus are assumed to be quiescent. Consequently, the transport of surfactant molecules in the bulk solution is often modeled as being purely diffusive when analyzing the experimental pendant-bubble DST data. In this Article, we analyze the experimental pendant-bubble DST data of the alkyl poly (ethylene oxide) nonionic surfactants, C12E4 and C12E6, and demonstrate that both surfactants exhibit "superdiffusive" adsorption kinetics behavior with characteristics that challenge the traditional assumption of a quiescent surfactant bulk solution. In other words, the observed superdiffusive adsorption behavior points to the possible existence of convection currents in the surfactant bulk solution. The analysis presented here involves the following steps: (1) constructing an adsorption kinetics model that corresponds to the fastest rate at which surfactant molecules adsorb onto the actual pendant-bubble surface from a quiescent solution, (2) predicting the DST behaviors of C12E4 and C12E6 at several surfactant bulk solution concentrations using the model constructed in step 1, and (3) comparing the predicted DST profiles with the experimental DST profiles. This comparison reveals systematic deviations for both C12E4 and C12E6 with the following characteristics: (a) the experimental DST profiles exhibit adsorption kinetics behavior, which is faster than the predicted fastest rate of surfactant adsorption from a quiescent surfactant bulk solution at time scales greater than 100 s, and (b) the experimental DST profiles and the predicted DST behaviors approach the same equilibrium surface tension values. Characteristic (b) indicates that the cause of the observed systematic deviations may be associated with the adsorption kinetics mechanism adopted in the model used rather than with the equilibrium behavior. Characteristic (a) indicates that the actual surfactant bulk solution in which the DST measurement was conducted, most likely, cannot be considered to be quiescent at time scales greater than 100 s. Accordingly, the observed superdiffusive adsorption behavior is interpreted as resulting from convection currents present in a nonquiescent surfactant bulk solution. Convection currents accelerate the surfactant adsorption process by increasing the rate of surfactant transport in the bulk solution. The systematic nature of the deviations observed between the predicted DST profiles and the experimental DST behavior for C12E4 and C12E6 suggests that the nonquiescent nature of the surfactant bulk solution may be intrinsic to the experimental pendant-bubble DST measurement approach. To validate this possibility, we identified generic features in the experimental DST data when DST measurements are conducted in a nonquiescent surfactant bulk solution, and the DST measurements are analyzed assuming that the surfactant bulk solution is quiescent. An examination of the DST literature reveals that these identified generic features are quite general and are observed in the experimental DST data of several other surfactants (decanol, nonanol, C10E8, C14E8, C12E8, and C10E4) measured using the pendant-bubble apparatus.