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 thes...

Coassembly Kinetics of Graphene Oxide and Block Copolymers at the Water/Oil Interface

“…This apparent “superdiffusivity” is a result of a convective flow. Such flow can be induced at the initial time of the drop formation. , The experimental difficulties to quantitatively analyze data from the pendant drop tensiometry have been pointed out by other researchers. , For these reasons, fitting the data using eq can be misleading.…”

“…28,29 The experimental difficulties to quantitatively analyze data from the pendant drop tensiometry have been pointed out by other researchers. 29,30 For these reasons, fitting the data using eq 3 can be misleading.…”

An axisymmetric model for the analysis of dynamic surface tension

“…Consequently, the observed systematic deviations may not be associated with the equilibrium surfactant adsorption models. Blankschtein and coworkers 29 have showed kinetics of surfactant adsorption to be faster than the predicted faster rate of surfactant adsorption from a quiescent solution at time scales greater than 100 s. In agreement with Blankschtein proposal, 29 this nding suggests that the actual surfactant bulk solution, in which the pendantbubble dynamic surface tension measurements were conducted, cannot be considered to be quiescent at time scales greater than 100 s, suggesting the possible existence of convective currents operating at time scales greater than 100 s in the surfactant bulk solution.…”

Self-Pinning on a Liquid Surface

“…The width l B is the only almost-free parameter of the model, for which we assume physically sound values around the characteristic adsorption length Γ m K L ≃0.23 mm. ,, Equal to Γ m K L for the smallest drop, l B is observed to increase linearly with t 1 and V 0 (to reach 0.4 mm for the biggest drop, see SI). This correlation makes sense if we consider that the depletion of surfactant in the aqueous solution close to the oil/water interface increases with time.…”

“…Particularly hard to grasp is the surfactant dragging induced by oil dissolution, which counterbalances the diffusion-controlled adsorption and delays it by a time t 1 . Rather than solving the fully coupled transport and transfer equations, we assume here, for simplicity, that the subsurface CTAB concentration in water, C S ( t ), obeys a first-order process: − for times greater than t 1 , for which a linear scaling with the initial drop volume V 0 according to t 1 / V 0 ≈ constant was experimentally found. In this equation, C S 0 is the value of C S ( t ) between t = 0 and t 1 and corresponds to the initial value γ o/w (0), C CAC is the surfactant aggregation concentration in the presence of dichloromethane, C CAC = 0.1 mmol L –1 , and τ S ≈ l B 2 / D S gives the time scale of CTAB diffusion over an “effective” finite boundary layer, , l B , which is assumed to sum up all the previously quoted effects (adsorption controlled by diffusion and dragging/desorption induced by transfer and dissolution).…”