Surfactant Adsorption and Marangoni Flow in Liquid Jets. 3. Modeling in the Presence of Micellar Surfactant

Abstract

We present a hybrid computational fluid dynamics (CFD) model of surfactant adsorption and Marangoni flow at the rapidly expanding surface of a gravity-driven, laminar liquid jet that takes account of the presence of micelles. Micellar diffusion and finite rates of micellar formation and degradation are included in the model. This hybrid CFD model, which is developed within the CFD code FIDAP, is an extension of one recently published hybrid CFD model for adsorption and Marangoni flow in the absence of micelles. A boundary-layer treatment of the jet flow near the nozzle exit-which assumes that the stress at the nozzle exit is not exceeded at any point on the jet surface-shows that the adsorption of surfactant causes the surface velocity, and also the surface concentration, to increase linearly from the point where the jet detaches from the nozzle. The two major results of this theory are used in the hybrid CFD model; these are that (i) the rate of surface expansion of the jet remains finite at the point of detachment and (ii) there is a finite surface concentration at the nozzle exit. The analytical solution for transport of surfactant monomers to the jet surface in the presence of micelles assumes infinitely fast micellar breakdown. In the numerical model, finite micellar breakdown rates can be accommodated. Only one micellar species is considered. The hybrid CFD model is used to establish the order of magnitude of the micellar disintegration rate constant and to study the effect of variations in the mean aggregation number of the micellar species. Computed results are presented for a micellar solution of aqueous C 16 TAB. These results are compared with experiments. Good agreement between the model and the experiments can be obtained when the rate constant for micellar breakdown takes a value O(10 2 ) s -1 , for an aggregation number of 90.