Adsorption of Mixed Surfactant Systems
Authors: Trogus F.J. , Schechter R.S. , Pope G.A. , Wade W.H. 
Published: December 2007

Adsorption maxima, observed in static experiments, gives unusual effects during the chromatographic movement of surfactant solutions through a porous medium. The model system consists of a binary surfactant mixture porous medium. The model system consists of a binary surfactant mixture flowing through a porous medium. Fractionation is shown to be more significant at low concentrations; it is also more important in the field than in laboratory models.

The Mechanism of Surfactant Adsorption
Trogus et al. proposed a theory for surfactant adsorption that accounts for all the features observed in static experiments, including both adsorption maxima and minima. Unusual isotherm behavior is attributed to the equilibrium between mixed micelles and the monomer, rather than the nature of the surface. Mixed micelles are composed of different surfactant species, such as those for petroleum sulfonates and xylene sulfonates. The latter surfactant is well-characterized in terms of molecular weight distribution, but is a complex mixture of isomers.
This paper investigates dynamic adsorption (surfactant breakthrough curves) in the presence of mixed micelle systems. The complex isotherm behavior observed in static systems can yield interesting breakthrough curves that differ significantly with changes in both surfactant concentration and composition. To appreciate the results fully, the mechanism of static adsorption is reviewed. Consider a binary surfactant mixture composed of components having different critical micelle concentrations (CMC) (Fig. 1). The CMC of Component 1, C1, is larger than that of Component 2, C2. The shape of the curves is interesting and is typical of many measured binary mixtures of linear alkylbenzene sulfonates. The curvature strongly suggests that the micellar phase is enriched in Component 2. Mysels and Otter developed the following equation relating the composition of surfactant in the micellar phase to that in the monomer.
Yi X1 C2* 0--- = --- ----, ................................(1)Y2 X2 C2*
where Y1 and Y2 are the respective mole fractions of Components 1 and 2 in the micellar phase, and X1 and X2 are the respective monomer concentrations. The parameter 0 is determined so that the CMC of the mixture can be predicted by the equation, predicted by the equation,(C1* C2*)0Cd 0 = -----------------------...................(2)X1(C2*) 0 + X2(C1*) 0
By adjusting 0, this equation then fits CMC data for binary mixtures of alkylbenzene sulfonates. Reasonable values are in the range of 1.4 less than 0 less than 2. Note that Eq. 2 can be derived using empirical arguments. The derivation of Eq. 1 starts with the same empirical equation, but also requires the micellar phase to be ideal. Since there are no reported measurements of micellar compositions, the validity of Eq. 1 can only be inferred. Mysels and Otters measured the electrical conductivity of the sodium decyl and dodecyl sulfates and found that composition differed between the micellar and dispersed phases, but that activity coefficients had to be incorporated into Eq. 1 to fit the calculated compositions.
In the following analysis, Eq. 1 will be used even though the micellar phase may not be ideal.
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