Surfactant distribution, calculated

Figures 4 and depict the calculated surfactant distribution, expressed as 0, for the bubble front and rear, respectively.

The balance of Marangoni and viscous stresses (8.153), reformulated in terms of T, is integrated to obtain the surfactant distribution and yields T as a function of ( ) and the dimensionless Marangoni number Ma. The surfactant distribution can be integrated over the cap region to obtain the total amount on the surface, M. The variable M is also computed independently from the surfactant conservation equations and equating the two expressions yields Once ( ) is specified, the drag coefficient and terminal velocity can be calculated. 

Figure 5 Size distributions calculated for Kcq = O.OSkT nm. The solid curves were calculated using 2 = 3/2 for the dashed ones, r = 1 was used. Going from the upper to the lower curves, the surfactant concentration was fixed at 50, 16.7, and 8.3 mM, respectively. The values of the other parameters are = 0.1 nm, (t = 1 nm, 2K + K = 3kT/2. (From Ref. 27.)...

The transfer work can be calculated from the coefficient Kfof the surfactant distribution coefficient between the two phases. The values of transfer work for a number of substances are tabulated, for example, in Ref 262. For a ho-... 

Kunieda intensified the studies on phase behavior and formation of microemulsions in mixed-surfactant systems [66-76], in order to understand the relationship between maximum solubilization of microemulsions and surfactant distribution of mixed surfactants at the water/oil interface in the microemulsion phase. He developed a method to calculate the net composition of each surfactant at the interface in the bicontinuous microemulsions assuming that the monomeric solubihty of each surfactant in oil is the same as in the oil microdomain of the microemulsions [69]. Using this approach, the distribution of surfactants in the different domains of bicontinuous microemulsions (Figure 9) could be quantified [70-75], even if the complete microstracture of these systems was not completely elucidated. 

The surface excess in the water-oil system was also calculated for the case of the surfactant distribution between the phases [26, 54]. 

When measuring the surface pressure isotherms, it is desirable that the values of the interfacial tension are not time-dependent. In this case, in the interfacial region a state is reached close to the equilibrium for the surfactant distribution between the phases [55]." If the surfactant is soluble in both phases, one should be careful in calculating the surface excess in such systems, and the surfactant distribution coefficient should be determined independently. For instance, trioctylmethylammonium chloride (Oct3MeNCl) in the benzene-water system has a distribution coefficient of the order of 10 [57]. The surface pressure isotherms at the benzene-water interface are almost independent of the phase in which Oct3MeNCl is dissolved. It means that in both cases Oct3MeNCl is almost completely located in the benzene phase, i.e. the surfactant distribution equilibrium is reached at the interface. Apparently, the anomalies in the... 

Figure 24-1. Nitrogen adsorption/desorption isotherms of a mesoporous film with cubic structure functionalized with -CNgroups after surfactant removal by solvent extraction were measured by a surface acoustic wave (SAW) technique andyieldeda type IVisotherm with a very narrow hysteresis loop that is typicalfor mesoporous materials. Inset is pore size distribution calculated from adsorption isotherm. (Liu, N., Assink, R. A. and Brinker, C. J. Chem. Commun. 2003 370-371, Reproduced by permission of The Royal Society of Chemistry)...

Equation (1) is generally used to estimate the rate constant, kin the micellar pseudophase, but for inhibited bimolecular reactions it provides an indirect method for estimation of otherwise inaccessible rate constants in water. Oxidation of a ferrocene to the corresponding ferricinium ion by Fe3 + is speeded by anionic micelles of SDS and inhibited by cationic micelles of cetyltrimethylammonium bromide or nitrate (Bunton and Cerichelli, 1980). The variation of the rate constants with [surfactant] fits the quantitative treatment described on p. 225. Oxidation of ferrocene by ferricyanide ion in water is too fast to be easily followed kinetically, but the reaction is strongly inhibited by anionic micelles of SDS which bind ferrocene, but exclude ferricyanide ion. Thus reaction occurs essentially quantitatively in the aqueous pseudophase, and the overall rate depends upon the rate constant in water and the distribution of ferrocene between water and the micelles. It is easy therefore to calculate the rate constant in water from this micellar inhibition. 

The bile salts and their ability to form mixed micelles is discussed in some detail in order to foster a better understanding of their applications. It is highly important for the electrophoretic characterization of the micellar phase, and therefore for the calculation of the distribution coefficients, to have a thorough understanding of the mode of micelle formation and structural changes achieved by alteration of the surfactant concentration and micelle composition as well as to develop strategies for micelle optimization. 

KP and v can, in contrast to kp, not be determined via the concentration gradient for binary and ternary mixed micelles, because for the calculation of the Nemstian distribution a constant CMC and an almost constant partial molar volume must be assumed. The calculation of aggregation constants of simple bile salt systems based on Eq. (4) yields similar results (Fig. 8b). Assuming the formation of several concurrent complexes, a brutto stability constant can be calculated. For each application of any tenside, suitable markers have to be found. The completeness of dissolution in the micellar phase is, among other parameters, dependent on the pH value and the ionic strength of the counterions. Therefore, the displacement method should be used, which is not dependent on the chemical solubilization properties of markers. For electrophoretic MACE studies, it is advantageous for the micellar constitution (structure of micelle, type of phase micellar or lamellar) to be known for the relevant range of concentrations (surfactant, lipids). 

As evidenced by the above equation, the distribution coefficient can be directly calculated from the retention factor and other easily measurable parameters. It is also worth noting that when the concentration of the micellar phase is sufficiently low, the denominator at the last term of the above equation can be approximated to be equal to unity and the retention factor is linearly proportional to the concentration of the surfactant into the BGE. Accordingly, Equation 6.46 is rewritten as... 

In the case of non—eutectic systems, the solid phase shows nearly ideal mixing, so that the surfactant components distribute themselves between the micelle and the solid in about the same relative proportions (i.e., both the mixed micelle and mixed solid are approximately ideal). However, in the case of the eutectic type system, the crystal is extremely non-ideal (almost a single component), while the micelle has nearly ideal mixing. As seen in earlier calculations for ideal systems, even though the total surfactant monomer concentration is intermediate between that of the pure components, the monomer concentration of an individual component decreases as its total proportion in solution decreases. As the proportion of surfactant A decreases in solution (proportion of surfactant B increases) from pure A, there is a lower monomer concentration of A. Therefore, it requires a lower temperature or a higher added electrolyte level to precipitate it. At some... 

Our results for HOC partitioning in the presence of sorbed surfactant and micelles demonstrate that large differences can exist in the HOC sorption capacity of surfactant aggregates in micellar versus sorbed forms. This can be seen quite readily by calculating Kss values as a function of surfactant dose from the experimental KD values. The distribution coefficient defines the HOC mass balance and can be expressed as ... 

Figure 6. Calculated percentages (based on distributed rate model optimal simulations) of TCE removed from the CFSTRs flushed with the non-surfactant solution, the 30 mg/L Triton X-100 solution, the 300 mg/L Triton X-100 solution, and the 3,000 mg/L Triton X-100 solution. The removal profiles shown are averages of the replicate experiments.

The gas-liquid chromatographic evaluation of n can obviously be performed on a single distribution C E but not on mixtures of distributions. Commercial surfactants always consist of mixed distribution. Only when the procedure is applicable, rt=Lxnrt is calculated from the observed distribution of the molecular fraction (x ) for various values of n. It should be checked that x =l. 

A more interesting way to look at the data is to plot the specific surface area of the emulsion droplets as a function of the surfactant concentration as shown in Figure 3. (The surface area was calculated from the full distribution rather than from a mean diameter.) Thus, it can be seen that, over the range studied, an increase in the amount of surfactant present causes a proportional increase in the surface area created. 

Figure 3. Specific surface area of internal phase versus surfactant concentration for emulsion systems A and B, as calculated from the full distributions.

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