Concentration of surfactant

The kinetic data are essentially always treated using the pseudophase model, regarding the micellar solution as consisting of two separate phases. The simplest case of micellar catalysis applies to unimolecTilar reactions where the catalytic effect depends on the efficiency of bindirg of the reactant to the micelle (quantified by the partition coefficient, P) and the rate constant of the reaction in the micellar pseudophase (k ) and in the aqueous phase (k ). Menger and Portnoy have developed a model, treating micelles as enzyme-like particles, that allows the evaluation of all three parameters from the dependence of the observed rate constant on the concentration of surfactant". ... 

The catalytic effect on unimolecular reactions can be attributed exclusively to the local medium effect. For more complicated bimolecular or higher-order reactions, the rate of the reaction is affected by an additional parameter the local concentration of the reacting species in or at the micelle. Also for higher-order reactions the pseudophase model is usually adopted (Figure 5.2). However, in these systems the dependence of the rate on the concentration of surfactant does not allow direct estimation of all of the rate constants and partition coefficients involved. Generally independent assessment of at least one of the partition coefficients is required before the other relevant parameters can be accessed. 

Berezin and co-workers have analysed in detail the kinetics of bimolecular micelle-catalysed reactions ". They have derived the following equation, relating the apparent rate constant for the reaction of A with B to the concentration of surfactant ... 

Herein Pa and Pb are the micelle - water partition coefficients of A and B, respectively, defined as ratios of the concentrations in the micellar and aqueous phase [S] is the concentration of surfactant V. ai,s is fhe molar volume of the micellised surfactant and k and k , are the second-order rate constants for the reaction in the micellar pseudophase and in the aqueous phase, respectively. The appearance of the molar volume of the surfactant in this equation is somewhat alarming. It is difficult to identify the volume of the micellar pseudophase that can be regarded as the potential reaction volume. Moreover, the reactants are often not homogeneously distributed throughout the micelle and... 

Herein [5.2]i is the total number of moles of 5.2 present in the reaction mixture, divided by the total reaction volume V is the observed pseudo-first-order rate constant Vmrji,s is an estimate of the molar volume of micellised surfactant S 1 and k , are the second-order rate constants in the aqueous phase and in the micellar pseudophase, respectively (see Figure 5.2) V is the volume of the aqueous phase and Psj is the partition coefficient of 5.2 over the micellar pseudophase and water, expressed as a ratio of concentrations. From the dependence of [5.2]j/lq,fe on the concentration of surfactant, Pj... 

Figure 5.3 shows the dependence of the apparent second-order rate constants (koi "/[5.2]i) on the concentration of surfactant for the Diels-Alder reactions of 5.If and 5.1 g with 5.2. The results of the analysis in terms of the pseudophase model are shown in the inset in Figure 5.3 and in the first two... 

Figure 5.4. Plot of the apparent second-order rate constant, kapp (= kotJ[5.2]i) versus the concentration of surfactant for the Diels-Alder reaction of S.lg with 5.2 in CTAB solution at 25 C. The inset shows the treatment of these data using Equation 5.6. From slope and intercut P j can be calculated (see Table 5.2).

The concentration of surfactant was 3.89 mM above the cmc in each case. Values taken from Chapter 2 and determined at a constant ionic strength of 2.0 M using KNOj as background electrolyte. 

Assuming complete binding of the dienophile to the micelle and making use of the pseudophase model, an expression can be derived relating the observed pseudo-first-order rate constant koi . to the concentration of surfactant, [S]. Assumirg a negligible contribution of the reaction in the aqueous phase to the overall rate, the second-order rate constant in the micellar pseudophase lq is given by ... 

Using Equation A3.4, the partition coefficient of 5.2 can be obtained from the slope of the plot of the apparent second-order rate constant versus the concentration of surfactant and the independently determined value of 1 . ... 

Addition of surfactant to the injection water (14,15) can displace the oil remaining near the well. The lower oil saturation results in an increase in the water relative permeabihty (5). Therefore, a greater water injection rate may be maintained at a given injection pressure. Whereas ultimate oil recovery may not be increased, the higher water injection rate can increase oil production rates improving oil recovery economics. Alternatively, a lower injection pressure can be used. Thus smaller and cheaper injection pumps may be used to maintain a given injection rate. The concentration of surfactant in the injection... 

An alternative to this process is low (<10 N/m (10 dynes /cm)) tension polymer flooding where lower concentrations of surfactant are used compared to micellar polymer flooding. Chemical adsorption is reduced compared to micellar polymer flooding. Increases in oil production compared to waterflooding have been observed in laboratory tests. The physical chemistry of this process has been reviewed (247). Among the surfactants used in this process are alcohol propoxyethoxy sulfonates, the stmcture of which can be adjusted to the salinity of the injection water (248). 

A reduction of the o/w interfacial tension has a disadvantage because it makes the contact angle 9 more sensitive to small differences between and y. After a certain concentration of surfactant in the oil phase has brought the contact angle to 90°, the process is repeated but with the surfactant added to the oil before the phases are brought into contact. If the water droplet does not spread and its contact angle is in excess of 90°, the surfactant is added to the aqueous phase. 

An evaluation of the retardation effects of surfactants on the steady velocity of a single drop (or bubble) under the influence of gravity has been made by Levich (L3) and extended recently by Newman (Nl). A further generalization to the domain of flow around an ensemble of many drops or bubbles in the presence of surfactants has been completed most recently by Waslo and Gal-Or (Wl). The terminal velocity of the ensemble is expressed in terms of the dispersed-phase holdup fraction and reduces to Levich s solution for a single particle when approaches zero. The basic theoretical principles governing these retardation effects will be demonstrated here for the case of a single drop or bubble. Thermodynamically, this is a case where coupling effects between the diffusion of surfactants (first-order tensorial transfer) and viscous flow (second-order tensorial transfer) takes place. Subject to the Curie principle, it demonstrates that this retardation effect occurs on a nonisotropic interface. Therefore, it is necessary to express the concentration of surfactants T, as it varies from point to point on the interface, in terms of the coordinates of the interface, i.e.,... 

Davies et al. (D9) have recently measured the rates of absorption of various gases into turbulently stirred water both with carefully cleaned surfaces and with surfaces covered with varying amounts of surfactants. That hydrodynamic resistances, rather than monolayer resistances, are predominant in their work is consistent with the high sensitivity of kL to very small amounts of surface contamination and also with the observation that a limit to the reduction in kL is found (D7, D9). This is in agreement with the results of Lindland and Terjesen (L9), who found that after a small concentration of surfactant had been used further additions caused but little change in terminal velocity (L9). 

The first two aspects entail relatively high concentrations of surfactants. In the last case, trace amounts are to be determined. When performing surfactant analysis, preconcentration and/or separation of the different surfactant classes are prerequisites for identifying and quantifying the compound in question. Furthermore, the trend is to analyze the individual components of any surfactant mixture. 

The log of the reciprocal of the bulk concentration of surfactant (C in mol/ L) necessary to produce a surface or interfacial pressure of 20 raN/m, log( 1 / On= 20 i e > a 20 mN/m reduction in the surface or interfacial tension, is considered a measure of the efficiency of a surfactant. The effectiveness of surface tension reduction is the maximum effect the surfactant can produce irrespective of concentration, (rccmc = [y]0 - y), where [y]0 is the surface tension of the pure solvent and y is the surface tension of the surfactant solution at its cmc. 

Alcohol sulfates are excellent foaming surfactants. According to the Kitchener and Cooper classification [148], alcohol sulfates form metastable foams. However, quantitative values cannot easily be compared because foam largely depends not only on the instrument used to produce and evaluate foam but also on the concentration of surfactant, impurities, temperature, and many other factors. In addition, a complete characterization of the foam capacity should take into account the initial amount of foam, its stability, and its texture. 

The Gibbs equation allows the amount of surfactant adsorbed at the interface to be calculated from the interfacial tension values measured with different concentrations of surfactant, but at constant counterion concentration. The amount adsorbed can be converted to the area of a surfactant molecule. The co-areas at the air-water interface are in the range of 4.4-5.9 nm2/molecule [56,57]. A comparison of these values with those from molecular models indicates that all four surfactants are oriented normally to the interface with the carbon chain outstretched and closely packed. The co-areas at the oil-water interface are greater (heptane-water, 4.9-6.6 nm2/molecule benzene-water, 5.9-7.5 nm2/molecule). This relatively small increase of about 10% for the heptane-water and about 30% for the benzene-water interface means that the orientation at the oil-water interface is the same as at the air-water interface, but the a-sulfo fatty acid ester films are more expanded [56]. 

The mechanisms that affect heat transfer in single-phase and two-phase aqueous surfactant solutions is a conjugate problem involving the heater and liquid properties (viscosity, thermal conductivity, heat capacity, surface tension). Besides the effects of heater geometry, its surface characteristics, and wall heat flux level, the bulk concentration of surfactant and its chemistry (ionic nature and molecular weight), surface wetting, surfactant adsorption and desorption, and foaming should be considered. 

Thus, the enhancement of heat transfer may be connected to the decrease in the surface tension value at low surfactant concentration. In such a system of coordinates, the effect of the surface tension on excess heat transfer (/z — /zw)/ (/ max — w) may be presented as the linear fit of the value C/Cq. On the other hand, the decrease in heat transfer at higher surfactant concentration may be related to the increased viscosity. Unfortunately, we did not find surfactant viscosity data in the other studies. However, we can assume that the effect of viscosity on heat transfer at surfactant boiling becomes negligible at low concentration of surfactant only. The surface tension of a rapidly extending interface in surfactant solution may be different from the static value, because the surfactant component cannot diffuse to the absorber layer promptly. This may result in an interfacial flow driven by the surface tension gradi-... 

The results obtained at Bn = 1.26 are presented in Fig. 6.17, for different concentrations of surfactant solutions. The onset of boiling corresponds to the curve ABCD for the runs with increasing heat flux. It follows the curve DCA for decreas-... 

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