Surface tension of mixtures

It has been pointed out [138] that algebraically equivalent expressions can be derived without invoking a surface solution model. Instead, surface excess as defined by the procedure of Gibbs is used, the dividing surface always being located so that the sum of the surface excess quantities equals a given constant value. This last is conveniently taken to be the maximum value of F. A somewhat related treatment was made by Handa and Mukeijee for the surface tension of mixtures of fluorocarbons and hydrocarbons [139]. 

Surfactant Activity in Micellar Systems. The activities or concentrations of individual surfactant monomers in equilibrium with mixed micelles are the most important quantities predicted by micellar thermodynamic models. These variables often dictate practical performance of surfactant solutions. The monomer concentrations in mixed micellar systems have been measured by ultraf i Itration (I.), dialysis (2), a combination of conductivity and specific ion electrode measurements (3), a method using surface tension of mixtures at and above the CMC <4), gel filtration (5), conductivity (6), specific ion electrode measurements (7), NMR <8), chromatograph c separation of surfactants with a hydrophilic substrate (9> and by application of the Bibbs-Duhem equation to CMC data (iO). Surfactant specific electrodes have been used to measure anionic surfactant activities in single surfactant systems (11.12) and might be useful in mixed systems. ... 

Measurements of the surface tensions of mixtures and solutions have been made in great numbers Musculus (1864) indicated that solutions may be classified into two groups according as the solute has little influence on the surface tension of the solvent (when Traube called it capillary inactive), or when it produces a marked lowering of surface tension (when Traube called it capillary active). A consideration of the second group is closely connected with adsorption phenomena, which are not dealt with here, the present discussion being mainly confined to solutions of the first group, especially electrolytes, and to mixtures of liquids. 

Richards s piezometer, 59 Richards and Rowe s results for specific heats of solutions, 223 Richardson s thermionic equation, 293 Rodenbeck s formula for surface tensions of mixtures, 200... 

Ay s ). Bardavid et al. ) reported positive deviations Ay for mixtures of 1,1.1.-trichloroethane and propanols at 298.15 K. Positive Ay s were also found for mixtures of 1-propanol and n-propylamine or n-butylamine ). The sign of Ay is determined by which of the two components preferentially enriches the surface (fig. 4.4b). An example of a convex y(x) curve, relating to hydrogen-bonding fluids, is given in fig. 4.9. The reader can find more data on the surface tension of mixtures in appendix 1, tables Al.16-18. 

Figure 4.9. Surface tension of mixtures of water (comjxtnent 1) and sulphuric acid (o) or hydrazine (A) at 25°C (component 2). Graphs constructed at 50°C from data by...

Table A1.17. Surface tensions of mixtures of water (1) and some inorganic and organic compounds (2).

LIQUIDS AND SOLUTIONS AT INTERFACES 445 A simple equation for the surface tension of mixtures is... 

The effect of temperature on the surface tension of mixtures of n-propanol/ -heptane has been investigated. The variation of surface tension by temperature (K) for pure components was... 

Fig. 2C. 1. Static and dynamic surface tension of mixtures of diethyl ether and acetone vs. mol fraction of acetone...

The problem of finding effectively the equation of state of a mixture of hard spheres of different diameters, incidentally, is of considerable interest in a number of applications, e.g., for finding the high temperature equation of state of mixtures of real gases and the surface tension of mixtures, amoi other things. While a number of the theories of fluids mentioned in Section IV of this chapter can also be reformulated " formally for mixtures,... 

The surface tension of mixtures of water and ethyl alcohol at 25 C has been measured by Bircumshaw (J. Chem. Soc. 1922, 887). Partial vapour pressures of these laiixtures also at 25 C have been determined by Dobson (J. Chem. Soc. 1925, 2866). These values, smoothed in accordance with the requirements of the Duhem-Margules relation are given with related quantities at rounded mole fractions in table 1 (Guggenheim and Adam, Proc. Roy. Soc. A 1933, 139, 218). The subscript 1 relates to water and 2 to alcohol, x denotes mole fraction, p partial pressure, and y surface tension. 

In fact, experimental surface tensions of mixtures of sodium decyl sulphate SDeS (component 1) and sodium dodecyl sulphate SDS (component 2) are described satisfactorily by Eq. (2.48) whereas the application of Eq. (2.51) leads to large differences between theory and experiment [67]. The best agreement between experimental and theoretical values of n was received by using the Frumkin analogue of Eqs. (2.48)-(2.50) with ai=0.7, a2=0.85 and ai2=(ai+a2)/2=0.77. Similarly, mixtures of decyl ammonium chloride and dodecyl ammonium chloride were very well described by these equations with ai=1.2, a2=1.56 and ai2=(ai+a2)/2=1.38 [16]. The latter system also reveals a reverse salting-out effect as an excess of inorganic counterions in the solution increases the adsorption activity of an ionic surfactant, by the same token such an excess in the surface decreases the adsorption activity. As a result, the effect of a second ionic surfactant with a common counterion on the surface pressure is smaller than it would have been according to the additivity rule for non-ionic surfactants expressed in Eq. (2.51). 

Similar variations in the densities and surface tensions of mixtures are also known. The density of a mixture of bromo- and chlorobenzene is equal to the arithmetic mean of the densities of the individual components, whereas the density of trichloromethane-diethyl ether is about 1.5% above the mean value. The surface tensions of the systems diethyl ether-benzene and benzene-carbon disulfide are equal to the calculated values. The surface tension of methanol-ethyl iodide is greater and that of benzene-ethanol and acetone-carbon disulfide are less than the calculated values. 

Both the surface tension of mixture and solvent diffusion affect the evaporation rate. This becomes a complex function dependent not only on the solvents present but also on influence of solutes on both surface tension and diffusion. These relationships affect the real evaporation rates of solvents from the complicated mixtures in the final products. In addition, solvent evaporation also depends on relative humidity and air movement. 

Fig. 8 Dynamic surface tension of mixtures between a highly surface-active model suspension and modified starches having the same cationicity, but different degrees of benzylation, DSbn. at a mixing ratio (volume suspensionrvolume starch) of 10 1 surface tension was measured using a profile analysis tensiometer (t = 1,200 s) [67]...

---