Logarithmic mixing rule

Because soap and injected synthetic surfactant have different properties, a mixing rale is needed to model the properties of the two-surfactant system. Based on experimental data, Salager et al. (1979a) proposed the following logarithmic mixing rule for optimum salinities ... 

Puerto and Gale (1977) used a linear mixing rale on optimum salinity to fit their data. In fact, the logarithmic mixing rule has been found to slightly... 

Based on Eq. 12.1, optimum salinity follows the logarithmic mixing rule. Mohammadi et al. (2008) replaced the ratio of oil to surfactant concentration shown in Figure 12.5 by soap molar fraction and used the more generally effective salinity in the vertical axis. They did so because they could get these values from UTCHEM simulation models. Based on the logarithmic mixing rule, both axes in such activity maps are in logarithmic scales, and the upper and lower boundaries should be linear. 

For mixed solvents, an empirical logarithmic mixing rule... 

From the experimental results obtained, it was concluded that the synthetic hinders were thermorheologically complex materials as a consequence of the formation of a multiphase system. In fact, their mechanical behaviour is different according to the range of temperatures studied. While at low temperatures the binder mimics the mechanical properties of the oil-resin phase, at high temperatures the mechanical behaviour of the binder seems to be due to the polymer. Finally, the complex viscosity of these blends can be predicted using a logarithmic mixing rule, as will be discussed later. 

The rheological behaviour of synthetic binders can be predicted by means of a simple logarithmic mixing rule using the means of the viscosities of the pure resin and the oil-polymer blend. A fitting model, based on the pnre components, is also possible but it has to take into acconnt the oil-polymer ratio. 

In systems in which two materials are dispersed homogeneously, the logarithmic mixing rule lnKco=VcelnKce+VmlnK , is applied. Table 9-2 shows the results of measurement of the thermal conductivity of LTCC copper... 

A.2 Use of the Logarithmic Mixing Rule. Redo Example 11.4 using a logarithmic decay in mechanical properties. 

On the other hand, for liquids, the mixing rule is logarithmic in the pure component viscosity ... 

He, H2, O2, Ar, N2, CH4 and CO2 are lower than those calculated from the semi-logarithmic additivity rule, indicating that PMMA is miscible with BCPC over the whole blend composition range. These permeation results can be interpreted in terms of the free volume contraction which has been proposed to describe gas transport behavior in polymer mixtures. Similar observations for the miscible blends of polycarbonate with a copolyester formed from 1,4-cydohexanedimetha-nol and a mixture of terephthalic and isophthaUc adds have been made using CO2 [100]. Negative deviations of both permeability and diffusion coeffidents from simple additivity relations have been observed, and interpreted qualitatively to have resulted from the decrease in volume when the blends were mixed. 

The properties of liquid ammonia with small amounts of dissolved gases are calculated by mixing the properties of the pure liquid NH3 with the corresponding properties of the dissolved gases calculated by the kinetic gas theory as explained below. The mixing rule is the logarithmic mean. 

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