Calculation of phase inversion in concentrated

Calculation of Phase Inversion in Concentrated Emulsions CAPICO... 

The Equivalent Alkane Carbon Number (EACN) is an empirical correlation which helps to evaluate the location of a balanced point for different emulsified oils and oil mixtures. The Calculation of Phase Inversion in Concentrates (CAPICO) method is similar to the EACN. 

The PIT phenomenon is predictable by parameters. With the help of characteristic variables for oil and emulsifiers, new formulations with desired components can be calculated on a computer by means of the CAPICO procedure (calculation of phase inversion in concentrates), so that development times can be dramatically reduced. ... 

The best physical explanation is given by a calculation of the concentration profiles. To calculate the concentration profiles in the polymer film during the (delayed demixed type of) phase inversion process, some assumptions and considerations must be made[35] ... 

Since we know the source composition, partition coefficients and phase abundances in molten sources, we can calculate the synthetic melt and mineral concentrations using equation (9.2.2). The five 4x3 matrices Ak can be built the first column of Table 9.4 is made of the melt concentrations ( lavas ). Mineral concentrations in the next two columns are computed from melt concentrations using the appropriate mineral liquid partition coefficients. High precision is needed to ensure accurate inversion. 

Because the inverse Debye length is calculated from the ionic surfactant concentration of the continuous phase, the only unknown parameter is the surface potential i/io this can be obtained from a fit of these expressions to the experimental data. The theoretical values of FeQx) are shown by the continuous curves in Eig. 2.5, for the three surfactant concentrations. The agreement between theory and experiment is spectacular, and as expected, the surface potential increases with the bulk surfactant concentration as a result of the adsorption equilibrium. Consequently, a higher surfactant concentration induces a larger repulsion, but is also characterized by a shorter range due to the decrease of the Debye screening length. 

The effect of the HLB of surfactant blends (calculated as the weight average) on the stability of the concentrated emulsions is presented in Fig. 11. (No w/o concentrated emulsion could be prepared using the surfactant blends employed in Fig. 11 because of the phase inversion that occurred at the beginning of the... 

In experimental studies, where the loss of fluidity is taken as marking the gel point, the conversion at the observed gel point is almost always found to be higher than that (calculated) at the theoretical gel point. This can be explained by the model proposed by Bobalek et al (1964) for the gelation process, as shown in Fig. 5.8. According to this model, at the theoretical gel point, a number of macroscopic three-dimensional networks (gel particles) form and undergo phase separation. The gel particles so formed remain suspended in the medium and increase in number as reaction continues. At the experimentally observed gel point, the concentration of gel particles reaches a critical value and causes phase inversion as well as a steep rise in viscosity. The lower value of pc predicted by the statistical approach is also attributed to the occurrence of some wasteful intramolecular cy-clization reactions not taken into account in the derivation and also in some cases to the limited applicability of the assumption of equal reactivity of all functional groups of the same type, irrespective of molecular size. 

Soil Organic Matter Organic compounds may exist in soil either in solution or the vapor phase and can be absorbed through the roots in either state, absorption from solution would be the most likely process. From the discussion of the sorption process in soil (see Sorption, Chapter 3) the concentration of the compound in aqueous solution, Caq, would be a function of the concentration in the soil (Csoii). and the soil distribution ratio, K, which in turn is dependent primarily on SOM content. One would predict that uptake would be inversely related to the level of SOM. Observations of the uptake of diel-drin by carrots raised in different soils provide an opportunity to evaluate this relation and demonstrate the dependence on the concentration of the compound in soil solution. If the uptake efficiency is defined by the ratio of the concentration of dieldrin in carrots to that in the soil it is clear that higher levels of soil organic matter reduce uptake by carrots (Table 5.6). The ATom for dieldrin is 6980 mL g from which values were calculated for dieldrin in each soil. Since = Cjoii/Caq the concentration of dieldrin in soil solution can be determined. If uptake is defined as Ccarrot/Caq consistent value... 

Calculations of relative amplitudes, quench vectors, and buffering of the species indicate that Per + and H2O2 are nonessential species. Since the enzymatic species are bound by a conservation constraint (their overall concentration is constant), the Jacobian matrix is singular and cannot be inverted. However, this can be circumvented by calculating the inverse of an auxiliary matrix [8], which provides concentration shifts with respect to only those species that are not involved in the conservation constraint. Leaving out the nonessential species, the concentration shifts with respect to admittable species (NAD, 0 , and O2) along with phase shifts relative to NAD (type X species) are summarized in table 11.12. 

By analyzing data of Figure 2.6, it was found that PHB forms a continuous matrix in the molten polymer at any ratio. The experimental values of the viscosity are close to the bottom theoretical curve, which corresponds to the calculation for the case of the formation of the matrix of PHB. Thus, during the melting of PHB observed phase inversion phenomenon in accordance with the laws of Ref. [4, 6] more fluid melt PHB forms a continuous phase in the entire range of concentrations. 

The factor in Eq. (36) accounts for the effect of finite surface viscosity (j/s) and has been computed by Desai and Kumar [61] as a function of the inverse of the dimensionless surface viscosity (y = 0.4387/i /5jiIt must be emphasized that their results for the calculation of Cy are valid only for foams because they neglected the viscosity of the dispersed phase. Equation (36) can be used for liquid liquid concentrated emulsions only when the surfaces are immobile (i.e., when Cy = 1). The pressure gradient (dp/dz) can be computed as follows. 

The elaborated in [R. V. Chepulskii, Analytical method for calculation of the phase diagram of a two-component lattice gas, Solid State Commun. 115 497 (2000)] analytical method for calculation of the phase diagrams of alloys with pair atomic interactions is generalized to the case of many-body atomic interactions of arbitrary orders and effective radii of action. The method is developed within the ring approximation in the context of a modified thermodynamic perturbation theory with the use of the inverse effective number of atoms interacting with one fixed atom as a small parameter of expansion. By a comparison with the results of the Monte Carlo simulation, the high numerical accuracy of the generalized method is demonstrated in a wide concentration interval. 

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