Phase inversion coefficient

Of interest here is the question relating to the value for the slope coefficient, k, from equation (1), when surfactant structures incorporating both ionic (say sulphonate) and nonionic moieties are included together. The Ghanges in electric double layer effects imparted from salt addition might dominate the packing constraints and therefore the phase inversion process, or perhaps oxyethylene dehydration effects from the presence of toluene could also play a role. 

Most of the plate height terms we have discussed are velocity sensitive. For gases, any term containing the mobile (gas) phase diffusion coefficient Dm (Dg for gases) is also pressure dependent, since Dg varies in inverse proportion to pressure p. For an ideal gas... 

Liquid-liquid dispersion involves two phases a continuous phase (one with large volume), and a dispersed phase (one with small volume). When the volume fractions of both phases are nearly the same, phase inversion occurs. In this case, which of the two phases becomes a continuous one depends on the starting conditions as well as the physical properties of the system. The range of volume fraction within which either of two immiscible liquids may be continuous is primarily a function of the viscosity ratio it is not strongly dependent upon vessel characteristics or stirring speed (Selker and Sleicher, 1965). Here we briefly evaluate the minimum speed of rotation required to disperse one phase completely into the other, the interfacial area, and the mass-transfer coefficient in liquid-liquid dispersion. 

Inverse Gas Chromatography. A technique that promises to circumvent many of the problems attendant to gravimetric sorption experiments is Inverse Gas Chromatography (IGO. Until recently, all reported applications of IGC to the measurement of diffusion coefficients have used packed chromatographic columns in which the stationary phase is supported on a granular substrate. Equations similar to those developed by van Deemter et al. (22) are used to calculate the stationary phase diffusion coefficient from the spreading of the elution profile. The equation developed by van Deemter is commonly written as... 

The phase behavior of surfactant formulations for enhanced oil recovery is also affected by the oil solubilization capacity of the mixed micelles of surfactant and alcohol. For low-surfactant systems, the surfactant concentration in oil phase changes considerably near the phase inversion point. The experimental value of partition coefficient is near unity at the phase inversion point (28). The phase inversion also occurs at the partition coefficient near unity in the high-surfactant concentration systems (31). Similar results were also reported by previous investigators (43) for pure alkyl benzene sulfonate systems. 

See Figure 20.1 for a schematic illustration of the general types of behavior often observed in multiphase systems containing components differing widely in a property. This figure also highlights the qualitative nature of the effects of phase co-continuity as well as of phase inversion which occurs in some (but not all) types of multiphase systems. While the illustration in Figure 20.1 is for the shear modulus, qualitatively similar behavior is often also observed for the other elastic moduli, the coefficients of thermal expansion, and the transport properties. 

Asymmetric phase-inversion membranes like the membranes employed in reverse osmosis are difficult to prepare as gas permeation is much more sensitive to micropores than RO due to the much higher diffusion coefficients of gases. For the same reason, the composite membrane differs from RO composite membranes in gas permeation, the top layer of the asymmetric support structure is responsible for the separation while it is the sole duty of the coating to plug the micropores. Consequently, the material of the coating chosen (silicone) has a high permeability but a low selectivity while the membrane material (poly-sulfone) has a high selectivity (and a much lower permeability). 

In liquid-liquid systems, upon increase of concentration of the dispersed phase, at a certain concentration suddenly the dispersed and continuous liquids exchange roles. This is known as a phase inversion. Salager et al. [1983] and Minana-Perez et al. [1986] reported two types of phase transition in ionic emulsions — in the first, viscosity goes through a minimum, whereas in the second it goes through a maximum. The first type of transition (normal) is associated with a decrease of the interfacial tension coefficient and formation of a micro-emulsion. The second (catastrophic) transition is associated with an inversion of unstable structure to a stable one. 

Vrc y,y r 11 o - volume fraction of dispersed and matrix phase, respectively - volume fraction of the crosslinked monomer units - volume fraction of phase i at phase inversion - maximum packing volume fraction - percolation threshold - shear strain and rate of shearing, respectively - viscosity - zero-shear viscosity - hrst and second normal stress difference coefficient, respectively... 

The adempts to rationalize GrifHn s HLB scale from a physicochemical point of view were made in a number of studies. Various correlations were shown to exist between the HLB numbers and the chemical structure or molecular composition of the siufactants. Correlations were also fotmd between the HLB number and physicochemical properties of surfactants and their solutions, for example, stffface and interfacial tension, solubility, and heat of solution, spreading and distribution coefficient, dielectric permittivity of the surfactant, cloud point and phase inversion point, critical micelle concenlration, foaminess, etc. These studies are reviewed in Ref. 262. However, the correlations found are not generally applicable moreover, the concept of the additivity of HLB numbers as such for mixtures of surfactants or oils cannot be proven expermentally when the surfactant characteristics are varied over a wider range (265). 

Soin N, Boyer D, Prashanthi K, Shaima S, Narasimulu AA, Luo J, et al. Exclusive self-aligned P-phase PVDE films with abnormal piezoelectric coefficient prepared via phase inversion. Chem Comm 2015 51 8257-60. 

Of course this equation can only be valid when the filler or dispersed phase can in fact undergo a phase inversion this cannot be the case for a rigid inorganic filler. Above Tg, equations (12.49) and (12.52) give almost the same values for these systems, and a linear additivity relationship holds. This presumably follows from the near equivalence of expansion coefficients so that the right-hand interaction term of equations (12.49) and (12.52) vanishes. 

On a perforated plate the liquid side mass transfer coefficient kLa and gas side mass transfer coefficient k( a, based on the column volume, vary linearly with the dispersion height. The true liquid- and gas-side mass transfer coefficients and first increase with the dispersion height and then go through a maximum and decrease slightly (123). Sharma and Gupta (124) attribute this to different behavior of the density of dispersion and the average bubble size with increase in gas flowrate, which leads to a phase inversion point. These authors correlate their experimental data for 10 cm i.d. perforated plates without downcomers by the following expressions... 

FIGURE 8.17 NMR diffusion coefficients across the phase inversion using a salinity scan. Reprinted from Guering and Lindman (1985) with permission. Copyright 1978 American Chemical Society. 

Figure 4.6 shows the change of the hquid flow rate and of components concentrations forn = 3 at the height of all the columns (the height of the columns is characterized by the inverse value of phase equihbrium coefficient of the reference component (the third one) l/Kf). As can be seen in Figs. 4.4 and 4.5, the... 

When standard tridymite is cooled below 380 C, several phase inversions occur with various changes in symmetry. These tend to produce a large shrinki e and therefore a high thermal coefficient of expansion between 0 -200 C, almost 400 X lO K-h... 

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