Constant internal phase

To explore the influence of p, the viscosity of the internal phase was varied over four decades, everything else being constant [149]. As can be seen in the log-log plot of Fig.. 9, dp (identically Cflcr) scales with the viscosity ratio as p - the low value of the exponent indicates that dp is only weakly dependent on p. In Fig. 1.20, the evolution of the polydispersity P as a function of p is plotted. As... 

In order to solve the mathematical model for the emulsion hquid membrane, the model parameters, i. e., external mass transfer coefficient (Km), effective diffu-sivity (D ff), and rate constant of the forward reaction (kj) can be estimated by well known procedures reported in the Hterature [72 - 74]. The external phase mass transfer coefficient can be calculated by the correlation of Calderback and Moo-Young [72] with reasonable accuracy. The value of the solute diffusivity (Da) required in the correlation can be calculated by the well-known Wilke-Chang correlation [73]. The value of the diffusivity of the complex involved in the procedure can also be estimated by Wilke-Chang correlation [73] and the internal phase mass transfer co-efficient (surfactant resistance) by the method developed by Gu et al. [75]. 

The HIPE is formed generally by careful addition of the internal phase to a solution of surfactant in the external phase, under constant agitation. HIPEs may form under other circumstances, however [26], When a centrifugal field is... 

In Fig. 3 c the schematic volume-temperature curve of a non crystallizing polymer is shown. The bend in the V(T) curve at the glass transition indicates, that the extensive thermodynamic functions, like volume V, enthalpy H and entropy S show (in an idealized representation) a break. Consequently the first derivatives of these functions, i.e. the isobaric specific volume expansion coefficient a, the isothermal specific compressibility X, and the specific heat at constant pressure c, have a jump at this point, if the curves are drawn in an idealized form. This observation of breaks for the thermodynamic functions V, H and S in past led to the conclusion that there must be an internal phase transition, which could be a true thermodynamic transformation of the second or higher order. In contrast to this statement, most authors... 

For a membrane that is symmetrically placed between two solutions S and 52 containing the primary ion, such as in a conventional ion-selective electrode with a constant internal reference solution S2 (Fig. 6.3), the Galvani potentials inside the membrane phase cancel out and (6.6) applies again. 

Consider a bubble rising in a fluidized bed. It is assumed that the bubble is solids-free, is spherical, and has a constant internal pressure. Moreover, the emulsion phase is assumed to be a pseudocontinuum, incompressible, and inviscid single fluid with an apparent density of pp(l — amf) + pamf. It should be noted that the assumption of incompressibility of the mixture is not strictly valid as voidage in the vicinity of the bubble is higher than that in the emulsion phase [Jackson, 1963 Yates et al., 1994]. With these assumptions, the velocity and pressure distributions of the fluid in a uniform potential flow field around a bubble, as portrayed by Fig. 9.10, can be given as [Davidson and Harrison, 1963]... 

The average ionic charge of polonium species in chloride solutions was measured using an anion-exchange method. The method is based on measurements of the distribution ratio of polonium at a constant internal chloride ion concentration of the anion-exchanger phase. At TOM hydrochloric acid or sodium chloride solutions at pH of 1.0, tracer concentration of Po(IV) exist in the amionic forms [PoCLi(OH)] and [PoCl4(OH)2].-2... 

The first term in the right hand side of (24) is related to the fraction 7 of internal surface area (or active sites) located in the mesopores which can be blocked and, therefore, contains the textural par uneters. The second term is related to the surface area in the macropores, which are too laxge to be blocked and in which deactivation only occurs by site coverage. Equation (25) is derived in a straightforward way from (2) or (3) and was already encountered in (10) It is valid for constant gas phase composition only. 

If the Hamaker constant for the oil phase is close to that of water (as is the case) for the water/isopropyl myristate/water systems investigated by the authors (23) the effect of replacing part of the oil drop with water is not great in fact in a typical type A drop the effect of large internal droplet on attractive energies is found to be insignificant. Only when the internal droplet almost fills the whole diameter of the multiple drop is the influence of the internal phase noticeable. 

A more rigorous technique involves the use of internal standards. An internal standard is a compound that is similar in chemical structure and physical properties to the sample being analysed. The internal standard should be added to the sample in question before extraction or assay commences and is then present in the sample matrix throughout the subsequent assay In the assay of complex samples, some sample pre-treatment is usually required and the recovery of the sample from the extraction process may not be 100%. If an internal standard is used, losses in sample will be mirrored by similar losses in the standard and the ratio of sample to standard should remain constant. Internal standards are particularly used in chromatographic analysis (especially gas chromatography and high-performance liquid chromatography), where fluctuations in instrumental parameters (e.g. flow rate of mobile phase) affect accuracy... 

As the first application of these criteria, consider the problem of identifying the state of equilibrium in a closed, nonreacting multicomponent system at constant internal energy and volume. To be specific, suppose N moles of species 1, moles of species 2, and so on are put into an adiabatic container that will be maintained at constant volume, and that these species are only partially soluble in one another, but do not chemically react. What we would like to be able to do is to predict the composition of each of the phases present at equilibrium. (A more difficult but solvable problem is to also predict the number of phases that will be present. This problem is briefly considered in Chapter 11.) In the analysis that follows, we develop the equation that will be used in Chapters 10, 11, and 12 to compute the equilibrium compositions. 

Emulsion Liquid Membranes. Emulsion liquid membranes have been modeled by numerous researchers. Chan and Lee (77) reviewed the various models. The simplest representation characterizes the emulsion globule (membrane phase) as a spherical shell of constant thickness surrounding a single Internal phase droplet. This representation Is equivalent to assuming that the membrane and internal phase are well mixed. In practice, this Is usually a poor assumption. 

This means that the value of the constant is of course to be determined experimentally in each case, and that Stokes s law is only indicative, and may turn out 10 be wrong when the internal phase proportion is high. In any case. Stokes s law indicates that the approach of the drops would be facilitated and accelerated whenever the drop size or density difference increases, while it would be slowed down by an increase in external phase viscosity. 

Provided that the emulsion remains stable over the change, the drop size stays constant, as do other related properties. If the internal phase content is increased by adding some amount of thi.s phase (under constant stirring as along path i in Fig. 21, emulsion viscosity is expected to augment from the increase in internal phase content, although other effects would have to be taken into account, such as the efficiency of the stirring required to proceed with emulsification of the added internal phase, or the eventual production of a bimodal distribution that could result in a viscosity reduction. 

Details of the emulsion-preparation procediues are described in the same paper, although it is worth mentioning that the oil/water ratio was held constant [40/60 (w/w)], and that the LS and Kraft lignin concentrations are reported on the basis of the internal phase weight. 

Viseosity increases in the normal region in the direction of higher internal-phase ratio (at constant formulation), so that the viscosity maximum is just near the inversion-line vertical branches. On the other hand, the viscosity de-... 

At constant formulation and stirring, the water/oil ratio does affect the breaking-coalescence equilibrium. It is found that the observed variation depends upon the oil viscosity (171). For instance, in the case of 0/W emulsions, and when the oil viscosity is 5—10 mPa.s or higher, the drop size always decreases as increasing amounts of internal phase are added, although the same stirring protocol is applied. With extremely low-viscosity oils, the drop size starts increasing as the oil content increases from zero to say 40 or 50%, then it decrease as in the previous case of more viscous oils (183). In both cases, and when the internal oil phase content reaches 70 or 80%, i.e., near the ver-... 

Another way to attain a fine drop emulsion at this (white circle) position is to start with a much higher internal-phase content OAV emulsion, e.g., where the (black circle) origin of arrow (2) is located. In such a position, the emulsification is carried out at low shear in a very efficient way, to produce a viscous fine emulsion (183). This emulsion is then diluted with an aqueous solution of hydrophilic surfactant (to maintain the SAD constant) along the arrow (2) path until the final (white circle) location is reached. Also in this case, the final emulsion attained will exhibit a drop size much smaller than the emulsion that could be attained from a pre-equilibrated system directly in these (white circle) conditions. 

The racemate of the monomer was found to be iso-stractural with its enan-tiomorph, as it crystallizes in the same space group as a sohd solution, where the sec-butyl groups of opposite handedness are disordered. However, an accurate determination of the phase diagram between S(+)l and R(—)1, under equilibrium conditions, revealed the presence of an immiscibiUty gap in the range 60 40 to 40 60 [49]. Therefore, the crystallization of a large batch of racemic 1 under thermodynamically controlled conditions was associated with the precipitation of equal amounts of crystals of either handedness, with a constant internal composition, as defined by the boundaries of the eutectic. The presence of an immiscibihty gap imphes two different effects on the one hand it interferes with the requirements of an absolute asymmetric synthesis from racemic 1, while on the other hand it provides a most efficient way in which to amplify chirahty via the crystalhzation of nonracemic mixtures of compositions, which are outside the boundaries of the eutectic. Enantiopure oHgomers could be generated from mixtures of molecular composition R S of 60 40 [50]. 

---