Single-liquid approximation

Considering a ternary system of two polymers, 2 and 3, and a solvent, 1, the Flory-Huggins free energy parameter Xi( 23) i-n the single liquid approximation is given by (3)... 

A study involving a multicomponent fibrous system can now be examined in terms of the above analysis. The tension required to maintain equilibrium between the crystalline and amorphous phases of cross-linked collagen has been deter-mined.(44) In these experiments the fiber is immersed either in a large excess of pure water or in an aqueous KCNS solution. The experiments were conducted over a wide temperature range. The equilibrium force at a given temperature was approximately independent of the total sample length and consequently the extent of the transformation. When the supernatant phase consists solely of pure water, the system is univariant and the aforementioned result is to be expected. However, the results obtained when the supernatant phase contains two components indicates that the single-liquid approximation is also valid in this particular case. 

The literature offers numerous calculation models for mass transfer in single liquid particles. However, they provide only a rough approximation to reality in industrial columns, since the processes in droplet swarms are much more complicated, especially when pulsing and rotating motion are superimposed. For estimation, the following relationships are sufficient ... 

The compositions of the vapor and liquid phases in equilibrium for partially miscible systems are calculated in the same way as for miscible systems. In the regions where a single liquid is in equilibrium with its vapor, the general nature of Fig. 13.17 is not different in any essential way from that of Fig. I2.9< Since limited miscibility implies highly nonideal behavior, any general assumption of liquid-phase ideality is excluded. Even a combination of Henry s law, valid for a species at infinite dilution, and Raoult s law, valid for a species as it approaches purity, is not very useful, because each approximates real behavior only for a very small composition range. Thus GE is large, and its composition dependence is often not adequately represented by simple equations. However, the UNIFAC method (App. D) is suitable for estimation of activity coefficients. 

The collision-induced polarizability is best manifested if it is the only reason for the phenomenon observed. In such a case the intermolecular interactions break the selection rules of isolated molecules and a process forbidden in the single-molecule approximation becomes allowed in concentrated gas or liquid. For example, it occurs when we observe the depolarized component of light... 

This expression has been used to describe uniaxial restricted molecular reorientation in liquid crystals [7.11, 7.41]. The above series expansion converges rapidly generally, only the first five terms are required [7.43]. Using the anisotropic viscosity model to describe the a— and / — motion, in the single exponential approximation it is found that... 

Efficient interaction of two or more components occurs if they are combined in a single liquid phase. The Diels-Alder reaction between (2 , 4 )-2,4-hexadien-l-ol and maleic anhydride occurs without solvent as the two components melt together over approximately 3 min [6], This reaction can be performed safely at a 5 mmole scale in a beaker, but doubling the reaction scale or performing the reaction in a smaller vessel causes an extremely exothermic reaction due to the lack of solvent as a heat sink. 

Predictions of the single-phase particle bed model were confronted with experimental observations of gas-fluidized beds in Chapter 9. The assumption of pp pf, which enabled the fluid-phase equations to be effectively removed from consideration in this case, would appear to render this approximation inappropriate for most cases of liquid fluidization. The above results, however, show that the single-phase approximation leads to stability predictions in reasonable harmony with the full two-phase model for liquid fluidization over a substantial range of particle density, down to perhaps three times that of the fluid. In this section we confront reported experimental observations relating to the stability of... 

Using the ternary tie-line data and the binary VLE data for the miscible binary pairs, the optimum binary parameters are obtained for each ternary of the type 1-2-i for i = 3. .. m. This results in multiple sets of the parameters for the 1-2 binary, since this binary occurs in each of the ternaries containing two liquid phases. To determine a single set of parameters to represent the 1-2 binary system, the values obtained from initial data reduction of each of the ternary systems are plotted with their approximate confidence ellipses. We choose a single optimum set from the intersection of the confidence ellipses. Finally, with the parameters for the 1-2 binary set at their optimum value, the parameters are adjusted for the remaining miscible binary in each ternary, i.e. the parameters for the 2-i binary system in each ternary of the type 1-2-i for i = 3. .. m. This adjustment is made, again, using the ternary tie-line data and binary VLE data. 

Furthermore, the extent to which we can effect a separation depends on the distribution ratio of each species in the sample. To separate an analyte from its matrix, its distribution ratio must be significantly greater than that for all other components in the matrix. When the analyte s distribution ratio is similar to that of another species, then a separation becomes impossible. For example, let s assume that an analyte. A, and a matrix interferent, I, have distribution ratios of 5 and 0.5, respectively. In an attempt to separate the analyte from its matrix, a simple liquid-liquid extraction is carried out using equal volumes of sample and a suitable extraction solvent. Following the treatment outlined in Chapter 7, it is easy to show that a single extraction removes approximately 83% of the analyte and 33% of the interferent. Although it is possible to remove 99% of A with three extractions, 70% of I is also removed. In fact, there is no practical combination of number of extractions or volume ratio of sample and extracting phases that produce an acceptable separation of the analyte and interferent by a simple liquid-liquid extraction. 

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