Cloud curve

General Comments. The (P, T) cloud curve for the PIB of > -2 xlO dissolved in 2-methylbutane agreed,within experimental error, with other values reported in the literature (6,2.) The slope of the curve differed from other results but this could have been caused by the molecular weight distribution exhibited by the sample used in this study. The cloud point curve for an infinite molecular weight polymer, i.e. 0 conditions, was established from our measurements and from literature data and is shown plotted in Figure 2. It can be seen that 0 increase as a function of applied pressure with a slope (dT/dP)c of 0.56. 

GAR Garcia Sakai, V., Higgins, J.S., and Trasler, Cloud curves of polystyrene or... 

Figure 6-16. Surface of binodals of a ternary liquid system with a two-phase region, CC5C, Connecting line for critical points AA2C5B, quasibinary line (cloud curve) (R. Koningsveld).

The main characteristics of type V phase behaviour compared to type I are the region of liquid-liquid immiscibility, the so-called cloud curve, close to the critical point of the more volatile component (the short-chain n-alkane), and the appearance of a three-phase line (L-L-V) close to the vapour pressure curve of the same component (see figure 1). Since demixing of the two components is the main difference between these two types of phase behaviour, a criterion to identify liquid-liquid immiscibility is developed. Such a criterion is introduced in the next section. A simplified version of the statistical associating fluid theory (SAFT-HS) is used to model the n-alkane molecules. This approach offers a good representation of the entire n-alkane series (Galindo et al., 1996) incorporating an intermolecular parameter, which describes the n-alkane size. In this... 

The temperature of the intersection of the baseline (reading of absorbance of unheated solution) with the tangent to the cloud curve drawn in the inflection... 

GAR Garcia Sakai, V., Higgins, J.S., and Trasler, J.P.M., Cloud curves of polystyrene or poly(methyl methacrylate) or poly(styrene-co-methyl methacrylate) in cyclohexanol determined with a thermo-optical apparatus, J. Chem. Eng. Data, 51, 743, 2006. 

Figure 4 illustrates the phase-equilibrium curves for mixtures of ethylene and two LDPEs of different molecular weights [16]. The cloud curves give the pressure at the cloud point when the mixture starts to separate. The coexistence curves give the composition of the phases. The left branch of a coexistence curve shows the composition of the ethylene-rich light phase and the right branch gives the composition of the polymer-rich dense phase. 

Outside the cloud curve, the mixture is homogeneous (single phase). Because polymers have a molecular-weight distribution, a phase separation in mixtures of polymers is always accompanied by a fractionation. As a result, the polymer in the polymer-rich phase has a higher polydispersity than the polymer in the ethylene-rich phase. 

The distribution of tracer molecule residence times in the reactor is the result of molecular diffusion and turbulent mixing if tlie Reynolds number exceeds a critical value. Additionally, a non-uniform velocity profile causes different portions of the tracer to move at different rates, and this results in a spreading of the measured response at the reactor outlet. The dispersion coefficient D (m /sec) represents this result in the tracer cloud. Therefore, a large D indicates a rapid spreading of the tracer curve, a small D indicates slow spreading, and D = 0 means no spreading (hence, plug flow). 

In Figure 6.16, the region originally occupied by the gas cloud is shaded, and the position and shape of the shock wave and the contact surface at different times following the explosion are shown as solid and dashed curves. The shape of the shock wave is almost elliptical, with ellipticity decaying to sphericity as the shock gradually degenerates into an acoustic wave. 

Radiation heat flux is graphically represented as a function of time in Figure 8.3. The total amount of radiation heat from a surface can be found by integration of the radiation heat flux over the time of flame propagation, that is, the area under the curve. This result is probably an overstatement of realistic values, because the flame will probably not bum as a closed front. Instead, it will consist of several plumes which might reach heights in excess of those assumed in the model but will nevertheless probably produce less flame radiation. Moreover, the flame will not bum as a plane surface but more in the shape of a horseshoe. Finally, wind will have a considerable influence on flame shape and cloud position. None of these eflects has been taken into account. 

When two atoms approach each other so closely that their electron clouds interpenetrate, strong repulsion occurs. Such repulsive van der Waals forces follow an inverse 12th-power dependence on r (1/r ), as shown in Figure 1.13. Between the repulsive and attractive domains lies a low point in the potential curve. This low point defines the distance known as the van der Waals contact distance, which is the interatomic distance that results if only van der Waals forces hold two atoms together. The limit of approach of two atoms is determined by the sum of their van der Waals radii (Table 1.4). 

We often refer to Heitler and London s method as the valence bond (VB) model. A comparison between the experimental and the valence bond potential energy curves shows excellent agreement at large 7 ab but poor quantitative agreement in the valence region (Table 4.3). The cause of this lies in the method itself the VB model starts from atomic wavefunctions and adds as a perturbation the fact that the electron clouds of the atoms are polarized when the molecule is formed. 

The critical point (Ij of the two-phase region encountered at reduced temperatures is called an upper critical solution temperature (UCST), and that of the two-phase region found at elevated temperatures is called, perversely, a lower critical solution temperature (LCST). Figure 2 is drawn assuming that the polymer in solution is monodisperse. However, if the polymer in solution is polydisperse, generally similar, but more vaguely defined, regions of phase separation occur. These are known as "cloud-point" curves. The term "cloud point" results from the visual observation of phase separation - a cloudiness in the mixture. 

Fig. 16-4 pH sensitivity to SO4- and NH4. Model calculations of expected pH of cloud water or rainwater for cloud liquid water content of 0.5 g/m. 100 pptv SO2, 330 ppmv CO2, and NO3. The abscissa shows the assumed input of aerosol sulfate in fig/m and the ordinate shows the calculated equilibrium pH. Each line corresponds to the indicated amoimt of total NH3 + NH4 in imits of fig/m of cloudy air. Solid lines are at 278 K, dashed ones are at 298 K. The familiar shape of titration curves is evident, with a steep drop in pH as the anion concentration increases due to increased input of H2SO4. (From Charlson, R. J., C. H. Twohy and P. K. Quinn, Physical Influences of Altitude on the Chemical Properties of Clouds and of Water Deposited from the Atmosphere." NATO Advanced Research Workshop Acid Deposition Processes at High Elevation Sites, Sept. 1986. Edinburgh, Scotland.)... 

Fig. 1.16 Calculated radius of a bubble in a bubble cloud as a function of time for one acoustic cycle at 29 kHz and 2.36 bar in frequency and pressure amplitude of ultrasound, respectively. The ambient radius is 5 pm. The dotted curve is the calculated result for an isolated bubble. The dashed one is the calculated result with the interaction only with neighboring bubbles. The solid one is the calculated result taking into account all the interactions with surrounding bubbles. Reprinted figure with permission from Yasui K, Iida Y, Tuziuti T, Kozuka T, Towata A (2008) Strongly interacting bubbles under an ultrasonic horn. Phys Rev E 77 016609 [http /Aink.aps.org/abstract/PRE/v77/ e016609]. Copyright (2008) by the American Physical Society...

The extinction curve of light which has passed through dust clouds tells us which particles are present in the cosmic dust ... 

Fig. 31 Phase diagram of type III for PVME in water with two different molar masses hand-drawn curves). T em Mw = 28000 gmol-1 ( ) and Mw = 147000 gmol-1 (A). Peak temperature Tmax Mw = 28 000 g mol-1 ( ) and Mw = 147 000 g mol-1 (T). Cloud point for Mw = 147000gmol-1 ( ). Scanning rate 0.1 °Cmin-1. (Reprinted with permission from Ref. [161] copyright 1997 American Chemical Society)...

---