Surface tension Parachor method

The parachor method is one of the most commonly used correlations for the surface tensions. The method was originally suggested by MacLeod [50] and Sugden [51] for a singlecomponent fluid and was extended to multicomponent systems by Weinaug and Katz [52]. An expression for the surface tension in this method is... 

The surface tension is calculated starting from the parachor and the densities of the phases in equilibrium by the Sugden method (1924) J... 

Liquid surface tension is calculated using the Sugden Parachor method [242]. Neglecting vapor density, surface tension for the liquid mixture is ... 

If reliable values of the liquid and vapour density are available, the surface tension can be estimated from the Sugden parachor which can be estimated by a group contribution method, Sugden (1924). 

For pure liquids, an empirical estimation method for surface tension is that of McLeod and Sudgen, based on the parachor (P), which be calculated from the chemical groups of the molecule [13]. 

Ixspcr has compiled the xurlave icnsiun ol ucetaldchsdc. propi waldehydc. and butyraldehyde at various tempera lure. I he surface tension ot formaldehyde wav estimated h the method described in Appendix A This method relate surface tension lo (he parachor. density, and molcculur weight I hr error is less than 50r. 

Table 8.2 compares the experimental values of the surface tension of polymers (obtained by different methods) and the calculated values, the latter being obtained by means of the parachor. The discrepancies between the different experimental values are reasonably small. The calculated values are, with a few exceptions, in reasonable agreement with the experimental values. 

The surface tension of pure ozone was determined by the capillary rise method in the apparatus used for viscosity measurements. The ratio of the capillary rise of liquid ozone to that of water at 20° C. was measured and zero contact angle was assumed. Results at —183° and —195.5° C. are given in Table III. The parachor for... 

Liquid Mixtures Compositions at the liquid-vapor interface are not the same as in the bulk liquid, and so simple (bulk) composition-weighted averages of the pure-fluid values do not provide quantitative estimates of the surface tension at the vapor-liquid interface of a mixture. The behavior of aqueous mixtures is more difficult to correlate and estimate than that of nonpolar mixtures because small amounts of organic material can have a pronounced effect upon the surface concentrations and the resultant surface tension. These effects are usually modeled with thermodynamic methods that account for the activity coefficients. For example, a UNIFAC method [Suarez, J. T. C. Torres-Marchal, and P. Rasmussen, Chem. Eng. Set, 44 (1989) 782] is recommended and illustrated in PGL5. For nonaqueous systems the extension of the parachor method, used above for pure fluids, is a simple and reasonably effective method for estimating a for mixtures. 

The surface tension, interfacial tension and adhesion phenomena will be discussed, and a new correlation for the molar parachor will be presented, in Chapter 7. The calculation of the interfacial tension from the surface tensions of the components will also be discussed, and shown to be in need for significant improvements. In this context, an introduction will also be provided to advanced numerical simulation methods that are becoming increasingly useful in modeling the interfacial phenomena and phasic behavior of polymer-containing systems. 

From Surface Tension Coefficients Among the different approaches used to calculate the surface tension coefficient, Vj, the most useful seems to be the parachor method [Sugden, 1924 Van Krevelen, 1976 Wu, 1982]. This parameter was defined as [Sugden, 1924] ... 

The example discussed suggests another more realistic formulation of the equilibrium problem. Under the conditions of the previous problem, instead of P, and Pg, we specify the pressure in one phase, say, Pg. The system of Eqs. (8) and (9) is completed by the Laplace equation in the form of Eqs. (23). In the second equation, (23), the dependence /(/ ) is supposed to be known from the geometry of the porous space. The surface tension and the wetting angle are defined as known functions of the thermodynamic conditions (e.g., the surface is assumed to be wet by the condensate and the surface tension is calculated by the parachor method). The volumetric hquid... 

The parachor method gives, according to some estimates, a good order-of-magnitude value of the surface tension, but the deviations for realistic mixtures may reach a few tens of percent [46,53,54]. That is why several improvements of the method have been developed. The first type of improvement is modification of the value of a in order to improve the agreement with experiments (and, in this case, a may be taken to be variable [53]) or to approach the scaling law characteristic of the surface tension close to the critical point [55]. Another way is the modification of the values of the parachors. The parachors are usually taken from the standard tables but their correlations with the critical properties are also available [46,47]. Different types of the parachor-like expression have also been proposed [55-57] ... 

Figure 8 expresses the dependence of the surface tension, calculated by the parachor method, on the distance from the dew point. The values of surface tension vary significantly with this distance in the region of retrograde condensation and less significantly (but still noticeably) in the region of normal condensation. Variation of the surface tension is due to the fact that... 

The dependence of the Kelvin radius on the relative pressure in the retrograde region is presented in Fig. 16. Unlike the capillary pressure, the Kelvin radius depends monotonously on the dew-point pressure, because it is mostly affected by the values of the surface tension a. These values (estimated by the parachor method) show a high variation 1.579 mN/m for Pj = 80 bar, 0.734 mN/m for Pj = 100 bar, and 0.206 mN/m for Pj = 120 bar. The variation of the ratio V i/Vi is not too strong. 

When not available, liquid surface tensions (pure compounds and solutions) can be estimated using predictive methods like those based on parachors and group contributions, solubility parametes (including Hansoi solubility parameters) and corresponding states. Alternatively, they can be estimated from thermodynamic models like UNIFAC and SAFT combined with the gradient or the density functional theories. For a review of the latter, see Kontogeorgis and Folas (2010). Some of the most important direct methods for estimating surface tension arc briefly described here. 

Example 3.2. Estimation of surface tension using the Parachor method. 

Estimate, using the parachor method of McLeod-Sugden, the surface tension of liquid isobutyric acid at 333 K. The liquid density is 0.912 g cm , the molecular weight is 88.107 g moF and it can be assumed that the liquid density is much higher than the vapour density. 

When not available, liquid surface tensions (pure compounds and solutions) can be estimated using predictive methods like those based on parachors and group contributions, solubility parameters (including Hansen parameters) and corresponding states. 

Problem 3.1 Estimation of the surface tension using the corresponding states method Estimate, using the corresponding states method, the surface tension of liquid ethyl mercaptan at 303 K. The critical temperature is 499 K, the boiling point temperature is 308.2 K and the critical pressure is 54.9 bar. Compare the result to the experimental value (22.68 mN m ) and the estimation using the parachor method (which results in a deviation of 9.1%). 

Problem 3.2 Estimation of the surface tension of liquid mixtures using the parachor method (data from Hammkk and Andrew (1929))... 

Estimate, using the parachor method for mixtures (both the fuU and the approximate method), the surface tension of a liquid mixture having a density of... 

From an application point of view, linear relationships allow for the simple prediction of the physical bulk properties from linear equations (see above). Moreover, they should allow for the prediction of many properties from group contribution methods. For single (pure) ionic liquids, this approach has been impressively shown by Deetlefs et al. [119]. For example, the parachor P, [120, 121] which correlates surface tension a to density p irrespective of temperature, can be obtained experimentally (1) or from a group contribution approach [122]. It can be used to predict either a ox p from existing data collections (M = molar mass) ... 

Table 2 shows that the parachors of pure ionic liquids calculated from density and surface tension data and the parachors estimated by the group contribution method agree very well [122]. Similarly, the molar refraction Rm,est was estimated and used to determine the refractive index R est by (2) (Lorentz-Lorenz equation), which is also compared to Ri,exp in Table 2 [123] ... 

Surface tension measurements were used for investigating molecular structures through parachor values. The method is no longer in use. 

In principle, therefore, Eq. (6.16) may be inverted to predict the surface tension of RTILs a = Pa/V), but this procedure makes the predicted a very sensitive to the values of the parachor (see the discrepancies in reported values mentioned above) and the molar volume, because of the fourth power dependence. Therefore this apparently simple method according to Lemraski and Zobeydi [236] is not recommended for the estimation of the unknown surface tension of RTILs. 

Lemraski EG, Zobeydi R (2014) Applying parachor method to the prediction of ionic liquids surface tension based on modified group contribution. J Mol Liq 193 204—209... 

Various paths have been used to circumvent the difficulty. The simplest is to obtain Yg extrapolation of the surface tensions of the polymer melt as a function of temperaturell (for data on surface and interfacial tensions of polymer melts see reference 12).Calcula-tions based on the parachors have also been undertakenl3, Other methods have been used to estimate the surface energy of polymers from various molecular properties (e.g., reference 14). 

Three other methods have been widely used to estimate polymer melt surface tensions. The oldest of these methods is based on the parachor method first proposed for small molecules by Sugden. ... 

Figures 3 and 4 compare calculated surface tensions of the present theory. Equation (6), with those of the parachor method. Equation (10), the modified solubility parameter method. Equation 11, the corresponding states relation. Equation 12, and with...

More and more publications have reported the physicochemical properties of some ILs, but the overall amount of property data measured by experimental methods are still not fulfilling the requirements for their broad apphcation, especially, due to the lack of data of IL homologues which would be helpful to improve the selection of more appropriate test candidates for different applications. A recently developed technical approach- based on the experimental data of densities and surface tensions of small number of ionic liquids -enables estimation and prediction of density, surface tension, molecular volume, molar volume, parachor, interstice volume, interstice fractions, thermal expansion coefficient, standard entropy, lattice energy and molar enthalpy of vaporization of their homologues. 

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