Surface tension calculation methods

If the radius of the capillary is large, so that (r/a) > 0.05, then the Basforth-Adams equation (Equation (481)) or the Lane equations (Equations (482) and (483)) can also be used in the surface tension calculation from the maximum bubble pressure method. This method can also be used to determine the surface tension of molten metals. It has been a popular method in the past, but now it is not very common in surface laboratories because of its poor precision. 

Experiments [3, p. 45] indicate that the surface tension calculated from drop weights on burettes by means of Eq. 17.7 must be multiplied by a factor which ranges up to 1.5 to agree with those obtained by the most reliable methods. Assuming that this is entirely due to the shape of the droplet just before breakaway, calculate the angle that the drop s surface makes with the vertical. 

Relatively new are the developments of microfluidic surface or interfacial tension methods. Such methods offer the potential for rapid, online measurements on small volume samples. Typically, use is made of a property change (such as droplet deformation or pressure drop) associated with fluid flow through some kind of constriction in a microchannel. The fundamental principles are usually the same as in the examples just given above, such as shape or pressure changes. If the device is used to generate bubbles, then the bubble formation frequency can be used as the basis for surface tension calculation. In a multiple-channel device, multiple bubbles or droplets are usually sensed simultaneously. These kinds of approaches have been applied to the determination of both surface and interfacial tensions [20-22]. 

Surface Tension Calculation in VOF Method Modeling interfacial tension effects is important because it is a potentially large force which is concentrated on the interface. There are two different approaches to modeling surface tension forces. The first mie is continuum surface force (CSF) defined as... 

We see from these data that the values of surface tension calculated from known forces of adhesion (which are equal to the capillary forces) are low in comparison with the actual values. The point is that these investigators failed to account for the disjoining pressure of the thin layer of liquid (see Fig. IV.6.c), which weakens the capillary interaction. This is why their method for determining surface tension by measurement of adhesive force did not give accurate results. 

The time dependent surface tension decay was measured according to the drop-volume technique as outlined by Tornberg [18,19]. The automatization procedure according to Arnebrant and Nylander [20] was employed. In this method surface tension reduction by macromolecules during adsorption at the air-water interface is measured by formation of drops of certain volumes. Time for detachment of the droplets is recorded. Surface tension calculated [19, 20] was plotted against detachment time and the value attained after 2000 seconds was set as the equilibrium value. The surface tension of the solutions is still decreasing after this period of time, but the rate of decrease is small, less than 0.05 mNm" per 100 seconds. The maximum error in surface tension values is 1.5%. 

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... 

A. Ghoufi, F. Goujon, V. Lachet, and P. Malfreyt,/. Chem. Phys., 128, 154716 (2008). Multiple Histogram Reweighting Method for the Surface Tension Calculation. 

The harmonic mean equation is generally considered to be applicable to low surface tension materials such as organic polymers and liquids. If y and y are known for two liquids, and the contact angles of those liquids on the solid of interest are measured, equation 36 produces two simultaneous equations that can be solved to find the surface tension and polarity of a solid polymer surface. Numerous assumptions have been made in developing the theory of fi actional polarity. For example, it ignores the possibility of induced polarity at the interface between polar and nonpolar materials (82). These assumptions limit the application of equation 36 to systems where at least one and preferably both of the components are relatively nonpolar. The theory breaks down when interfacial interactions lead to molecular rearrangements at the interface between solid and liquid. In addition, it was foimd that pairs of liquids with similar dispersive and polar components of surface tension gave umeasonable results for the substrate surface tension calculated by the harmonic mean method (83). 

Surface tension calculated by harmonic-mean method. 

The surface tension component method assumes that surface tension can be partitioned into different components, which address different intermolecular interactions individually. The overall surface tension will be the sum of all the components according to the linear free energy relationship. In the original Fowkes method [14], only the dispersion interaction is considered. The component method has been subsequentiy extended to include polar component and later divided the polar component into dipolar interaction and H-bonding interaction. The vOCG model appeared as a refined version of the surface tension component methodology. It assumes the existence of both additive and nonadditive components. The Lifshitz-van der Waals component (/ ) is additive, and the electron donor and acceptor components (7 and 7" ) are nonadditive. The solid surface tension (7sv) can be calculated by using three Uquids with known y, y and y values. Since this is a semiempirical approach, the calcu-... 

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

General hydrodynamic theory for liquid penetrant testing (PT) has been worked out in [1], Basic principles of the theory were described in details in [2,3], This theory enables, for example, to calculate the minimum crack s width that can be detected by prescribed product family (penetrant, excess penetrant remover and developer), when dry powder is used as the developer. One needs for that such characteristics as surface tension of penetrant a and some characteristics of developer s layer, thickness h, effective radius of pores and porosity TI. One more characteristic is the residual depth of defect s filling with penetrant before the application of a developer. The methods for experimental determination of these characteristics were worked out in [4]. 

The surface tension of a liquid is determined by the drop weight method. Using a tip whose outside diameter is 5 x 10 m and whose inside diameter is 2.5 x 10 m, it is found that the weight of 20 drops is 7 x 10 kg. The density of the liquid is 982.4 kg/m, and it wets the tip. Using r/V /, determine the appropriate correction factor and calculate the surface tension of this liquid. 

This equation describes the additional amount of gas adsorbed into the pores due to capillary action. In this case, V is the molar volume of the gas, y its surface tension, R the gas constant, T absolute temperature and r the Kelvin radius. The distribution in the sizes of micropores may be detenninated using the Horvath-Kawazoe method [19]. If the sample has both micropores and mesopores, then the J-plot calculation may be used [20]. The J-plot is obtained by plotting the volume adsorbed against the statistical thickness of adsorbate. This thickness is derived from the surface area of a non-porous sample, and the volume of the liquified gas. 

The simplified method of calculation outhned includes no allowance for the effect of surface tension. Stroebe, Baker, and Badger (loc. cit.) found that by adding a small amount of surface-... 

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

Recently, Samec et al. [38] have investigated the same system by the video-image pendant drop method. Surface tension data from the two studies are compared in Fig. 2, where the potential scale from the study [36] was shifted so that the positions of the electrocapillary maxima coincide. The systematic difference in the surface tension data of ca. 3%, cf. the dotted line in Fig. 2, was ascribed to the inaccurate determination of the drop volume, which was calculated from the shape of the drop image and used further in the evaluation of the surface tension [38]. A point of interest is the inner-layer potential difference A (pj, which can be evaluated relative to the zero-charge potential difference A cpp c by using Eq. 

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