Good-Girifalco equations

If the initial spreading coefficient for liquid b spreading on liquid n is to be just zero, what relationship between ya and 7 is impair by the simple Girifalco-Good equation ... 

Calculate 7ab of Problem 5 using the simple Girifalco-Good equation, assuming to be 1.0. How does this compare with experimental data ... 

B. Semiempirical Models The Girifalco-Good-Fowkes-Young Equation... 

When Equations 5 and 7 are combined and rearranged, a Girifalco-Good-type equation results as" "... 

From the form of Equation 11, it is clear that the slope, a, will be independent of the aqueous surfactant solution. However, b in the intercept, 1 + (bA sw will not be zero in fact, it will not even be independent of the aqueous surfactant solution, Therefore, the conventional methods of Girifalco-Good plot analysis with an intercept of unity will not work for the detergency systems of interest in this work. The impediment to the Girifalco-Good analysis method is obvious from Figure 9, where no set of data points (3 or more) lies on a line passing... 

The Girifalco-Good equation for the soil-water interfacial tension... 

The quantity Yfw can be calculated by the simultaneous solution of two Girifalco-Good equations for Yfw ... 

The last quantity to be calculated is g, which can be determined from the Girifalco-Good equation for Y g as... 

In this version the relationship is called the Girifalco-Good-Fowkes equation. (We use a similar approach again in Chapter 10, e.g., see Equations (10.77) and (10.78), to determine the Hamaker constant for the van der Waals interaction forces.) Although we use y and yd interchangeably, it is important to recognize that yd values are determined by a particular strategy as illustrated in Example 6.5. 

EXAMPLE 6.5 Estimation of Interfacial Tensions Using the Girifalco-Good-Fowkes Equation. The following are the interfacial tensions for the various two-phase surfaces formed by n-octane (O), water (W), and mercury (Hg) for n-octane-water, y = 50.8 mJ m 2 for n-octane-mercury, y = 375 mJ m 2 and for water-mercury, y = 426 mJ m 2. Assuming that only London forces operate between molecules of the hydrocarbon, use Equation (100) to estimate y d for water and mercury. Do the values thus obtained make sense Take y values from Table 6.1 for the interfaces with air of these liquids. 

Finally, we turn our attention to the third contribution to van der Waals attraction, London (or dispersion) forces between a pair of induced dipoles. It will be noted that (at least) one permanent dipole is needed for the preceding sources of attraction to be operative. No such restriction is present for the London component. Therefore this latter quantity is present between molecules of all substances, whether or not they have a permanent dipole. These are the same forces that we considered in Chapter 6 when we discussed the Girifalco-Good-Fowkes equation. 

The same logic that we used to obtain the Girifalco-Good-Fowkes equation in Section 6.10 suggests that the dispersion component of the surface tension yd may be better to use than 7 itself when additional interactions besides London forces operate between the molecules. Also, it has been suggested that intermolecular spacing should be explicitly considered within the bulk phases, especially when the interaction at d = d0 is evaluated. The Hamaker approach, after all, treats matter as continuous, and at small separations the graininess of matter can make a difference in the attraction. The latter has been incorporated into one model, which results in the expression... 

Laplace equation A thermodynamic derivation Determining surface tension from the Kelvin equation Heat of immersion from surface tension and contact angle Surface tension and the height of a meniscus at a wall Interfacial tensions from the Girifalco-Good-Fowkes equation... 

The model of Girifalco, Good, and Fowkes has been extended to other interactions. For example, if we assume that the surface energies are the sum of van der Waals (dispersive) and polar interactions, one often uses the equation [272]... 

Equation 2.7 is also referred as the Girifalco-Good equation. Alternative equahons have been proposed by Owens and Wendt [34] ... 

How can we explain this phenomenon Before explaining its mechanism, let me briefly review a classical theoretical treatment for the wettability of the flat solid surface. It is commonly evaluated in terms of the CA, which is given by either Young equation [5] or Girifalco-Good (G-G) equation [6]. By combining Young and G-G equations, the CA can be simply expressed as follows ... 

In this table, is calculated from the Girifalco-Good-Fowkes-Young equation [20] using -hexadecane as the sole contact angle test liquid ... 

Equation (7.29) is known as the Girifalco-Good-Fowkes-Young equation. By using this relationship, the dispersion components of the solid or liquid surface tension could be evaluated. 

Notice that, unlike the Girifalco-Good equation, the cross term includes a contribution only from the dispersion forces. Thus, the Fowkes equation is based on the fundamental assumption that the crossinteraction term across the interface (work of adhesion) is due to dispersion forces alone. 

Many theories for estimating the interfacial tensions have been presented in Sections 3.5.1-3.5.3. The equations for the surface and interfacial tensions as well as for the work of adhesion are summarized in Table 3.6. Notice that the work of adhesion corresponds to the cross term of the interfacial tension expression (under the square roots), which reflects different contributions of intermolecular forces, according to the various theories (either the total surface tensions in Girifalco—Good and Neumann, only those contributions due to dispersion forces in Fowkes, due to both dispersion and specific forces in Owens-Wendt, separately dispersion, polar and hydrogen bonding ones in Hansen/Beerbower, or the van der Waals and as5mimetric acid/base effects in van Oss et ai). 

Appendix 3.2 The V parameter of the Girifalco-Good equation (Equation 3,16) for liquid-liquid interfaces. Data from Girifalco and Good (1957,1960)... 

A very simple theory for the interfacial tension that performs satisfactorily in some simple cases is given by a modified form of the Girifalco-Good equation (using a correction parameter equal to one) ... 

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