Contact angle estimation

EXAMPLE 6.3 Determination of Heat of Immersion from Surface Tension and Contact Angle. Estimate the heat of immersion for the system for which y and 6 are 22 mJ m 2 and 30°,... 

When air pockets are present on a rough surface, the Cassie-Baxter equation can also be applied to the contact angle estimate of a water drop on such a surface. Since the contact angle of water in air is equal to 180°, by taking 02 = 180°, which corresponds to (cos ft = -1), Equation (676) then becomes... 

Schmidt s correlation is sensitive to the contact angle estimate [both in Eqs. (8.35) and (8.38)]. Table 8.5 lists the range of applicability of Schmidt s correlation. The Schmidt correlation is bas on data for Raschig and Pall rings (102), mainly for positive-surface-tension systems (58),... 

Ruch and Bartell [84], studying the aqueous decylamine-platinum system, combined direct estimates of the adsorption at the platinum-solution interface with contact angle data and the Young equation to determine a solid-vapor interfacial energy change of up to 40 ergs/cm due to decylamine adsorption. Healy (85) discusses an adsorption model for the contact angle in surfactant solutions and these aspects are discussed further in Ref. 86. 

The critical surface tension concept has provided a useful means of summarizing wetting behavior and allowing predictions of an interpolative nature. A schematic summary of 7 values is given in Fig. X-10 [123]. In addition, actual contact angles for various systems can be estimated since )3 in Eq. X-38 usually has a value of about 0.03-0.04. 

Here, x denotes film thickness and x is that corresponding to F . An equation similar to Eq. X-42 is given by Zorin et al. [188]. Also, film pressure may be estimated from potential changes [189]. Equation X-43 has been used to calculate contact angles in dilute electrolyte solutions on quartz results are in accord with DLVO theory (see Section VI-4B) [190]. Finally, the x term may be especially important in the case of liquid-liquid-solid systems [191]. 

Using the data of Table X-2, estimate the contact angle for benzene on aluminum oxide and the corresponding adhesion tension. 

A number of methods have been developed for estimating advancing contact angles of Hquids on surfaces. These methods can be used to estimate wettabUity of a given Hquid—soHd system. 

Extrapolating this line to cos0a = 1 (contact angle = 0°) gives the surface tension required for a Hquid to wet the soHd. Given a surface of known CST and a Hquid of known surface tension, an estimate of advancing contact angles can be made. 

There are several other methods for estimating the contact angles that specific Hquids wiU make on surfaces. These methods depend upon breaking... 

It is easy to estimate the undercooling that we would need to get heterogeneous nucleation with a 10° contact angle. From eqns (7.11) and (7.3) we have... 

It should be noted that one may obtain an estimate for the surface energy of a solid from a single contact angle measurement by combining Eq. 9 or Eq. 11 with Eq. 3. One then has ... 

Section 4.1 briefly describes some of the commonly employed experimental tools and procedures. Chaudhury et al., Israelachvili et al. and Tirrell et al. employed contact mechanics based approach to estimate surface energies of different self-assembled monolayers and polymers. In these studies, the results of these measurements were compared to the results of contact angle measurements. These measurements are reviewed in Section 4.2. The JKR type measurements are discussed in Section 4.2.1, and the measurements done using the surface forces apparatus (SFA) are reviewed in Section 4.2.2. 

Summary of methods for estimating surface energy from the contact angle data... 

The adsorption of gas onto a solid surface can also be used to estimate surface energy. Both inverse gas chromatography (IGC) and isotherm measurement using the BET method [19] have been used. Further discussion and detailed references are given by Lucic et al. [20] who compare the application of IGC, BET and contact angle methods for characterising the surface energies of stearate-coated calcium carbonate fillers. 

The surface forces apparatus (Section 2.3) enables the estimation of a surface energy term, Fq (Eq. 9), providing sufficiently smooth surfaces can be produced. In recent years Chaudhury, Pocius and colleagues have made a valuable contribution to the field of adhesion by developing the technique to study energies of adhesion and of surface energies of polymers [81-85]. These SFA results provide alternatives to values based on traditional destructive tests or contact angle measurements. 

Induction period measurements can also be used to determine interfacial tensions. To validate the values inferred, however, it is necessary to compare the results with an independent source. Hurley etal. (1995) achieved this for Cyanazine using a dynamic contact angle analyser (Calm DCA312). Solid-liquid interfacial tensions estimated from contact angle measurements were in the range 5-12 mJ/m which showed closest agreement with values (4—20mJ/m ) obtained from the log-log plots of induction time versus supersaturation based on the assumption of — tg. 

When the contact angle is close to r/2 (for example, for the system water/steel 0 0.45 r), the ratio H/ro is small, we estimate the order of magnitude of the terms in Eqs. (9.2-9.4) and conditions (9.5-9.7). Choosing the meniscus as characteristic scales of length in the longimdinal and transversal directions H and ro, respectively, we obtain... 

Consider a liquid-solid system for which the contact angle is close to 90° (for example, the contact angle for the water-steel system is 70° < 0 < 90° (Grigoriev and Zorin 1982)). The projections of the velocity vector v on x-, y-, z-axes are M = v sin0, v = w = v cos0. For the surface, which is weakly bent, cos 0 v = w. Analogously,... 

In this section the influence of the pressure in the capillary and the heat flux fluctuations on the stability of laminar flow in a heated capillary tube is analyzed. All the estimations performed in the framework of the general approach and developed in the previous section are kept also in the present cases. Below we will assume that the single cause for capillary pressure oscillations is fluctuations of the contact angle due to motion of the meniscus, whereas heat flux oscillations are the result of fluid temperature fluctuations only. 

For aq.KOH on mica, the dependence of the effective contact angle on droplet height is mnch weaker than that for the aq.KOH-graphite system. The estimated Hamaker constant of the van der Waals interaction for this system is -1.9 X 10 ° J (repnlsive), and the fitting gives ... 

Equation (52) allows us to estimate the impact of viscoelastic braking on the capillary flow rate. As an example, we will consider that the liquid is tricresyl phosphate (TCP, 7 = 50 mN-m t = 0.07 Pa-s). The viscoelastic material is assumed to have elastic and viscoelastic properties similar to RTV 615 (General Electric, silicone rubber), i.e., a shear modulus of 0.7 MPa (E = 2.1 MPa), a cutoff length of 20 nm, and a characteristic speed, Uo, of 0.8 mm-s [30]. TCP has a contact angle at equilibrium of 47° on this rubber. 

The predominant form of released petroleum products is a liquid that is immiscible with water this is called the free product (in this section it will be referred to as oil). The behavior of water and oil in soil depends on the interaction of the three phases water, oil, and soil. The affinity of water or oil with the soil can be estimated by establishing the contact angle of oil/water/soil triple line. 

Young s equation is a plausible, widely used result, but experimental verification is often rendered difficult e.g., the two terms which involve the interface between the solid and the two other phases cannot be measured independently. Furthermore, many complications can arise with contact angle measurements ys values of ionic solids based on contact angle measurements are different from those estimated from solubility (Table 6.1) (cf. Table A.4.1). 

Gurau et al. [194] proposed a method to estimate the internal contact angle to water by combining the Washburn technique with the Owens-Wendt... 

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