Contact Angle flat surfaces

As an extension of Problem 11, integrate a second time to obtain the equation for the meniscus profile in the Neumann method. Plot this profile as y/a versus x/a, where y is the vertical elevation of a point on the meniscus (above the flat liquid surface), x is the distance of the point from the slide, and a is the capillary constant. (All meniscus profiles, regardless of contact angle, can be located on this plot.)... 

If the contact angle is zero, as in Fig. XIII-8e, there should be no tendency to adhere to a flat surface. Leja and Poling [63] point out, however, that, as shown in Fig. XIII-8/, if the surface is formed in a hemispherical cup of the same radius as the bubble, then for step la, the free energy change of attachment is... 

This description is traditional, and some further comment is in order. The flat region of the type I isotherm has never been observed up to pressures approaching this type typically is observed in chemisorption, at pressures far below P. Types II and III approach the line asymptotically experimentally, such behavior is observed for adsorption on powdered samples, and the approach toward infinite film thickness is actually due to interparticle condensation [36] (see Section X-6B), although such behavior is expected even for adsorption on a flat surface if bulk liquid adsorbate wets the adsorbent. Types FV and V specifically refer to porous solids. There is a need to recognize at least the two additional isotherm types shown in Fig. XVII-8. These are two simple types possible for adsorption on a flat surface for the case where bulk liquid adsorbate rests on the adsorbent with a finite contact angle [37, 38]. 

To investigate the influence of swelhng of the substrate by the contacting liquid, the contact angle 6 of sessile drops of tricresylphosphate, TCP (drop volume 2 p,L, viscosity t = 70 cP, surface tension = 40.9 mN m ), has been measured as a function of time after deposition, t, on flat, smooth, horizontal surfaces of soft and rigid solids at 20°C. The method of measurement of contact angle is the same as in Section Ill.A. 

Equation (2-14) provides a way to calculate the liquid temperature in equilibrium with the ready-to-grow bubble if the saturation pressure or temperature, the value of B, and the cavity radius are known (Shai, 1967). Several modified versions of nucleation criteria have since been advanced. An example is the model proposed by Lorenta et al. (1974), which takes into account both the geometric shape of the cavity and the wettability of the surface (in terms of contact angle < >). Consider an idealized conical cavity with apex angle ip, and a liquid with a flat front penetrating into it (Fig. 2.3a). Assume that once the vapor is trapped in by the liquid front, the interface readjusts to form a cap with radius of curvature rn. Conservation of vapor... 

The measured contact angle of mercury on various samples can range from 112 to 170° [39], but for most applications the average value of 140° is used. It should be noted, however, that the accuracy of the pore radii measurement is limited by the accuracy of the contact-angle measurement [40]. Contact angles can readily be measured on flat surfaces or compacts of powders [6], and the measurement of contact angles with powder systems has also been reported [41]. 

While direct, this method is the most difficult experimentally due to the diminutive nature of fiber diameters and the uncertainty involved with contact angle measurements and hysteresis. The value i ) can also be measured on flat sheets of the fiber material but due to fabric finishes and different surface properties incurred during manufacture, the surface energetics of the sheet and fiber may be very dissimilar. Therefore, the value of co8i i was determined in the following manner from detergency data. The Kubelka-Munk Equation (12-13),... 

The value of the equilibrium contact angle (9) at the three-phase line (TPL) produced by a liquid droplet placed on a flat, solid substrate is determined by the balance of interfacial energies at each surface. Thomas Young derived an equation describing this situation in 1804 ... 

Wilhelmy (1863) suggested that the interfacial tension of liquids could be determined by measuring the maximum force required to pull a glass plate vertically from the interface. In his experiment, he was careful to ensure that the glass plate was extremely clean so that the angle of contact ((p) was relatively small or close to zero. The force, F, exerted on the plate raises the meniscus of the fluid above the level of the flat surface as shown in Figure D3.6.7. The mass of the liquid that is elevated above the fluid interface increases to some maximum value as F increases. Once the meniscus is fully formed, the force acting on the plate is equal to... 

Given a flat solid surface, the actual measurement of contact angles to 1° is relatively straightforward. The complications associated with contact angle measurement relate to the system itself and include the following ... 

If a moderately large area of flat solid surface is available, contact angles are usually measured directly from a projection of a sessile drop of the liquid. Alternatively, the tilting-plate method illustrated... 

Here ft is a correction factor to allow for the complex shape of the liquid just before break-away and for the non-vertical surface tension forces. Tabulations of ft are given in the literature. Again zero contact angle is required (attainable with an extremely clean ring) and the ring must lie flat on a quiescent liquid surface. For interfaciai tension measurements the ring must be preferentially wetted by the lower liquid. 

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