Capillary pressure, meniscus profile

The rise h of a liquid inside a partially wetted capillary (a < 90°), or the depression a > 90°) is related to ycosa, so that from h the contact angle can be obtained if y and the meniscus profile are known. In sec. 1.3a this method was used the other way around, i.e. to obtain y if a is known. Usually fully wetted cylinders are then used so that the contact angle does not enter the equations. What was said there about the profile remains applicable. This also applies to the deviations in the Laplace profile, incurred as a result of disjoining pressure 1). 

At equilibrium and in the flat portion of a thin-liquid film, the disjoining pressure, O, equals the capillary pressure. Pc- Therefore, measurements of the capillary pressure are used to evaluate fl. Two methods can be utilized to determine Pc, i.e. direct pressure measurements and lamella-profile measurements. In the latter case, the mean curvature of the meniscus is obtained and Pc is determined by using Laplace s equation. 

In the case of equilibrium liquid drops and menisci (see Section 2.3), they are supposed to be always at equilibrium with flat films with which they are in contact with in the front. Only the capillary pressure acts inside the spherical parts of drops or menisci, and only the disjoining pressure acts inside thin flat films. However, there is a transition zone between the bnlk liquid (drops or menisci) and the thin flat film in front of them. In this transition zone, both the capillary pressure and the disjoining pressure act simultaneously (see Section 2.3 for more details). A profile of the transition zone between a meniscus in a flat capillary and a thin a-fllm in front of it, in the case of partial wetting, is presented in Figure 2.5. It shows that the liquid profile is not always concave but changes its curvature inside the transition zone. Just this peculiar liquid shape in the transition zone determines the static hysteresis of contact angle (see Chapter 3)... 

Usually one varies the head of mercury or applied gas pressure so as to bring the meniscus to a fixed reference point [118], Grahame and co-workers [119], Hansen and co-workers [120] (see also Ref. 121), and Hills and Payne [122] have given more or less elaborate descriptions of the capillary electrometer apparatus. Nowadays, the capillary electrometer is customarily used in conjunction with capacitance measurements (see below). Vos and Vos [111] describe the use of sessile drop profiles (Section II-7B) for interfacial tension measurements, thus avoiding an assumption as to the solution-Hg-glass contact angle. 

The profile of a liquid in the transition zone between a capillary meniscus and a wetting film has been calculated for two types of disjoining pressure isotherms... 

When the whole isotherm of the disjoining pressure is within the region n > 0, i.e., in the case where complete wetting is realized, the concept of the contact angle cannot be introduced, as the radius of the meniscus, of the circumference of the existent transition zone does not intersect the surface of the capillary (see Chapter 2, Section 2.4, where the profile of the transition zone was calculated analytically). 

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