Angle of contact

Similarly, the identical expression holds for a liquid that completely fails to wet the capillary walls, where there will be an angle of contact between the liquid and the wall of 180°, a convex meniscus and a capillary depression of depth h. 

It is observed that in most instances a liquid placed on a solid will not wet it but remains as a drop having a definite angle of contact between the liquid and solid phases. The situation, illustrated in Fig. X-2, is similar to that for a... 

From the Kelvin equation it follows that the vapour pressure p over a concave meniscus must be less than the saturation vapour pressure p°. Consequently capillary condensation of a vapour to a liquid should occur within a pore at some pressure p determined by the value of r for the pore, and less than the saturation vapour pressure—always provided that the meniscus is concave (i.e. angle of contact <90°). 

It must always be borne in mind that when capillary condensation takes place during the course of isotherm determination, the pore walls are already covered with an adsorbed him, having a thickness t determined by the value of the relative pressure (cf. Chapter 2). Thus capillary condensation occurs not directly in the pore itself but rather in the inner core (Fig. 3.7). Consequently the Kelvin equation leads in the first instance to values of the core size rather than the pore size. The conversion of an r value to a pore size involves recourse to a model of pore shape, and also a knowledge of the angle of contact 0 between the capillary condensate and the adsorbed film on the walls. The involvement of 0 may be appreciated by consideration... 

Fig. 3.8 Relation between r of the Kelvin equation (Equation (3.20)) and the core radius r for a cylindrical pore with a hemispherical meniscus 6 is the angle of contact.

Now, in principle, the angle of contact between a liquid and a solid surface can have a value anywhere between 0° and 180°, the actual value depending on the particular system. In practice 6 is very difficult to determine with accuracy even for a macroscopic system such as a liquid droplet resting on a plate, and for a liquid present in a pore having dimensions in the mesopore range is virtually impossible of direct measurement. In applications of the Kelvin equation, therefore, it is almost invariably assumed, mainly on grounds of simplicity, that 0 = 0 (cos 6 = 1). In view of the arbitrary nature of this assumption it is not surprising that the subject has attracted attention from theoreticians. 

In general there are two factors capable of bringing about the reduction in chemical potential of the adsorbate, which is responsible for capillary condensation the proximity of the solid surface on the one hand (adsorption effect) and the curvature of the liquid meniscus on the other (Kelvin effect). From considerations advanced in Chapter 1 the adsorption effect should be limited to a distance of a few molecular diameters from the surface of the solid. Only at distances in excess of this would the film acquire the completely liquid-like properties which would enable its angle of contact with the bulk liquid to become zero thinner films would differ in structure from the bulk liquid and should therefore display a finite angle of contact with it. 

Section 3.7, the gas adsorption method breaks down for practical reasons. Since the angle of contact of mercury with solids is 140° (see later), and therefore more than 90°, an excess pressure Ap is required to force liquid mercury into the pores of a soh d. The idea of using mercury intrusion to measure pore size appears to have been first suggested by Washburn who put forward the basic equation... 

These are long centre drives with small slips. The slack side of the belt is kept on the top side to increase the angle of contact with the pulleys by sag on the top side. This is essential for an efficient transfer of load. The recommended maximum power that can be transmitted by one belt of different cross-sectional areas is provided by the belt manufacturer and some ratings are given in Table 8.1. When selecting these drives, the following parameters should be borne in mind ... 

Figure 8.10 Angle of contact with a flat-belt drive...

Heterogeneous nucleation is most likely to occur when there is a strong tendency for the crystal to stick to the surface of the catalyst. This sticking tendency can be described by the angle of contact, 6, shown in Fig. 7.3 the smaller 6, the better the adhesion. Anyone who has tried to get electronic solder to stick to a strip of copper will understand this well. If the copper is tarnished the solder will just roll around as a molten blob with 6 = 180°, and will not stick to the surface at all. If the tarnished... 

Wettability Design of treatment/recovery Angle of contact related to... 

Rand-wert, m. boimdary value, -winkel, m. angle of contact. 

A very simple, though indirect, method of surface analysis is the measurement of the angle of contact that a liquid makes with the solid surface being analyzed. This method has been widely used to study changes introduced in a polymer surface by various treatments. 

Figure 3-22 shows the general dimensions of an open-belt drive. For V belt drives, the pulling diameter D and d are pitch diameters [11]. The quantity C in the center distance, 0 in the contact angle for the smaller pulling, and 2x is the angular deviation from a 180° angle of contact. 

Angle of itirap or angle of contact is the angular section of a sprocket that is in contact with the chain. 

With large ratios, the angle of contact becomes smaller and the number of teeth engaged with the chain decreases. For angles less than 120°, 0 increasingly becomes a critical factor in the design of chain drives. 

Very finely disperse solids, which are adsorbed at the liquid/liquid interfaces, forming films of particles around the disperse globules. Certain powders can very effectively stabilize against coalescence. The solid s particle size must be very small compared with the emulsion droplet size and must exhibit an appropriate angle of contact at the three-phase (oil/water/solid) boundary [141]. 

The process depends on the existence, or development, of a selective affinity of one of the constituents for the envelopes of the gas bubbles. In general, this affinity must be induced, and the reagents which increase the angle of contact between the liquid and one of the materials are known as promoters and collectors. Promoters are selectively adsorbed on the surface of one material and form a monomolecular layer. The use of excess material destroys the effect. Concentrations of the order of 0.05 kg/Mg of solids are usually required. A commonly used promoter is sodium ethyl xanthate ... 

During the rarefaction cycle of the acoustic wave, as the pressure in the liquid decreases the liquid gas interface becomes increasingly more convex, its angle of contact decreases, until, at sufficiently low pressure it breaks away from the surface to produce a bubble of radius, Rj. 

The structure and orientation of the deposited amphiphile molecules have been found to be governed by the angle of contact between the monolayer and the solid surface. The deposited monolayers, in general, have been characterized as X- Y-, and Z -type, and their molecular arrangements can be described as follows. 

When three bubbles come into contact, the equilibrium angle will be 120°. The angle of contact relates to system s equilibrium state. If four bubbles are attached to each other, then the angle will at equilibrium be 109° 28° (Figure 8.4). 

There is at present no means of measuring satisfactorily the energy at any solid surface but the two energies of this kind may be eliminated from the calculation by taking into consideration the angle of contact, in the following manner (Poynting and Thomson, Properties of Matter, p. 139). 

Let A represent the solid, B, G the two fluids, EG, GD, GF the two solid-fluid and the fluid-fluid interfaces respectively, the line GF forming an angle a with EB. This angle is called the angle of contact of the system. Then since FG represents an equilibrium configuration the potential energy of the system in this position must be a minimum, so that an infinitesimal displacement of GF to G F will not cause an alteration in the energy of the system. 

Hence the difference between the tensions at the two solid-fluid interfaces which is the quantity always involved in equations of equilibrium can be expressed in terms of the fluid-fluid tension and an angle, called the angle of contact which is plainly susceptible of direct measurement. 

Emulsification produced by the addition of a dispersed solid to the two liquid phases must likewise be imagined to take place by reason of the solid going to the dineric surface (see p. 106) and being wetted but possessing a different angle of contact for each liquid. A microscopic examination of water emulsified in benzene stabilised with lamp black indicated that this was actually the case. rimr nTTh Benzene... 

Now Antonow s rule appears to be valid for two liquids provided that saturation be carefully defined and it is true for solid and liquid interfaces provided that the angle of contact be zero. 

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