Line of contact

In practice, it may be possible with care to float somewhat larger particles than those corresponding to the theoretical maximum. As illustrated in Fig. XIII-7, if the particle has an irregular shape, it will tend to float such that the three-phase contact occurs at an asperity since the particle would have to be depressed considerably for the line of contact to advance further. The resistance to rounding a sharp edge has been investigated by Mason and co-workers [62]. 

As worm gears tend to slide along their lines of contact, it is virtually impossible to maintain a hydrodynamic oil... 

The elements of gear teeth common to all gears are tooth surface and profile, flank, top and bottom land, crown, root and pitch circle, gear center, line of centers, pitch point, line of action, line of contact, and point of contact. Figure 57.27 labels many of the common gear tooth elements. Figure 57.28 labels the common rack tooth elements. 

An idea of the.diktributibh bf galvanic corrosion in the atmosphere is prp vided by the location of the corrosion of magnesium exposed in intimate contact with steel in the assembly shown in Fig. 19.28 after exposure in the salt atmosphere 25 m from the ocean at Kure Beach, North Carolina, for 9 years. Except where ledges or crevices may serve to trap unusual amounts of electrolyte, it may be assumed that, even with the most incompatible metals, simple galvanic effects will not extend more than about 4-5 mm from the line of contact of the metals in the couple. 

A modification of the specimen shown in Fig. 19.30 may be made simply by lapping a panel of one material over a panel of another one. The greatest effects may be observed when such panels are exposed with the laps facing up so as to favour retention of corrosive liquids along the line of contact. To permit observations of secondary effects of corrosion products, or exhaustion of corrosive constituents, the relative positions of the dissimilar metals should be changed from top to bottom in duplicate test assemblies. 

Fig. 11 —Nominal contact zone and real contact areas between rough surfaces in contact, (a) film thickness profile along the central line of contact, (b) a contour plot of the contact geometry where the white circular area and gray spots inside the circle correspond to the nominal and real contact area, respectively.

Figure 6.9 Two-dimensional projection of equilibrium at a plane of contact between three phases a, ft and % where the angles between the three two-phase boundaries meeting in a line of contact are denoted Qa, 9 and 9X.

We must imagine that some of the molecules in the crystalline solid have carboxyl groups wetted by the water on the line of contact, these groups although attached to the water cannot pull off the hydrocarbon chain at low temperatures. At 17° C., however, in the case of stearic acid the force of dissolution and the kinetic energy of the molecule are sufficient to permit of rupture. The molecule now floats freely on the surface of the water. During the course of time a number of molecules are so detached, they do not however exert any appreciable action on the tension of the water... 

Phenomena at Liquid Interfaces. The area of contact between two phases is called the interface three phases can have only a line of contact, and only a point of mutual contact is possible between four or more phases. Combinations of phases encountered in surfactant systems are L—G, L—L—G, L—S—G, L—S—S—G, L—L, L—L—L, L—S—S, L—L—S—S—G, L—S, L—L—S, and L—L—S—G, where G = gas, L = liquid, and S = solid. An example of an L—L—S—G system is an aqueous surfactant solution containing an emulsified oil, suspended solid, and entrained air (see Emulsions Foams). This embodies several conditions common to practical surfactant systems. First, because the surface area of a phase increases as particle size decreases, the emulsion, suspension, and entrained gas each have large areas of contact with the surfactant solution. Next, because interfaces can only exist between two phases, analysis of phenomena in the L—L—S—G system breaks down into a series of analyses, ie, surfactant solution to the emulsion, solid, and gas. It is also apparent that the surfactant must be stabilizing the system by preventing contact between the emulsified oil and dispersed solid. Finally, the dispersed phases are in equilibrium with each other through their common equilibrium with the surfactant solution. 

Turning now to the configuration of the top surface of the capillary we have the fact, as previously discussed, that this surface will be determined by the vector triangle of the tensions involved at. the common line of contact. The pressure at any point on this surface will be given by Eq (15-1). 

The actual form of lenses of non-spreading liquids on the surface of another immiscible liquid has been recently studied by Lyons3 and Langmuir.4 Langmuir shows that, in addition to the surface tension, if the lens is not of very large size, the linear tension / at the curved line of contact between the two liquids makes an appreciable difference to the thickness of the lens. The actual shape of the lenses is dependent on a rather complicated balance between the spreading coefficient the densities of the liquids, and the linear tension / round the perimeter of the lens, whose radius is R. If Dlt Z>2 are the densities of the lower and the upper liquids, respectively, the thickness t of a lens so large that its upper surface may be taken as flat, in the centre, is... 

For metals promoting other metals, an interesting case was studied by Hurst and Rideal.2 In the combustion of mixtures of hydrogen and carbon monoxide, using copper as the basic catalyst the ratio of the gases burnt depends on the temperature, and also on the amount of small additions of palladium made to the copper. The proportion of carbon monoxide burnt is increased by addition of palladium, a maximum proportion of carbon monoxide being burnt when 0-2 per cent, of palladium is. present. With further amounts of palladium, the ratio CO H2 burnt falls off slowly until, with 5 per cent, palladium, it is nearly the same as with pure copper. This effect of palladium is ascribed to the introduction of a new type of surface, the line of contact between palladium and copper, though the proof that this is the cause of promotion is perhaps not complete. Mit-tasch and others,3 in elaborate studies of the promotion of various metal catalysts, particularly molybdenum, for the synthesis or decomposition of ammonia, concluded that the formation of intermetallic compounds... 

The contact angle between two liquids and air varies,3 with an applied potential, in a manner very similar to the interfacial tension between mercury and water this is to be expected, since the angle depends on the three surface tensions meeting at the line of contact, of which the liquid-liquid tension probably varies most as the potential is changed. 

The Wilhelmy method. In the top picture a plate of the solid surface is lowered into a submerging liquid. The liquid pushes up on the solid sample with force due to the buoyancy and the surface tension, and these forces are measured by instruments attached to the arm above the sample and depend on the length d, surface tension n, and wetted length / (the perimeter of the sample along the line of contact of the air, liquid, and solid). In the bottom picture the sample is being raised and the liquid exerts a downward force. 

A theoretically well supported and experimentally well documented phenomenon is a through-the-vacuum influence of a promoter placed on the metal surface (or of the influence of a support, along the lines of contact between the metal and the support). The following is important with regard to this interaction. 

It is by rearranging this equation and assuming 9 to be zero that we obtain Eq. (4). For practical purposes, plates that are about 2 cm wide satisfy the theoretical requirement of infinite width. For such a plate (assumed to have a uniform surface), the line of contact is straight in the central part of the plate for all liquids of moderate surface tension, including water. If we assume g. A(0, and )/ V to be known, the task of determining a contact angle is reduced to the measurement of a length (the capillary rise h), which can be determined optically, e g., with a cathetometer. 

The line of contact of the liquid on the solid appears as a sharp light-dark border when the specimen is illuminated with light from the direction of the cathetometer telescope (illumination from within the telescope is best). The contrast may not be great, but it is usually possible to observe the boundary quite distinctly. 

Dynamic advancing and receding contact angles can be measured by moving the plate up or down. It may be possible to choose a rate in a range such that the position of the line of contact is essentially independent of rate, about I mm/min or less. The motion can. of course, be stopped and the angle measured after a specified time. 

Wetting Is an umbrella term describing all phenomena involving contacts between three phases, of which at least two are fluid. At that line of contact three interfaces meet, each with its own excess Helmholtz energy and interfacial tension. 

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