Contact coefficient

The derivative of P, vs. t at 1=0 gives VoK. Thus the slope of the recorded load-time curve at 1=0 (see Fig. 3) together with the known speed at impact, gives the value of k,. This parameter, which depends only on the machine, was obtained at a speed of 0.5 m/s. With this value of k,. Mean also be calculated by fitting Eq (17) to the experimental register, which will be used in the calculus of the tup/specimen contact coefficients. 

When the heat is conducted through two adjacent materials with different thermal conductivities, the third boundary condition comes from a requirement that the temperature at the interface is the same for both materials (in cases when the contact resistance may be neglected) or there is a discontinuity in temperature distribution at the interface described by either contact resistance R,c or thermal contact coefficient h,c, defined by ... 

Figure 9.13 Stribeck diagram for a lubricated friction contact. Coefficient of friction [X versus r V(il pP is plotted, where p is the density of the lubricant, vo the velocity, and P the contact pressure. From left to right, there are three...

Here a - surface tension pa - atmospheric pressure 9 - contact angle of crack s wall wetting by penetrant n - coefficient, characterizing residual filling of defect s hollow by a penetrant before developer s application IT and h - porosity and thickness of developer s layer respectively W - minimum width of crack s indication, which can be registered visually or with the use of special optical system. The peculiarity of the case Re < H is that the whole penetrant volume is extracted by a developer. As a result the whole penetrant s volume, which was trapped during the stage of penetrant application, imbibes developer s layer and forms an indication of a defect. 

A complication now arises. The surface tensions of A and B in Eq. IV-2 are those for the pure liquids. However, when two substances are in contact, they will become mutually saturated, so that 7a will change to 7a(B) and 7b to 7B(A). That is, the convention will be used that a given phase is saturated with respect to that substance or phase whose symbol follows in parentheses. The corresponding spreading coefficient is then written 5b(A)/a(B)-... 

The coefficient of friction /x between two solids is defined as F/W, where F denotes the frictional force and W is the load or force normal to the surfaces, as illustrated in Fig. XII-1. There is a very simple law concerning the coefficient of friction /x, which is amazingly well obeyed. This law, known as Amontons law, states that /x is independent of the apparent area of contact it means that, as shown in the figure, with the same load W the frictional forces will be the same for a small sliding block as for a laige one. A corollary is that /x is independent of load. Thus if IVi = W2, then Fi = F2. 

The basic law of friction has been known for some time. Amontons was, in fact, preceded by Leonardo da Vinci, whose notebook illustrates with sketches that the coefficient of friction is independent of the apparent area of contact (see Refs. 2 and 3). It is only relatively recently, however, that the probably correct explanation has become generally accepted. 

In the absence of skidding, the coefficient of static friction applies at each instant, the portion of the tire that is in contact with the pavement has zero velocity. Rolling tire friction is more of the type discussed in Section XII-2E. If, however, skidding occurs, then since rubber is the softer material, the coefficient of friction as given by Eq. XII-5 is determined mainly by the properties of the rubber used and will be nearly the same for various types of pavement. Actual values of p, turn out to be about unity. 

A number of friction studies have been carried out on organic polymers in recent years. Coefficients of friction are for the most part in the normal range, with values about as expected from Eq. XII-5. The detailed results show some serious complications, however. First, n is very dependent on load, as illustrated in Fig. XlI-5, for a copolymer of hexafluoroethylene and hexafluoropropylene [31], and evidently the area of contact is determined more by elastic than by plastic deformation. The difference between static and kinetic coefficients of friction was attributed to transfer of an oriented film of polymer to the steel rider during sliding and to low adhesion between this film and the polymer surface. Tetrafluoroethylene (Telfon) has a low coefficient of friction, around 0.1, and in a detailed study, this lower coefficient and other differences were attributed to the rather smooth molecular profile of the Teflon molecule [32]. 

Finally, if the sliding surfaces are in contact with an electrolyte solution, an analysis indicates that the coefficient of friction should depend on the applied potential [41]. 

As load is increased and relative speed is decreased, the film between the two surfaces becomes thinner, and increasing contact occurs between the surface regions. The coefficient of friction rises from the very low values possible for fluid friction to some value that usually is less than that for unlubricated surfaces. This type of lubrication, that is, where the nature of the surface region is... 

The lubricating properties of tears are an important feature in normal blinking. Kalachandra and Shah measured the coefficient of friction of ophthalmic solutions (artificial tears) on polymer surfaces and found no correlation with viscosity, surface tension or contact angle [58]. The coefficient of friction appears to depend on the structure of the polymer surfaces and decreases with increasing load and sliding speed. 

It is known that even condensed films must have surface diffusional mobility Rideal and Tadayon [64] found that stearic acid films transferred from one surface to another by a process that seemed to involve surface diffusion to the occasional points of contact between the solids. Such transfer, of course, is observed in actual friction experiments in that an uncoated rider quickly acquires a layer of boundary lubricant from the surface over which it is passed [46]. However, there is little quantitative information available about actual surface diffusion coefficients. One value that may be relevant is that of Ross and Good [65] for butane on Spheron 6, which, for a monolayer, was about 5 x 10 cm /sec. If the average junction is about 10 cm in size, this would also be about the average distance that a film molecule would have to migrate, and the time required would be about 10 sec. This rate of Junctions passing each other corresponds to a sliding speed of 100 cm/sec so that the usual speeds of 0.01 cm/sec should not be too fast for pressurized film formation. See Ref. 62 for a study of another mechanism for surface mobility, that of evaporative hopping. 

Figure C2.5.8. Plot of the folding times Tp as a fimction of cr nfor tlie 22 sequences. This figure shows tlrat under tire external conditions when tire NBA is tire most populated tlrere is a remarkable correlation between ip and The correlation coefficient is 0.94. It is clear tlrat over a four orders of magnitude of folding times Xp = expf-a, / Oq) where CTq is a constant. The filled and open circles correspond to different contact interactions used in C2.5.1. The open squares are for A = 36.

Thus, under conditions of plastic defonnation the real area of contact is proportional to the nonnal force. If the shear force during sliding is proportional to that area, one has the condition that the shear force is proportional to the nonnal force, thus leading to the definition of a coefficient of friction. 

Equation (8.97) shows that the second virial coefficient is a measure of the excluded volume of the solute according to the model we have considered. From the assumption that solute molecules come into surface contact in defining the excluded volume, it is apparent that this concept is easier to apply to, say, compact protein molecules in which hydrogen bonding and disulfide bridges maintain the tertiary structure (see Sec. 1.4) than to random coils. We shall return to the latter presently, but for now let us consider the application of Eq. (8.97) to a globular protein. This is the objective of the following example. 

Film Theory. Many theories have been put forth to explain and correlate experimentally measured mass transfer coefficients. The classical model has been the film theory (13,26) that proposes to approximate the real situation at the interface by hypothetical "effective" gas and Hquid films. The fluid is assumed to be essentially stagnant within these effective films making a sharp change to totally turbulent flow where the film is in contact with the bulk of the fluid. As a result, mass is transferred through the effective films only by steady-state molecular diffusion and it is possible to compute the concentration profile through the films by integrating Fick s law ... 

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