Contact region

Fig. X-16. (a) Microscopic appearance of the three-phase contact region, (b) Wetting meniscus against a vertical plate showing the meniscus only, adsorbed film only, and joined profile. (From Ref. 226 with permission. Copyright 1980 American Chemical Society.)...

Fig. Xn-9. Contact region in boundary lubrication according to Hardy. (From Ref. 45.)...

Detennining the contact area between two rough surfaces is much more difficult than the sphere-on-flat problem and depends upon the moriDhology of the surfaces [9]. One can show, for instance, that for certain distributions of asperity heights the contact can be completely elastic. However, for realistic moriDhologies and macroscopic nonnal forces, the contact region includes areas of both plastic and elastic contact with plastic contact dominating. 

The separation of two surfaces in contact is resisted by adhesive forces. As the nonnal force is decreased, the contact regions pass from conditions of compressive to tensile stress. As revealed by JKR theory, surface tension alone is sufficient to ensure that there is a finite contact area between the two at zero nonnal force. One contribution to adhesion is the work that must be done to increase surface area during separation. If the surfaces have undergone plastic defonnation, the contact area will be even greater at zero nonnal force than predicted by JKR theory. In reality, continued plastic defonnation can occur during separation and also contributes to adhesive work. 

Whereas the contact region is the basis in the Connolly method, the center of the solvent-sphere determines the shape of the molecular. surface in the SAS method. In this case, the resulting surface is larger and the transition between the different atoms is more significant. 

Interfacial Mass-Transfer Coefficients. Whereas equiHbrium relationships are important in determining the ultimate degree of extraction attainable, in practice the rate of extraction is of equal importance. EquiHbrium is approached asymptotically with increasing contact time in a batch extraction. In continuous extractors the approach to equiHbrium is determined primarily by the residence time, defined as the volume of the phase contact region divided by the volume flow rate of the phases. 

Fretting corrosion (36,37) can lead to high contact resistance of base metal contacts, such as tin plate in electronic connectors. Small cycHcal displacements of the connector halves occur because of external vibration or differential thermal expansion and contraction of the mating contacts. The wear debris that is formed remains in the contact zone. The accumulation of oxide debris in the contact region leads to increased contact resistance. Solutions to this problem are stmctures that do not permit movement of contact surfaces with respect to one another, the use of gold as a contact finish, and the appHcation of thick coatings of contact lubricants and greases, which reduce the rate of wear and restrict access of air to the contact surfaces. 

The force required to crush a single particle that is spherical near the contact regions is given by the equation of Hertz (Timoschenko and Goodier, uieory ojEla.sticity, 2ded., McGraw-Hill, New York, 1951). 

Tomato bushy stunt virus is a T = 3 plant virus with 180 chemically identical subunits. Each polypeptide chain is divided into several domains. The subunits preserve quasi-equivalent packing in most contact regions by conformational differences of the protein chains, especially a large change in... 

Figure 4 Positive-ion mass spectrum acquired from the contact region of a control sample. Copper ion signals are absent.

The classical theory of contact mechanics, due to Hertz, treats the bodies in contact with a hard wall repulsive interaction, i.e. there is no attractive interaction whatsoever, and a steep repulsion comes into play when the surfaces of the bodies are in contact. The Hertzian theory assumes that only normal stresses exist, i.e. the shear stress in the contact region is zero. Under these conditions, the contact radius a), central displacement (3) and the distribution of normal stress (a) are given by the following expressions ... 

Viscoelastic contact problems have drawn the attention of researchers for some time [2,3,104,105]. The mathematical peculiarity of these problems is their time-dependent boundaries. This has limited the ability to quantify the boundary value contact problems by the tools used in elasticity. The normal displacement (u) and pressure (p) fields in the contact region for non-adhesive contact of viscoelastic materials are obtained by a self-consistent solution to the governing singular integral equation given by [106] ... 

Once it is recognized that particles adhere to a substrate so strongly that cohesive fracture often results upon application of a detachment force and that the contact region is better describable as an interphase [ 18J rather than a sharp demarcation or interface, the concept of treating a particle as an entity that is totally distinct from the substrate vanishes. Rather, one begins to see the substrate-particle structure somewhat as a composite material. To paraphrase this concept, one could, in many instances, treat surface roughness (a.k.a. asperities) as particles appended to the surface of a substrate. These asperities control the adhesion between two macroscopic bodies. 

Equilibrium is established when the attractive surface forces are balanced by elastic repulsion forces between the materials. The DMT model states that the elastic repulsion force is related to the attractive force within the contact region Fs by... 

According to the theory proposed by Maugis and Pollock, hereafter referred to as the MP model, if the adhesion induced stresses cause at least one of the contacting materials to yield and undergo a totally plastic response, the contact region formed will increase in size until the force causing the yielding is balanced... 

Figure 52.10 Comparison of the apparent viscosities of a gear oil and a gear grease. The grease flows readily in the tooth-contact region, where shear stress is high, but resists leakage at seals and joints...

The definition of different lubrication regimes is a historic problem [41 ]. In boundary lubrication, molecules will be absorbed on a solid surface of a tribo-pair and form a monomo-lecular absorbed layer as described by Hardy [42] as shown in Fig. 1 (a). If the film thickness of lubricants in the contact region is from a few nanometres to tens of nanometres, different layers will be formed as shown in Fig. 1 (b) proposed by Luo et al. [3,4]. The layer close to the surfaces is the adsorbed film that is a monomolecular layer. The layer in the... 

Fig. 4—Film thickness in the central contact region [18]. The ball is 23.5 mm in diameter and the lubricant is mineral oil CN13604 with no additives. Temperature is 25 C and load 4 N. The film thickness in Curve b is the data of the total thickness (Curve a) minus the static film thickness. The data of Curve c is calculated from Hamrock-Dowson formula (1981).

The shape of interference fringes of oil film in the contact region at different speeds are shown in Fig. 8. In the static state, fringes are regular circles as in Fig. 8(a). When the ball starts rolling, an outlet effect appears as shown in Fig. 8(h), which will become much stronger as the speed increases. 

The film shape for the elliptoid contact region with an ellipticity parameter k = 2.9 is shown in Fig. 11 [45], which gives all characteristic features of medium loaded point... 

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