Contact area, between rough surfaces

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.

Surface roughness is also an important variable. In most cases the surfaces of the contacting particles will not be perfectly smooth and surface roughness will reduce the area of contact and hence the bond strength. For rough particles the surface irregularities can certainly be comparable in size with the thickness of the adsorbed layer and can considerably reduce the effective contact area between particles. Surface debris on particles or the presence of fine coating particles can have the same effect and keep particles apart. ... 

The model first calculates the real contact area between wafer surface and asperities. The distribution of the pad asperity height is assumed to follow a normal distribution function. The wafer surface is assumed to be a smooth plane as a result of much lower roughness compared to the pad. The real contact area of a wafer with nominal area under reference pressure P can be expressed as... 

Greenwood J A 1967 On the area of contact between rough surfaces and flats J. Lub. Tech. (ASME) 1 81... 

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. 

V < Vdrainage, the friction incrcascs with the roughness due to the enhanced contact area between the gel and the substrate. At Vdrainage < v < Vf, the gel does not have sufficient time to form complete contacts with the surface asperities and the contact area decreases, which leads to a decrease in friction with the velocity. At... 

Scatter in adhesive forces may also be due to the indeterminacy of contact area between particles and surface this may in turn reflect the roughness of the contact surfaces and different relationships between the sizes of the adherent particles and the parameters characterizing the roughness of the solid surface (see Section 21). 

The greater importance of the electrical component for weakly adherent particles is explained on the basis that these particles are located on peaks of the rough surface. The contact area between particle and surface is at a minimum for such particles, and both the electrical and molecular forces of adhesion drop off the molecular forces, which are inversely proportional to the square of the distance between the contiguous bodies as indicated in Eq. (11.24), drop off more rapidly than the electrical forces. In this case, therefore, the adhesion is determined mainly by the electrical component. 

From these results we can distinguish three cases characterizing the influence of substrate roughness on particle adhesion. The first case occurs (Fig. V.2.a) when the contact surfaces are ideally smooth, for example, in the adhesion of spherical glass particles to a fused glass surface or to metal surfaces with a Class 13 finish. Only in this case may the contact area be calculated from the Hertz formula (11.59). The second case (Fig. V.2.b) occurs when the height of the asperities is less than the particle size. In this case the true contact area between... 

Contact surface roughness is therefore a significant factor in the frictional behaviour of solid surfaces and thus applicable to any moving particulate system. Particle movement can be conceptualised either as a model of smooth contact between particles and walls (Hertzian Hertz 1882) or as a model which has rough contact area between the particulate system and wall (Archardian Archard 1953, 1957). Both models have been used to predict the physical behaviour between particles and particles or between particles and a wall. 

Fig. 22.27 Examples of the mixture between Mannitol carrier particles (dso.s 80 pm) of different morphology and the API (dso.s 3 pm). The API inside the dents is not separated during inhalation (a). The gusset is destroyed when the carrier particles are separated by the aerodynamic forces upon application. The fine particle fraction is satisfactory (b) [47]. The roughness (c) guarantees for an increased contact area between carrier and API. If this force is too large, the separation process is hindered, but a minimum force is needed to attach the API to the surface [45]...

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