Modeling surface roughness

Choo, J. W., Glovnea, R. R, Olver, A. V., and Spikes, H. A., The Effects of Three-Dimensional Model Surface Roughness Fea- [58] tures on Lubricant Film Thickness in EFIL Contacts," ASME J. IHbol,Voi. 125,2003,pp. 533-542. 

Inaccuracies in the basic assumptions about the target. The calculation assumes that the sample is a flat homogenous slab of the given composition. Any departure from this model (surface roughness, compositional variation with depth, etc.) will introduce an error in the calculated relative intensity of the X-ray lines. 

A number of refinements and applications are in the literature. Corrections may be made for discreteness of charge [36] or the excluded volume of the hydrated ions [19, 37]. The effects of surface roughness on the electrical double layer have been treated by several groups [38-41] by means of perturbative expansions and numerical analysis. Several geometries have been treated, including two eccentric spheres such as found in encapsulated proteins or drugs [42], and biconcave disks with elastic membranes to model red blood cells [43]. The double-layer repulsion between two spheres has been a topic of much attention due to its importance in colloidal stability. A new numeri-... 

The effect of surface roughness on contact angle was modeled by several authors about 50 years ago (42, 45, 63, 64]. The basic idea was to account for roughness through r, the ratio of the actual to projected area. Thus = rA. lj apparent and similarly for such that the Young equation (Eq.-X-18) becomes... 

Lin et al. [70, 71] have modeled the effect of surface roughness on the dependence of contact angles on drop size. Using two geometric models, concentric rings of cones and concentric conical crevices, they find that the effects of roughness may obscure the influence of line tension on the drop size variation of contact angle. Conversely, the presence of line tension may account for some of the drop size dependence of measured hysteresis. 

As of this time, no one has solved the problem of the effect of asperities on a curved surface nor has anyone addressed the issue of crystalline facets. Needless to say, the problem of asperities on an irregular surface has not been addressed. However, Fuller and Tabor [118] have proposed a model that addresses the effects of variations of asperity size on adhesion for the case of planar surfaces. Assuming elastic response to the adhesion-induced stresses, they treated surface roughness as a random series of asperities having a Gaussian height distribution (f> z) and standard deviation o. Accordingly,... 

The jet-plume model only simulates vertical jets. Terrain is assumed to be flat and unobstructed. Application is limited to surface roughness mush less than the dispersing layer. User experti.se is required to ensure that the selected runtime options are self-consistent and actually reflect the physical release conditions. Documentation needs improvement there is little guidance... 

Fig. 8. X-ray reflection diagram of a thin polystyrene film on float glass [160]. The reflectivity R is plotted against the glancing angle . The film is spin coated from solution. A model fit (dashed line) to the reflectivity data is also shown where the following parameters are obtained film thickness = 59.1 0.1 nm, interface roughness glass-polymer = 0.4 0.1 nm, surface roughness polymer-air = 0.6+1 nm, mean polymer density = 1.05 + 0.01 g/cm-3. The X-ray wavelength is 0.154nm...

The CPE model has been used152,154,270-274 and it has been found that for electrochemically polished surfaces, the surface roughness is very small compared with mechanically polished surfaces. 

It is noteworthy that several studies exhibit contradictory results for both the mechanical and thermal characteristics of the flow. This is generally due to differences in the many parameters that characterize these studies such as the geometry, shape and surface roughness of the channels, the fluid, the boundary conditions and the measuring methodology itself. These discrepancies indicate the need for extension of the experimental base to provide the necessary background to the theoretical model. 

The statistic models consider surface roughness as a stochastic process, and concern the averaged or statistic behavior of lubrication and contact. For instance, the average flow model, proposed by Patir and Cheng [2], combined with the Greenwood and Williamsons statistic model of asperity contact [3] has been one of widely accepted models for mixed lubrication in early times. 

When the film thickness is of the order of roughness heights, the effects of roughness become significant which have to be taken into account in a profound model of mixed lubrication. The difficulty is that the stochastic nature of surface roughness results in randomly fluctuating solutions that the numerical techniques in the 1970s are unable to handle. As... 

As the statistical models for rough surface lubrication and contact are established, a mixed lubrication model can be thus constructed in the following procedure. 

Understanding the role of surface roughness in mixed lubrication is a first step toward the microscopic study of tribology. It has been an effort for more than 30 years, starting from statistic models, but it is the deterministic approach that provides a powerful means to explore the tribological events occurring at the micrometre scale. 

Patir, N., Effects of Surface Roughness on Partial Film Lubrication Using an Average Flow Model Based on Numerical Simulation. Ph.D. Thesis, Northwestern University, 1978. 

---