Effect of Roughness on Particle Adhesion

It is obvious that a particle sitting on a surface will adhere diffeently when there is roughness. This is clear from Fig. 9.11 which shows three situations smooth surfaces, wavy surfaces with large diameter roughness, and rough surfaces with small diameter asperities. 

The smooth sphere on a smooth surface shown in Fig. 9.11 (a) requires a removal force 

Because of the importance of particle adhesion in photocopiers, Mizes used an atomic force microscope to measure both surface roughness and adhesion simultaneously and showed that they were related by this argument. He demonstrated on four different surfaces that the adhesion fluctuations were directly related to the surface curvatme fluctuations, as shown in Fig. 9.12. 

The problem gets worse when more complex surface roughnesses exist at the particle contact. A realistic description of contact under these circumstances was provided by Greenwood and Williamson, who showed that three parameters were needed to describe the contact adequately a the standard deviation of the height distribution, P the radius of each asperity, and N the number of asperities per unit area. They then presented data for real surfaces which satisfied the relationship 

Fuller and Tabor used such a model to show that adheaon was reduced drastically by minor surface roughness. They made the simplifying assumption that all the asperities had the same curvature, but had heights following a Gaussian distribution. Experimental results on the adhesion of smooth rubber 

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