Sampling effect on contact and transport properties between fractal surfaces

In this work, we are interested in the contact between a self-affine fractal surface pressed against a smooth and perfectly rigid plane. The purpose is to analyze the influence of both sampling interval ΔΔ and sampling length LL, on the determination of surface roughness parameters, contact areas and viscous and diffusive flow through the aperture field resulting from the contact under load. To accomplish this analysis, fractal surfaces used in this work are obtained from numerical simulations. Models for synthesizing a fractal surface, computing mechanical deformation of asperities as well as determining viscous and diffusive flow are briefly presented. At the macroscopic scale, viscous and diffusive flow are fully characterized by the transmissivity K and effective diffusivity D tensors, respectively. Results show that fractal dimension DfDf and arithmetic roughness RaRa are almost insensitive to ΔΔ and L under conditions that are discussed. Contact areas are invariant whatever L   and become increasingly sensitive to ΔΔ while decreasing the arithmetic roughness Ra. The impact of L   and ΔΔ in the determination of transport properties also increases K and D decrease, i.e. for small Ra and large average contact pressure Pca.