Adhesion between an elastic body and a randomly rough hard surface.

I have developed a theory of adhesion between an elastic solid and a hard randomly rough substrate. The theory takes into account that partial contact may occur between the solids on all length scales. I present numerical results for the case where the substrate surface is self-affine fractal. When the fractal dimension is close to 2, complete contact typically occurs in the macro-asperity contact areas, while when the fractal dimension is larger than 2.5, the area of (apparent) contact decreases continuously when the magnification is increased. An important result is that even when the surface roughness is so high that no adhesion can be detected in a pull-off experiment, the area of real contact (when adhesion is included) may still be several times larger than when the adhesion is neglected. Since it is the area of real contact which determines the sliding friction force, the adhesion interaction may strongly affect the friction force even when no adhesion can be detected in a pull-off experiment.