Influence of self-affine surface roughness on the friction coefficient for rubbers

For a viscous rubber sliding onto a self-affine rough surface, the friction coefficient increases monotonically with decreasing roughness exponent H and at a rapid rate for H<0.5. This is because the surface becomes rougher (with decreasing H) at short roughness wavelengths (<ξ) leading therefore to increased friction. Similar is also the behavior with decreasing the in-plane roughness correlation length ξ (for fixed roughness amplitude w). Nevertheless, the roughness exponent H appears to influence more the friction coefficient than the in-plane correlation length ξ. For relatively low sliding speeds, analytic calculations of the coefficient friction were also feasible for the limiting roughness exponents H=0 and H=1. Finally, under conditions of incomplete contact the friction coefficient was shown to decrease below its value of complete contact for contact lengths λcon<ξ and relatively high sliding velocities