I present a simple model of the time dependence of the contact area between
solid bodies, assuming either a totally uncorrelated surface topography, or a
self affine surface roughness. The existence of relaxation effects (that I
incorporate using a recently proposed model) produces the time increase of the
contact area A(t) towards an asymptotic value that can be much smaller than
the nominal contact area. For an uncorrelated surface topography, the time
evolution of A(t) is numerically found to be well fitted by expressions of
the form [A(∞)−A(t)]∼(t+t0)−q, where the exponent q depends on
the normal load FN as q∼FNβ, with β close to 0.5. In
particular, when the contact area is much lower than the nominal area I obtain
A(t)/A(0)∼1+Cln(t/t0+1), i.e., a logarithmic time increase of the
contact area, in accordance with experimental observations. The logarithmic
increase for low loads is also obtained analytically in this case. For the more
realistic case of self affine surfaces, the results are qualitatively similar.Comment: 18 pages, 9 figure