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I present a simple model of the time dependence of the contact area betweensolid bodies, assuming either a totally uncorrelated surface topography, or aself affine surface roughness. The existence of relaxation effects (that Iincorporate using a recently proposed model) produces the time increase of thecontact area $A(t)$ towards an asymptotic value that can be much smaller thanthe nominal contact area. For an uncorrelated surface topography, the timeevolution of $A(t)$ is numerically found to be well fitted by expressions ofthe form [$A(\infty)-A(t)]\sim (t+t_0)^{-q}$, where the exponent $q$ depends onthe normal load $F_N$ as $q\sim F_N^{\beta}$, with $\beta$ close to 0.5. Inparticular, when the contact area is much lower than the nominal area I obtain$A(t)/A(0) \sim 1+C\ln(t/t_0+1)$, i.e., a logarithmic time increase of thecontact area, in accordance with experimental observations. The logarithmicincrease for low loads is also obtained analytically in this case. For the morerealistic case of self affine surfaces, the results are qualitatively similar.

Towards a modeling of the time dependence of contact area between solid bodies