From dewetting to adhesion rupture - moving lines in dissipative, heterogeneous systems

Thirty five years ago, two theories for the pinning of elastic lines by heterogeneities have appeared almost simultaneously (Joanny & de Gennes, J. Chem. Phys. 81 (1984) 552; Rice, J. Appl. Mech 52 (1985) 571). Starting from these results, a large number of models and simulations have greatly advanced our understanding of complex line phenomena, and especially wetting hysteresis and fracture toughness of heterogeneous materials. However, these theories provide quasistatic pictures and they do not tell us much about what happens beyond the depinning treshold in the rather ubiquitous case where the response of the material itself is dissipative (e.g. viscous liquids or viscoelastic solids). In fact, even for homogeneous systems, evaluating the dissipation is still often a problematic question and the most simple cases - dewetting newtonian liquid or adhesion rupture for a linear viscoelastic solid - are far from being completely understood, especially when confrontion with experimental results is intended... Here we consider the dynamics of a front in a dissipative material moving on a heterogeneous surface at finite velocity. Based on recent numerical results for periodic substrates, we will first show how heterogeneities renormalize the dynamics of newtonian fluids near the dynamic wetting transition and actually obliterate some of the details of the wetting problem. We will then discuss the generalization to the case of dissipative soft solids.