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We investigate propagating fronts in disordered media that belong to theuniversality class of wetting contact lines and planar tensile crack fronts. Wederive from first principles their nonlinear equations of motion, using thegeneralized Griffith criterion for crack fronts and three standard mobilitylaws for contact lines. Then we study their roughness using the self-consistentexpansion. When neglecting the irreversibility of fracture and wettingprocesses, we find a possible dynamic rough phase with a roughness exponent of$\zeta=1/2$ and a dynamic exponent of z=2. When including the irreversibility,we conclude that the front propagation can become history dependent, and thuswe consider the value $\zeta=1/2$ as a lower bound for the roughness exponent.Interestingly, for propagating contact line in wetting, where irreversibilityis weaker than in fracture, the experimental results are close to 0.5, whilefor fracture the reported values of 0.55--0.65 are higher.

Roughness of moving elastic lines - crack and wetting fronts