We examine whether cubic nonlinearities, allowed by symmetry in the elastic energy of a contact line, may result in a different universality class at depinning. Standard linear elasticity predicts a roughness exponent $\zeta =1/3$ (one loop), $\zeta =0.388\pm 0.002$ (numerics) while experiments give $\zeta \approx 0.5$. Within functional renormalization group methods we find that a nonlocal Kardar-Parisi-Zhang-type term is generated at depinning and grows under coarse graining. A fixed point with $\zeta \approx 0.45$ (one loop) is identified, showing that large enough cubic terms increase the roughness. This fixed point is unstable, revealing a rough strong-coupling phase. Experimental study of contact angles $\theta$ near $\pi /2$, where cubic terms in the energy vanish, is suggested.

• Received 2 December 2004

DOI:https://doi.org/10.1103/PhysRevLett.96.015702