Can non-linear elasticity explain contact-line roughness at depinning?

Pierre Le Doussal, Kay Jörg Wiese
CNRS-Laboratoire de Physique Théorique de l'Ecole Normale Supérieure, 24 rue Lhomond, 75005 Paris, France
Elie Raphael², Ramin Golestanian³
²Laboratoire de Physique de la Matière Condensé, Collèege de France, 11 place Marcelin Berthelot, 75005 Paris, France
³Institute for Advanced Studies in Basic Sciences, Zanjan 45195-159, Iran

Abstract

We examine whether cubic non-linearities, 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 ζ=1/3 (one loop), ζ=0.39 (numerics) while experiments give ζ about 0.5. Within functional RG we find that a non-local KPZ-type term is generated at depinning and grows under coarse graining. A fixed point with ζ of about 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. An experimental test is proposed at contact angle θ near π/2, where cubic terms vanish; thus the linear elasticity class should be recovered.

cond-mat/0411652 [pdf]
Phys. Rev. Let. 96 (2005) 015702 [pdf]