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Roughness of moving elastic lines: Crack and wetting fronts E. Katzav,* M. Adda-Bedia, M. Ben Amar, and A. Boudaoud
 

Summary: Roughness of moving elastic lines: Crack and wetting fronts
E. Katzav,* M. Adda-Bedia, M. Ben Amar, and A. Boudaoud
Laboratoire de Physique Statistique de l'Ecole Normale Supérieure, CNRS UMR 8550, 24 rue Lhomond,
75231 Paris Cedex 05, France
Received 30 July 2007; published 16 November 2007
We investigate propagating fronts in disordered media that belong to the universality class of wetting contact
lines and planar tensile crack fronts. We derive from first principles their nonlinear equations of motion, using
the generalized Griffith criterion for crack fronts and three standard mobility laws for contact lines. Then we
study their roughness using the self-consistent expansion. When neglecting the irreversibility of fracture and
wetting processes, we find a possible dynamic rough phase with a roughness exponent of =1/2 and a dynamic
exponent of z=2. When including the irreversibility, we conclude that the front propagation can become history
dependent, and thus we consider the value =1/2 as a lower bound for the roughness exponent. Interestingly,
for propagating contact line in wetting, where irreversibility is weaker than in fracture, the experimental results
are close to 0.5, while for fracture the reported values of 0.55­0.65 are higher.
DOI: 10.1103/PhysRevE.76.051601 PACS number s : 68.08.Bc, 62.20.Mk, 05.40. a
I. INTRODUCTION
The propagation of fronts or lines in disordered media
occurs in a number of fields 1 . In particular, the propaga-
tion of cracks in heterogeneous materials and the wetting of
disordered substrates involve lines with long-range elasticity.

  

Source: Adda-Bedia, Mokhtar - Laboratoire de Physique Statistique, Département de Physique, École Normale Supérieure
Boudaoud, Arezki - Laboratoire de Physique Statistique, Département de Physique, École Normale Supérieure

 

Collections: Physics