Elasticity of a contact-line and avalanche-size distribution at depinning

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 82, Issue 1, 2010, Pages

  Le Doussal, Pierre ^a   Wiese, Kay Jörg ^a  

^a CNRS   (France)

Author keywords

[No Author keywords available]

Indexed keywords

CONTACT LINES; DEPINNING; DIAGONALIZATIONS; ELASTIC MODES; NONLINEAR EQUILIBRIUM; QUASI-STATIC;

CONTACT ANGLE; ELASTICITY; SIZE DETERMINATION;

SIZE DISTRIBUTION;

EID: 77954523725     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.82.011108     Document Type: Article

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35. introduce the capillary length L c ad hoc as a cutoff for the contact-line profile in response to a δ -like force.
36. Note that height correlations decay with the capillary length. Thus, if one has a system which is much larger (in units of the capillary length) than the observation window, one will not see any finite size effects.
37. Note that the integration by part of σ y produces no surface term. This can be made rigorous considering a periodic modulation h (y). We thus restrict here to functions that can be written as sum of periodic modulations, or have compact support.
38. In the experiment of Ref., there is an additional slowly varying offset.
39. Statics means the following: If we could get the contact line to relax, and find its true minimal-energy configuration as a function of plate position-maybe by waiting hundred years-then we could take one snapshot every hundred years, and deduce the avalanche sizes from the snapshots. Our statement says that this statistics and the driven one would differ only at two-loop order.
40. Note that the variable Φ (x) entering in S Φ and a Φ bears no relation to the plate angle φ introduced previously.