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Can nonlinear elasticity explain contact-line roughness at depinning?
Pierre Le Doussal1, Kay Jörg Wiese, Elie Raphael
1CNRS-Laboratoire de Physique Théorique de l'Ecole Normale Supérieure, 24 rue Lhomond 75005 Paris, France.
Physical Review Letters
|February 21, 2006
Summary
Cubic nonlinearities in contact line depinning can lead to a rougher phase. Our findings suggest a new universality class, differing from standard predictions and experimental observations.
Area of Science:
- Soft matter physics
- Surface science
- Nonlinear dynamics
Background:
- Contact line depinning is crucial in various physical phenomena.
- Standard models predict a roughness exponent of zeta = 1/3.
- Experimental results suggest a different roughness exponent, approximately zeta = 0.5.
Purpose of the Study:
- Investigate the role of cubic nonlinearities in contact line depinning.
- Determine if these nonlinearities lead to a different universality class.
- Reconcile theoretical predictions with experimental observations.
Main Methods:
- Utilizing functional renormalization group methods.
- Analyzing the generation and growth of a nonlocal Kardar-Parisi-Zhang-type term.
- Identifying a new fixed point for the roughness exponent.
Main Results:
- A nonlocal Kardar-Parisi-Zhang-type term is generated at depinning.
- This term grows under coarse graining, indicating increased roughness.
- A new fixed point with zeta approximately = 0.45 (one loop) is identified.
- This fixed point is unstable, suggesting a rough strong-coupling phase.
Conclusions:
- Cubic nonlinearities can indeed alter the universality class of contact line depinning.
- The identified fixed point suggests a rougher phase than predicted by linear elasticity.
- Further experimental studies near contact angles of pi/2 are recommended.