Macroscopic contact angle and liquid drops on rough solid surfaces via homogenization and numerical simulations

Mathematical Modelling and Numerical Analysis

Volumn 47, Issue 3, 2013, Pages 837-858

  Cacace, S ^a   Chambolle, A ^b   De Simone, A ^c   Fedeli, L ^d  

^a SAPIENZA UNIVERSITY OF ROME   (Italy)

^b CENTRE DE MATHÉMATIQUES APPLIQUÉES   (France)

^c SISSA   (Italy)

^d CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Augmented Lagrangian; Contact angle hysteresis; Homogenization; Nonsmooth optimization; Super hydrophobic surfaces; Total variation; Wetting

Indexed keywords

EID: 84996138326     PISSN: 0764583X     EISSN: 12903841     Source Type: Journal    
DOI: 10.1051/m2an/2012048     Document Type: Article

References (18)

1. G. Alberti and A. DeSimone, Wetting of rough surfaces: a homogenization approach. Proc. R. Soc. A 461 (2005) 79-97.
2. G. Alberti and A. DeSimone, Quasistatic evolution of sessile drops and contact angle hysteresis. Arch. Rat. Mech. Anal. 202 (2011) 295-348.
3. L. Ambrosio, N. Fusco and D. Pallara, Functions of bounded variation and free discontinuity problems, Oxford Mathematical Monographs, The Clarendon Press Oxford University Press, New York (2000)
4. L.A. Caffarelli, The obstacle problem revisited. J. Fourier Anal. Appl. 4 (1998) 383-402.
5. L.A. Caffarelli and A. Mellet, Capillary drops on an inhomogeneous surface, Perspectives in nonlinear partial differential equations. Contemp. Math. 446 (2007) 175-201.
6. A. DeSimone, N. Grunewald and F. Otto, A new model for contact angle hysteresis. Netw. Heterog. Media 2 (2007) 211-225.
7. J. Eckstein and D.P. Bertsekas, On the Douglas-Rachford splitting method and the proximal point algorithm for maximal monotone operators. Math. Program. 55 (1992)
8. E. Esser, Applications of Lagrangian-Based Alternating Direction Methods and Connections to Split Bregman (2009)
9. L.C. Evans and R.F. Gariepy, Measure theory and fine properties of functions. CRC Press, Boca Raton, FL (1992).
10. L. Fedeli, A. Turco and A. DeSimone, Metastable equilibria of capillary drops on solid surfaces: a phase field approach. Contin. Mech. Thermodyn. 23 (2011) 453-471.
11. H. Federer, Geometric measure theory. Springer-Verlag New York Inc., New York (1969).
12. R. Finn, Some properties of capillary surfaces. Milan J. Math. 70 (2002) 1-23.
13. M. J. Lai, B. Lucier and J. Wang, The convergence of a central-difference discretization of Rudin-Osher-Fatemi model for image denoising, Scale Space and Variational Methods in Computer Vision. Springer (2009) 514-526.
14. P.L. Lions and B. Mercier, Splitting Algorithms for the Sum of Two Nonlinear Operators. SIAM J. Numer. Anal. 16 (1979) 964-979.
15. D. Quere, Wetting and Roughness. Annu. Rev. Mater. Res. 38 (2008) 71-99.
16. J.E. Taylor, Boundary regularity for solutions to various capillarity and free boundary problems. Commun. Partial Differ. Equ. 2 (1977) 323-357.
17. H. Yang, A. Buguin, J.M. Taulemesse, K. Kaneko, S. Mery, A. Bergeret and P. Keller, Micron-Sized Main-Chain Liquid Crystalline Elastomer Actuators with Ultralarge Amplitude Contractions. J. Amer. Chem. Soc. 131 (2009) 15000-15004.
18. J. Wang and B.J. Lucier, Error Bounds for Finite-Difference Methods for Rudin-Osher-Fatemi Image Smoothing. SIAM J. Numer. Anal. 49 (2011) 845-868.