Effective contact angle for rough boundary

Abstract We provide rigorous justification for the classical Wenzel equation for the roughness enhanced effective contact angle. The minimization of the total surface energy is reformulated into a variational problem. As the size of the roughness becomes small, we show convergence of the minimizer. The limiting minimizer and effective contact angle are explicitly calculated to verify the Wenzel equation.

[1]  Srikanth Vedantam,et al.  Comment on How Wenzel and Cassie Were Wrong by Gao and McCarthy. , 2007, Langmuir : the ACS journal of surfaces and colloids.

[2]  E. Giusti.  Direct methods in the calculus of variations , 2003 .

[3]  Neelesh A. Patankar,et al.  On the Modeling of Hydrophobic Contact Angles on Rough Surfaces , 2003 .

[4]  L. Schwartz,et al.  Contact angle hysteresis on heterogeneous surfaces , 1985 .

[5]  R. N. Wenzel.  RESISTANCE OF SOLID SURFACES TO WETTING BY WATER , 1936 .

[6]  Xianmin Xu,et al.  The modified Cassie’s equation and contact angle hysteresis , 2013, Colloid and Polymer Science.

[7]  Edward Bormashenko,et al.  The rigorous derivation of Young, Cassie–Baxter and Wenzel equations and the analysis of the contact angle hysteresis phenomenon , 2008 .

[8]  G McHale,et al.  Cassie and Wenzel: were they really so wrong? , 2007, Langmuir : the ACS journal of surfaces and colloids.

[9]  François Alouges,et al.  Wetting on rough surfaces and contact angle hysteresis: numerical experiments based on a phase field model , 2009 .

[10]  Xianmin Xu,et al.  Derivation of the Wenzel and Cassie Equations from a Phase Field Model for Two Phase Flow on Rough Surface , 2010, SIAM J. Appl. Math..

[11]  A. Cassie,et al.  Wettability of porous surfaces , 1944 .

[12]  Ping Sheng,et al.  Molecular scale contact line hydrodynamics of immiscible flows. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[13]  DERIVATION OF WENZEL’S AND CASSIE’S EQUATIONS FROM A PHASE FIELD MODEL FOR TWO PHASE FLOW ON ROUGH SURFACE∗ , 2010 .

[14]  Abraham Marmur,et al.  When Wenzel and Cassie are right: reconciling local and global considerations. , 2009, Langmuir : the ACS journal of surfaces and colloids.

[15]  A. DeSimone,et al.  Wetting of rough surfaces: a homogenization approach , 2005, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[16]  Gershon Wolansky,et al.  Apparent contact angles on rough surfaces: the Wenzel equation revisited , 1999 .

[17]  Ping Sheng,et al.  Moving contact line on chemically patterned surfaces , 2008, Journal of Fluid Mechanics.

[18]  T. J. McCarthy,et al.  How Wenzel and cassie were wrong. , 2007, Langmuir : the ACS journal of surfaces and colloids.

[19]  R. H. Dettre,et al.  Contact Angle Hysteresis. III. Study of an Idealized Heterogeneous Surface , 1964 .

[20]  Lc Gao,et al.  Reply to "Comment on How Wenzel and Cassie Were Wrong by Gao and McCarthy" , 2007 .