A new look on wetting models: continuum analysis

In this study, we considered the wetting phenomenon on a general substrate from a new viewpoint of continuum mechanics. The analyses first show how the Wenzel and the Cassie models deviate the practical results in some special substrates, and then elucidate the mechanism of the triple contact line (TCL) moving. Based upon variational theory of the total free functional dealing with the movable boundary condition, we show that the macroscopic contact angle (MCA) expression is the corresponding transversality condition. It manifests that the MCA depends only on the chemical and geometric property at the TCL, and is not affected by the gravity of the droplet and the contact area beneath the liquid. Our continuum model also shows the exploration of the pinning effect on a sharp wedge or the interface between two different phases. This investigation will help designing super-hydrophobic materials for novel micro-fluidic devices.

[1]  R. Blossey.  Self-cleaning surfaces — virtual realities , 2003, Nature materials.

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

[3]  N. Pugno,et al.  AFM nanoindentation: tip shape and tip radius of curvature effect on the hardness measurement , 2008 .

[4]  Xi-Qiao Feng,et al.  Towards Understanding Why a Superhydrophobic Coating Is Needed by Water Striders , 2007 .

[5]  Uwe Thiele,et al.  Wetting of textured surfaces , 2002 .

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

[7]  D. Pease.  The Significance of the Contact Angle in Relation to the Solid Surface , 1945 .

[8]  Kazuhito Hashimoto,et al.  Effects of Surface Structure on the Hydrophobicity and Sliding Behavior of Water Droplets , 2002 .

[9]  P. Gennes.  Wetting: statics and dynamics , 1985 .

[10]  C. W. Wu,et al.  Micronanostructures of the scales on a mosquito's legs and their role in weight support. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[11]  T. Young.  III. An essay on the cohesion of fluids , 1805, Philosophical Transactions of the Royal Society of London.

[12]  W. Barthlott,et al.  Hierarchically sculptured plant surfaces and superhydrophobicity. , 2009, Langmuir : the ACS journal of surfaces and colloids.

[13]  Xi Zhang,et al.  Surface gradient material: from superhydrophobicity to superhydrophilicity. , 2006, Langmuir : the ACS journal of surfaces and colloids.

[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]  Xi-Qiao Feng,et al.  Buoyant force and sinking conditions of a hydrophobic thin rod floating on water. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[16]  Michael Nosonovsky,et al.  On the range of applicability of the Wenzel and Cassie equations. , 2007, Langmuir : the ACS journal of surfaces and colloids.

[17]  C. Extrand.  Contact Angles and Hysteresis on Surfaces with Chemically Heterogeneous Islands , 2003 .

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

[19]  Xi-Qiao Feng,et al.  Superior water repellency of water strider legs with hierarchical structures: experiments and analysis. , 2007, Langmuir : the ACS journal of surfaces and colloids.

[20]  F. E. Bartell,et al.  Surface Roughness as Related to Hysteresis of Contact Angles. II. The Systems Paraffin–3 Molar Calcium Chloride Solution–Air and Paraffin–Glycerol–Air , 2002 .

[21]  E. Bormashenko.  Young, Boruvka–Neumann, Wenzel and Cassie–Baxter equations as the transversality conditions for the variational problem of wetting , 2009 .

[22]  Kai Zhang,et al.  Effect of triple-phase contact line on contact angle hysteresis , 2012 .

[23]  David Quéré,et al.  Rough ideas on wetting , 2002 .

[24]  Neelesh A. Patankar,et al.  A roughness-based wettability switching membrane device for hydrophobic surfaces , 2005 .

[25]  Lei Zhai,et al.  Stable Superhydrophobic Coatings from Polyelectrolyte Multilayers , 2004 .

[26]  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.

[27]  W. Dai,et al.  An Electrowetting Model for Rough Surfaces Under Low Voltage , 2008 .

[28]  Reinhard Lipowsky,et al.  Wetting and dewetting of structured and imprinted surfaces , 2000 .

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

[30]  T. J. McCarthy,et al.  An attempt to correct the faulty intuition perpetuated by the Wenzel and Cassie "laws". , 2009, Langmuir : the ACS journal of surfaces and colloids.

[31]  R. Lipowsky,et al.  Contact Angles on Heterogeneous Surfaces: A New Look at Cassie's and Wenzel's Laws , 1998, cond-mat/9809089.

[32]  Gareth H. McKinley,et al.  Superhydrophobic Carbon Nanotube Forests , 2003 .

[33]  Ya-Pu Zhao,et al.  Deformation of PDMS membrane and microcantilever by a water droplet: comparison between Mooney-Rivlin and linear elastic constitutive models. , 2009, Journal of colloid and interface science.

[34]  J. M. Bush,et al.  The hydrodynamics of water strider locomotion , 2003, Nature.

[35]  Itaru Honma,et al.  Superhydrophobic perpendicular nanopin film by the bottom-up process. , 2005, Journal of the American Chemical Society.

[36]  R. Xia,et al.  A new wetting mechanism based upon triple contact line pinning. , 2011, Langmuir : the ACS journal of surfaces and colloids.

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

[38]  Tomohiro Onda,et al.  Super-Water-Repellent Fractal Surfaces , 1995 .

[39]  Quanzi Yuan,et al.  Topology-dominated dynamic wetting of the precursor chain in a hydrophilic interior corner , 2012, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[40]  Feng Xiqiao,et al.  Directional Motion of Droplets in a Conical Tube or on a Conical Fibre , 2007 .

[41]  Wilhelm Barthlott,et al.  Characterization and Distribution of Water-repellent, Self-cleaning Plant Surfaces , 1997 .

[42]  A. Parker,et al.  Water capture by a desert beetle , 2001, Nature.

[43]  Ya-Pu Zhao,et al.  Precursor film in dynamic wetting, electrowetting, and electro-elasto-capillarity. , 2010, Physical review letters.

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

[45]  D. Quéré.  Model droplets , 2004, Nature materials.

[46]  Abraham Marmur,et al.  Partial wetting of chemically patterned surfaces: the effect of drop size. , 2003, Journal of colloid and interface science.