Theory of adhesion: role of surface roughness.

We discuss how surface roughness influences the adhesion between elastic solids. We introduce a Tabor number which depends on the length scale or magnification, and which gives information about the nature of the adhesion at different length scales. We consider two limiting cases relevant for (a) elastically hard solids with weak (or long ranged) adhesive interaction (DMT-limit) and (b) elastically soft solids with strong (or short ranged) adhesive interaction (JKR-limit). For the former cases we study the nature of the adhesion using different adhesive force laws (F ∼ u(-n), n = 1.5-4, where u is the wall-wall separation). In general, adhesion may switch from DMT-like at short length scales to JKR-like at large (macroscopic) length scale. We compare the theory predictions to results of exact numerical simulations and find good agreement between theory and simulation results.

[1]  P. Nayak,et al.  Random Process Model of Rough Surfaces , 1971 .

[2]  Kellar Autumn,et al.  Gecko Adhesion: Structure, Function, and Applications , 2007 .

[3]  David Tabor,et al.  The effect of surface roughness on the adhesion of elastic solids , 1975, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[4]  Stanislav N. Gorb,et al.  Biologically Inspired Mushroom-Shaped Adhesive Microstructures , 2014 .

[5]  W. Sawyer,et al.  Adhesion: role of bulk viscoelasticity and surface roughness , 2013, Journal of physics. Condensed matter : an Institute of Physics journal.

[6]  B. V. Derjaguin,et al.  Effect of contact deformations on the adhesion of particles , 1975 .

[7]  Stanislav N. Gorb,et al.  The effect of surface roughness on the adhesion of elastic plates with application to biological systems , 2003 .

[8]  Giuseppe Carbone,et al.  Asperity contact theories: Do they predict linearity between contact area and load? , 2008 .

[9]  A. Jagota,et al.  An easy-to-implement numerical simulation method for adhesive contact problems involving asymmetric adhesive contact , 2011 .

[10]  B. Persson.  Contact mechanics for randomly rough surfaces , 2006, cond-mat/0603807.

[11]  W. Sawyer,et al.  Optical In Situ Micro Tribometer for Analysis of Real Contact Area for Contact Mechanics, Adhesion, and Sliding Experiments , 2011, Tribology Letters.

[12]  A. Jagota,et al.  Discharge During Detachment of Micro-Structured PDMS Sheds Light on the Role of Electrostatics in Adhesion , 2012 .

[13]  J. Barbera,et al.  Contact mechanics , 1999 .

[14]  A. Volokitin,et al.  Contact electrification and the work of adhesion , 2013, 1305.2709.

[15]  B N J Persson,et al.  Wet adhesion with application to tree frog adhesive toe pads and tires , 2007 .

[16]  J. Shea,et al.  Sliding Friction-Physical Principles and Applications , 1998, IEEE Electrical Insulation Magazine.

[17]  M. Müser,et al.  Single-asperity contact mechanics with positive and negative work of adhesion: Influence of finite-range interactions and a continuum description for the squeeze-out of wetting fluids , 2014, Beilstein journal of nanotechnology.

[18]  Wolf B. Dapp,et al.  Self-affine elastic contacts: percolation and leakage. , 2012, Physical review letters.

[19]  K. Kendall,et al.  Surface energy and the contact of elastic solids , 1971, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[20]  M. Müser,et al.  Elastic contact between self-affine surfaces: comparison of numerical stress and contact correlation functions with analytic predictions , 2008, 0804.0062.

[21]  Johnson,et al.  An Adhesion Map for the Contact of Elastic Spheres , 1997, Journal of colloid and interface science.

[22]  D. Maugis.  Adhesion of spheres : the JKR-DMT transition using a dugdale model , 1992 .

[23]  D. Maugis.  On the contact and adhesion of rough surfaces , 1996 .

[24]  Martin H. Müser,et al.  On the Contact Area and Mean Gap of Rough, Elastic Contacts: Dimensional Analysis, Numerical Corrections, and Reference Data , 2013, Tribology Letters.

[25]  B. Persson,et al.  Contact mechanics: contact area and interfacial separation from small contact to full contact , 2008, 0803.4146.

[26]  B. Derjaguin,et al.  On the influence of molecular forces on the deformation of an elastic sphere and its sticking to a rigid plane , 1980 .

[27]  B. Derjaguin,et al.  Untersuchungen über die Reibung und Adhäsion, IV , 1934 .

[28]  B N J Persson,et al.  Contact mechanics for layered materials with randomly rough surfaces , 2012, Journal of physics. Condensed matter : an Institute of Physics journal.

[29]  Wolf B. Dapp,et al.  Systematic analysis of Persson’s contact mechanics theory of randomly rough elastic surfaces , 2014, Journal of physics. Condensed matter : an Institute of Physics journal.

[30]  B. Derjaguin,et al.  Electronic Theory of Adhesion , 1967 .

[31]  J. A. Greenwood,et al.  Adhesion of elastic spheres , 1997, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[32]  B. Persson,et al.  Adhesion between an elastic body and a randomly rough hard surface , 2002, The European physical journal. E, Soft matter.

[33]  Mark O. Robbins,et al.  Contact between rough surfaces and a criterion for macroscopic adhesion , 2013, Proceedings of the National Academy of Sciences.

[34]  B. Persson.  Relation between interfacial separation and load: a general theory of contact mechanics. , 2007, Physical review letters.

[35]  B N J Persson,et al.  Influence of surface roughness on adhesion between elastic bodies. , 2005, Physical review letters.

[36]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[37]  J. Greenwood,et al.  Contact of nominally flat surfaces , 1966, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[38]  K. Johnson,et al.  The adhesion of two elastic bodies with slightly wavy surfaces , 1995 .

[39]  B. Persson,et al.  Interfacial separation between elastic solids with randomly rough surfaces: Comparison between theory and numerical techniques , 2011, 1102.5412.

[40]  B. Persson,et al.  Adhesion of cellulose fibers in paper , 2013, Journal of physics. Condensed matter : an Institute of Physics journal.

[41]  Stanislav N. Gorb,et al.  Contact Mechanics and Friction on Dry and Wet Human Skin , 2013, Tribology Letters.

[42]  G. Carbone,et al.  Adhesive contact of rough surfaces: Comparison between numerical calculations and analytical theories , 2009, The European physical journal. E, Soft matter.

[43]  D. Dini,et al.  A numerical model for the deterministic analysis of adhesive rough contacts down to the nano-scale , 2014 .

[44]  Bo N. J. Persson,et al.  On the mechanism of adhesion in biological systems , 2003 .

[45]  B. Persson.  Theory of rubber friction and contact mechanics , 2001 .

[46]  Etienne Barthel,et al.  Adhesive elastic contacts: JKR and more , 2008 .

[47]  A. Roberts.  Surface charge contribution in rubber adhesion and friction , 1977 .

[48]  B. Lorenz,et al.  Contact mechanics and rubber friction for randomly rough surfaces with anisotropic statistical properties , 2009, The European physical journal. E, Soft matter.

[49]  B. Persson,et al.  Adhesion between elastic solids with randomly rough surfaces: Comparison of analytical theory with molecular-dynamics simulations , 2011, 1112.5275.