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Calculation of adhesion between elastic spheres from molecular forces

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If you have a question about this talk, please contact Ms Helen Gardner.

The Johnson, Kendall,& Roberts (JKR) theory of adhesion in effect uses fracture mechanics to show that the adhesive force between two elastic spheres will be. But earlier Bradley, by integration of the forces between every pair of “molecules” of the two spheres, calculated the force to be: and since the JKR value is independent of the elastic modulus, it too applies to rigid spheres, and we have a conflict. Tabor offered a resolution of the conflict, later confirmed when Derjaguin and his collaborators introduced a method of analysing the problem by assuming that the forces due to the molecular interactions could be replaced by a surface force law acting across the gap between the two bodies, and that the surface force law could be treated as applying a surface traction to the bodies. The deformation is then calculated by the usual methods of elastic contact mechanics. The unexpected results of this analysis will be described; and are generally accepted when the spheres are large and the region of interaction small….. in effect for a “Hertzian” geometry. But recent advances in MEMS and in studying biological adhesion, as well as in powder technology, have drawn attention to small spheres with large areas of ‘contact’: and here the basic equivalence between the molecular forces and a surface force law is suspect. Various ‘improvements’ will be described: particularly the author’s preferred option with its absurd conclusion that the radius of the ‘contact’ area can exceed the radius of the sphere!

This talk is part of the Engineering Department Bio- and Micromechanics Seminars series.

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