An Adhesion Map for the Contact of Elastic Spheres

✍ Scribed by K.L. Johnson; J.A. Greenwood

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 220 KB
• Volume: 192
• Category: Article
• ISSN: 0021-9797
• DOI: 10.1006/jcis.1997.4984

✦ Synopsis

where the reduced radius of the spheres R Å [1/R 1 / Several continuum mechanics models of the adhesion between 1/R 2 ] 01 . The maximum adhesive force-the pull-of f force elastic spheres have found application to compliant materials such P c -occurs when z Å z 0 and has the value 02pwR. as rubber and to fine particles in the air or in colloidal suspension. Elastic deformation of the spheres was first introduced by More recently they are being used in connection with experimental Johnson et al. (2) (JKR) and Derjaguin et al. (3) (DMT). techniques such as the surface force apparatus and the atomic These two models appeared at first to be contradictory, which force microscope. The appropriate model to use depends on the led to a sharp debate in the Journal of Colloid and Interface conditions: the size and elasticity of the spheres and the load to Science, until it was pointed out by Tabor (8) that the two which they are subjected. To guide this choice a map has been theories applied to opposite extremes of a spectrum of the constructed with nondimensional coordinates m and P V , where the elasticity parameter m can be interpreted as the ratio of elastic parameter deformation resulting from adhesion to the effective range of surface forces and the load parameter P V is the ratio of the applied m å ͩ Rw 2 E* 2 z 3 0 ͪ 1/3 [3] load to the adhesive force. A closed form solution to the problem based on a Dugdale force-separation law is outlined and used to construct the map. The errors introduced by the Dugdale approxiwhere the combined elastic modulus of the spheres E* Å mation are assessed by comparison with numerical solutions using the Lennard-Jones force law.