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Adhesion of elastic spheres and nano-tribology
Small spheres, such as the powders involved in chemical- and food-processing industries, readily stick
together. For clean, dry surfaces this is due to the intrinsic surface energy of the solids, and the
behaviour can be explained by the JKR theory [1] originally devised to explain the behaviour of rubber
spheres (and arising out of work being done on the friction of windscreen wiper blades). There has long been
some controversy over the theoretical magnitude of the 'pull-off' force needed to separate the spheres, and a
recent paper upset the balance by claiming that the JKR value is not the small-sphere/very-elastic asymptote.
Detailed calculations using idealised laws governing the atomic forces between surfaces show that paper to be
wrong and that the JKR value is indeed the asymptote, and provide information about the 'jump-on' and
'jump-off' by which contacts are made and broken [2]. A new analytical model has been proposed, with simpler
equations but giving similar results to the now classical Maugis model. Work is in progress to extend the JKR
theory to rate-dependent viscoelastic materials.
This information has recently become of considerable interest because of the development of
nano-tribology, in which sliding friction experiments between atomically smooth surfaces are performed
in the Atomic Force Microscope and the Surface Force Apparatus. It has been suggested that experimental
values of friction in nano-contacts can be correlated with the area predicted by the JKR theory. More
generally, there is renewed interest in the relation between adhesion and friction, and continuum models of
the combined effect of adhesion and friction are currently being developed. Two specific problems are being
studied: adhesion in the surface force apparatus, where the surface layer of mica, the glue backing layer and
the glass substrate all contribute to the contact deformation; and adhesion with viscoelastic solids
[3-12].
Relevant/recent publications
- Johnson, K. L. Kendall, K. and Roberts, A. D. 'Surface energy and the contact of elastic solids'.
Proc. Roy Soc., A324, pp301-320 (1971).
- Greenwood, J. A. 'Adhesion of elastic spheres' Proc. Roy. Soc., A453, pp1277-1297
(1997).
- Johnson, K. L. 'Continuum mechanics modelling of adhesion and friction' Langmuir, 12,
pp1277-1297 (1997).
- Johnson, K. L. 'Adhesion and friction between a smooth elastic asperity and a plane surface' Proc.
Roy. Soc., A453, pp163-179 (1997).
- Johnson, K. L. and Greenwood, J. A. 'An Adhesion Map for the Contact of Elastic Spheres' J. Colloid
& Interface Science, 192, pp326-333 (1997).
- Kim, K. S. , McMeeking, R. M. & Johnson, K. L. (1998) 'Adhesion, Slip, Cohesive Zones and Energy
Fluxes for Elastic Spheres in Contact' J. Mech. Phys. Solids (to appear).
- Sridhar, I. , Johnson K. L. , Fleck, N. A. 'Adhesion mechanics of the surface force apparatus' J.
Phys. D: Appl. Phys., 30, pp1710-1719 (1997).
- Johnson, K. L. 'Mechanics of adhesion' Trib. Int., 31, pp 413-418 (1998).
- Johnson, K. L. 'Contact mechanics and the adhesion of visco-elastic spheres.' Proc. ACM Symposium on the
Tribology of Polymer Surfaces, Boston, 1998 (in press).
- Johnson, K. L. 'The contribution of micro/nano tribology to the interpretation of dry friction.' Proc.
Istn. Mech. Engrs. Pt C J. Engng Trib. (Millenium volume) (in press).
- Greenwood, J. A. and Johnson, K. L. 'An alternative to the Maugis model of adhesion between elastic
spheres. ' J. Phys. D: Appl.Phys., 31, pp3279-3290 (1998). [Department of Engineering report
CUED/C-Mech TR.75].
- Greenwood, J.A. 'Adhesion at single point contacts.' Proc. 25rd Leeds-Lyon Symposium on Tribology, Lyon ,
Sept. 1998.
Contact Details
For further information on the work summarised above contact Dr J A Greenwood at Cambridge University
Engineering Department, Trumpington St, Cambridge, CB2 1PZ, UK. Tel: 01223 332733, Fax: 01223 332662. E-mail:
jag@eng.cam.ac.uk
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