A Study of Particles Adhesion to Compliant Substrates with a Modified Sphere Contact Model

For small particles adhesion to compliant substrates, the ratio of the contact radius to the particle radius can be rather large. To take into consideration the effects in modeling small sphere contacts, the extended solutions of Johnson–Kendall–Roberts (JKR) adhesive contact theory by Maugis for exact sphere contacts are further modified in this work by incorporating the interfacial adhesion energy defined on real spherical contact area rather than its projected flat area. The numerical calculations indicate that the contact radius of an adhesive sphere contact under zero loads predicted by the modified sphere model is between the predicted results by JKR and Maugis models for small sphere contacts and approach to JKR results for large sphere contacts. By comparing with the published experiment results on particles adhesion, it is shown that the predicted results by the modified sphere contact model agree with the experiment results better compared with JKR and Maugis predicted results.