Adhesive force between a spherical rigid particle and an incompressible elastic substrate

Adhesion between a spherical rigid particle and an incomprssible elastic substrate is studied on the basis of the Lennard–Jones (L–J) potential, and the aim is to explore limitations of the well-known Derjaguin approximation. A new expression of the adhesive force is derived, in which the contribution from the elastic deformation of the substrate is incorporated naturally. Numerical results show that the Derjaguin approximation is valid down to particle radii of the order of the interaction range.

► We give a new derivation of adhesive force between a spherical particle and an incompressible elastic substrate.
► For very small particles the adhesive force exhibits features quite different from those in the previous models.
► New findings about the pull-off force of small particles.