On the influence of molecular forces on the deformation of an elastic sphere and its sticking to a rigid plane

• Published in: Journal of colloid and interface science 1980-01, Vol.77 (1), p.91-101
• Main Authors: Muller, V.M, Yushchenko, V.S, Derjaguin, B.V
• Format: Article
• Language: English
• ISSN: 0021-9797; 1095-7103
• DOI: 10.1016/0021-9797(80)90419-1

In this paper we have examined what influence the molecular interaction of spherical elastic particles with the rigid substrate exerts on their adhesion, the form close to the contact zone, and the dimensions of that zone. By having recourse to the computer numerical solution of the equations of the theory of elasticity (the interaction with the substrate was modeled by the Lennard-Jones potential), the distribution of pressures within the contact zone and around it, the profile of a particle in the vicinity of the contact, and the contact and noncontact components of the force of interaction of the particle with the substrate at different approaches of the particle to the plane have been ascertained. The dependence of the particle tearing-off force on the single dimensionless parameter μ = ( 32 3 π) × [2ϕ 2R(1 − η 2) 2/πE 2ϵ 3] 1 3 was established, this parameter comprising the radius of the particle, R, its elastic constants, E and η, and the characteristics of the potential of interaction with the substrate, ϕ and ϵ. The applicability limits have been determined of each of the two existing theories describing the tearing off of an elastic particle from the substrate, i.e., the theories of Derjaguin et al. and Johnson et al. It is proved that at μ < 1 the sticking force is completely determined by Derjaguin's formula and at ⌣ the difference from this formula consists in the appearance of a factor, 3 4 . It is demonstrated that for the most part of dispersions of colloidal grade of dispersity the applicability of Derjaguin's formula is quite justified and does not require any revision.