Mechanics of Particle Adhesion

The fundamentals of particle-particle adhesion for ultrafine particles (d < 10 μm) are presented using continuum mechanics approaches. The models for elastic (Hertz, Huber), elastic-adhesive (Derjaguin, Johnson, Maugis, Greenwood), viscoelastic (Yang), plastic-adhesive (Krupp, Molerus, Johnson, Maugis & Pollock) contact displacement response of a single, normal loaded, isotropic, smooth contact of two spheres are discussed. The force-displacement behaviours of elastic-plastic (Schubert, Thornton), elastic-dissipative (Sadd), plastic-dissipative (Walton), plastichardening (Vu-Quoc, Castellanos) and viscoplastic-adhesive (Rumpf) contacts are also shown. Hook’s linear elastic tangential force-displacement relation, non-linear contact loading paths up to Coulomb friction as its limit (Fromm, Föppl, Sonntag, Mindlin), the effect of adhesion (Derjaguin, Thornton) and different non-linear paths for load, unload, reload, reverse shear load, unload and load (Mindlin & Deresiewicz, Walton & Braun, Thornton) are compiled in a comprehensive literature review. Based on these theories, a general approach for the time and deformation rate dependent and combined viscoelastic, plastic, viscoplastic, adhesion and dissipative behaviours of a contact between spherical particles is derived and explained. Using the new model “stiff particles with soft contacts”, the influence of elastic-plastic repulsion in a “representative particle contact” (RPC) is shown by a contact force equilibrium. The attractive particle adhesion contribution is described by surface forces, i.e. van der Waals forces. A sphere-sphere adhesion model without any contact deformation is combined with a plate-plate adhesion model for the nanocontact flattening. Using this model, various contact deformation paths for loading, unloading, reloading and contact detachment are comfortably to discuss. Thus, the varying adhesion forces between particles depend directly on this “frozen” irreversible deformation, the so-called contact history. The contribution of this history or load dependent adhesion on the tangential force in an elasticplastic frictional contact is derived. With this increasing flattening, normal and tangential contact stiffness, rolling and twisting resistance, energy absorption and friction work increase. For colliding particles with adhesion, the correlation between particle impact velocity and contact deformation response is obtained using energy balance. Thus, the constitutive model approach is generally applicable for solid microor nanocontacts but has been shown here for ultrafine limestone particles (median particle size d50,3 = 1.2 μm) as typical example of a cohesive powder.