An Attachment Theory for Microsphere Adhesion

A theory of the mechanics of adhesion between a microsphere and substrate is presented. When a force is applied to an elastic body, the deformation depends not only on the magnitude of the force but also its location and distribution. Molecular adhesion between bodies is a surface force localized to the contact area. In contrast, applied forces such as from gravity, flow fields, inertia, etc., are distributed over the volume (body forces) and/or surface areas. Effects of different types of force systems on deformation, particularly when these forces are combined, can influence adhesion. The Hertzian structural stiffness parameter K does not reflect the effects of differently distributed multiple forces. A theory is developed that takes into account simultaneous application of the adhesion force and applied forces through the development of a reduced stiffness, K R . The paper also develops an equivalent Hertzian process for the condition of adhesion forces alone so that the mechanics of adhesion can be modeled completely by Hertzian theory. Illustrations of how adhesion alone is handled and how the reduced stiffness behaves are provided using experimental data from compressed, crossed rods and from hard particles in static equilibrium with both relatively hard and soft substrates.