Adhesional Contact between Rigid Sphere and Elastic Plane Covered with Thin Liquid Film Considering Contact-Angle Hysteresis

Abstract

This paper proposes a contact model between a rigid sphere and an elastic plane covered with a thin liquid film. The elastic contact is determined by Johnson–Kendall–Roberts theory, which deals with the energy equilibrium of elastic and interfacial energies. In elastic contact under presence of thin liquid film, the energy needed to separate the two bodies is defined as the summation of the interfacial energy among the sphere, liquid, and plane. Capillary force affects the two bodies because a liquid bridge is formed between them. Shape of the liquid bridge, assumed by the Clark’s toroidal approximation, determines the capillary force. The hysteresis of the liquid contact angles and that of the liquid volume between loading and unloading processes are considered. In loading process, the liquid film is squeezed out from the contact area and accumulates at the contact edge with increasing the liquid contact angles. In unloading process, the accumulated liquid is dragged to the contact edge, and the contact angles decrease. An irreversible force curve is obtained from these two hystereses, and the effect of liquid bridge is discussed based on the calculated results. In addition, the adhesion-hysteresis mechanisms caused by the capillary force are discussed.

Keywords

• adhesion contact
• analytical model
• capillary force
• liquid contact angle
• sphere
• elastic half space