A Generalized Formulation for the Contact Between Elastic Spheres: Applicability to Both Wet and Dry Conditions

The interaction between two elastic spheres with an intervening liquid film of given volume is studied theoretically. Using an energy minimization approach, equilibrium contact configurations are determined through numerical computation. Several dimensionless groups are identified that govern the character of the solution. Curve fits are performed to reveal analytical relationships among the dimensionless groups. At extreme values of particular parameters, the curve fits are found to recover the analytical results of the well-known Hertzian and Johnson–Kendall–Roberts elastic (dry contact) models, as well as the force of a liquid bridge between rigid spheres. Qualitative agreement is found between the current model and some published experiments.