Lubricated Friction and the Hersey Number

Most frictional contacts are lubricated in some way, but is has proven difficult to measure and predict lubrication layer thicknesses and assess how they influence friction at the same time. Here we study the problem of rigid-isoviscous lubrication between a plate and a sphere, both experimentally and theoretically. The liquid layer thickness is measured by a novel method using inductive sensing, while the friction is measured simultaneously. The measured values of the layer thickness and friction on the disk are well described by the hydrodynamic description of liquid flowing through a contact area. This allows us to propose a modified version of the Hersey number that compares viscous to normal forces and allows us to rescale data for different geometries and systems. The modification overcomes the shortcomings of the commonly used Hersey number, adds the effects of the geometry of the configuration on the friction, and successfully predicts the lubrication layer thickness.