Rotation and Torque in Conforming and non-Conforming Lubricated Contacts

Relative sliding motion between a rigid object and a soft substrate produces a symmetry-breaking deformation of the substrate, resulting in an elastohydrodynamic torque on the object. Here, we calculate this torque numerically for a wide range of sliding velocities in a two-dimensional configuration. This torque depends on the mechanical properties of the soft elastic substrate as well as the fluid properties and is analyzed for vanishingly thin and very thick substrates. In the limit of non-conforming contacts, corresponding to large velocities, we identify scaling relations for the elastohydrodynamic torque as a function of the speed. In the opposite limit of vanishingly small velocities (Hertzian contacts), the torque is dominated by the flow in a thin film of fluid that is entrained between the object and the elastic substrate. We show that for highly compliant substrates, the object behaves as it were rolling without slip on a solid frictional surface. We also discuss situations where the soft lubrication flow can be controlled by the application of an external torque.