Capillary-lubrication Force Between Rotating Cylinders Separated by a Fluid Interface

Two cylinders rotating next to each other generate a large hydrodynamic forceif the intermediate space is filled with a viscous fluid. Herein, we explorethe case where the cylinders are separated by two layers of viscous immisciblefluids, in the limit of small capillary deformation of the fluid interface. Asthe interface deformation breaks the system's symmetry, a novel forcecharacteristic of soft lubrication is generated. We calculate thiscapillary-lubrication force, which is split into velocity-dependant andacceleration-dependant contributions. Furthermore, we analyze the variationsinduced by modifying the viscosity ratio between the two fluid layers, theirthickness ratio, and the Bond number. Unlike standard elastic cases, where arepelling soft-lubrication lift force has been abundantly reported, the currentfluid bilayer setting can also exhibit an attractive force due to thenon-monotonic deflection of the fluid interface when varying the sublayerthickness. Besides, at high Bond numbers, the system's response becomesanalogous to the one of a Winkler-like substrate with a viscous flow inside.