Traversing a thin film lubricant in finite time

The formation of a persistent thin film of fluid between solid surfaces in close proximity in a fluid domain is the foundational principle of oil lubrication. The intercalary lubricant is expected to beget large hydrodynamic pressures that prevent the surfaces from ever coming into contact. In this context, it is interesting to contemplate if any two surfaces approaching each other will ever be in true contact – i.e., squeeze out the lubricant film. To investigate this, we track the kinematics of a metallic sphere settling under gravity towards a plane (‘floor’) in a highly viscous Newtonian oil, close to the floor. The lubrication approximation suggests that the sphere will traverse the thin film gap with a velocity that scales with time, t, as t^-3. This deceleration has been suggested to originate from added drag due particle-wall interactions [1] or deviation from Newtonian behavior [2]. To investigate these, we add a magnetic twist to this experiment, placing a permanent magnet beneath the floor. The sphere now behaves as an induced magnetic dipole and is progressively accelerated as it settles. We contrast this with the previous case to examine the conditions for the spherical surface to achieve contact with the floor in finite time.



[1] G. Z. Ramon, H. E. Huppert, J. R. Lister, and H. A. Stone, Physics of Fluids 25, 073103 (2013).

[2] T. Chastel and A. Mongruel, Phys. Rev. Fluids 4, 014301 (2019).