Experiments on a sphere settling towards a boundary in a viscous liquid under the influence of a magnetic force

Magnets have been utilised widely for their ability to induce rapid contact – such as snapping between magnets and ferromagnetic materials. Yet, how such interactions proceed under immersion in a viscous fluid remains poorly understood. Here, we study this problem using the classical configuration of a smooth solid sphere approaching a plane in a quiescent fluid. Induced magnetic attraction, a spatially varying force analogous to short-range dispersion forces, offers a plausible route to overcome the constraint of a diverging hydrodynamic drag, which is well understood using the framework of classical lubrication theory. Instinctively, one might expect it to enable finite-time contact. However, our experiments reveal a counterintuitive result: while magnetic forces accelerate the sphere towards the surface, reducing the approach time by two orders of magnitude compared with gravity, they ultimately fail to effectuate contact in finite time, as induced magnetic interactions are unable to mitigate lubrication drag, which is singular at the thin gap limit, and transitions to an exponential descent characteristic of constant forcing. We support these findings with a simple theoretical model that accurately predicts the magnetic force law from purely kinematic observations. Finally, we outline the conditions under which spatially varying forces can enable true finite-time contact and discuss future experimental directions.