Near-contact dynamics of a sphere-wall collision in a viscous medum

As a sphere falling under gravity through a viscous medium approaches a wall, there is a large increase in the pressure in the thin layer of fluid being squeezed out between the sphere and wall. At low enough Stokes number, this leads to settling, and above a threshold Stokes number, the sphere bounces. Our earlier experiments have shown that even near this threshold, bouncing involves direct mechanical contact with the bottom plate [SK Birwa et al., Physical Review Fluids, 3(4), 044302, (2018)]. This is in contradiction with lubrication theory (LT) which says that the pressure diverges in the fluid and contact is not made in finite time. To study this difference, we conduct experiments to measure optically and interferometrically the dynamics of a sphere until the micrometer scale preceding the normal collision. The sphere is found to be decelerating slower than predicted by LT. We present an attempt to go beyond LT by accounting for the inertial terms neglected while making the boundary layer approximation, and by defining an appropriate non-orthogonal coordinate system. We obtain a single parametric differential equation which provides us with the time-evolution of the velocity profiles at different radii.