Physical possibility of contactless rebound for deformable solids

Determine whether a deformable elastic solid immersed in a viscous incompressible fluid can undergo a physically realizable contactless rebound under standard no-slip boundary and interface conditions, despite the no-contact paradox.

Background

The paper studies a deformable elastic disk falling under gravity toward a rigid bottom wall in a viscous incompressible fluid. Under standard no-slip conditions, lubrication forces in the narrowing fluid gap become singular as the gap closes, and the classical no-contact paradox states that smooth rigid bodies cannot reach contact in finite time. Numerical and theoretical evidence suggests that an elastic body may nevertheless reverse its motion before contact because deformation changes the effective lubrication resistance, producing a contactless rebound.

The physical status of this phenomenon remains unresolved because no experiment has yet demonstrated a contactless rebound. The paper compares no-slip formulations, which are intended to approximate contactless rebound, with porous-layer Darcy models that permit genuine contact, but does not determine which behavior is physically correct. Experimental validation is identified as necessary to resolve the issue.