On the collision of a rigid sphere with a deformable membrane in a viscous fluid

We analyse the model problem of rigid, spherical pendula impacting on rubber membranes at different Reynolds numbers to understand the contact dynamics in deformable bodies in a viscous fluid. We have investigated the problem both by laboratory and numerical experiments and a new contact model has been developed to perform the simulations. We have found that the collision dynamics depends on many parameters, the most important ones being the impact Stokes number (St) and the ratio of the membrane thickness (e) to sphere diameter (2R). For e/(2R) = 0.1 the pendulum rebounds for St >= 18 and this threshold increases as the membrane thickness decreases. Also, the membrane surface affects the dynamics of the impact by delaying the rebound for smaller membranes.