Impact of a rigid sphere on a highly compressible porous layer imbibed with a Newtonian liquid

Abstract

The process of liquid flow takes place inside a highly compressible porous layer (HCPL) many times. In these cases, elastic forces of the HCPL solid phase are negligible, compared with hydrodynamic (HD) forces. Such processes were named ex-poro-HD (XPHD). A study of the impact process under XPHD conditions for circular and rectangular aligned plates was recently performed and presented by the authors. The impact of a rigid sphere on an HCPL, imbibed with a Newtonian liquid, under XPHD conditions, is analysed in the present paper. The Kozeny—Carman equation was used to compute the permeability variation as a function of compacticity/porosity. The Bowden and Tabor model for squeeze under impact was extended for XPHD conditions. The obtained model gives the impact pressure and force variations as the layer thickness decreases, so the damping capacity of the HCPL was evaluated. The maximum value of the absorbed energy, given by the optimal compacticity/porosity of the HCPL, is established. A comparison with the impact of a rigid sphere on a Newtonian liquid film under HD conditions is also done, keeping the same geometry and same kinematic and dynamic parameters, inherited from the XPHD model. The damping capacity of an HCPL is several orders of magnitude greater than that of the Newtonian liquid layer. The theoretical model was validated by two experiments, in which the HCPL is impacted by free falling ball tests.