A mixed contact model for an immersed collision between two solid surfaces

Experimental evidence shows that the presence of an ambient liquid can greatly modify the collision process between two solid surfaces. Interactions between the solid surfaces and the surrounding liquid result in energy dissipation at the particle level, which leads to solid liquid mixture rheology deviating from dry granular flow behaviour. The present work investigates how the surrounding liquid modifies the impact and rebound of solid spheres. Existing collision models use elastohydrodynamic lubrication (EHL) theory to address the surface deformation under the developing lubrication pressure, thereby coupling the motion of the liquid and solid. With EHL theory, idealized smooth particles are made to rebound from a lubrication film. Modified EHL models, however, allow particles to rebound from mutual contacts of surface asperities, assuming negligible liquid effects. In this work, a new contact mechanism, 'mixed contact', is formulated, which considers the interplay between the asperities and the interstitial liquid as part of a hybrid rebound scheme. A recovery factor is further proposed to characterize the additional energy loss due to asperity liquid interactions. The resulting collision model is evaluated through comparisons with experimental data, exhibiting a better performance than the existing models. In addition to the three non-dimensional numbers that result from the EHL analysis the wet coefficient of restitution, the particle Stokes number and the elasticity parameter a fourth parameter is introduced to correlate particle impact momentum to the EHL deformation impulse. This generalized collision model covers a wide range of impact conditions and could be employed in numerical codes to simulate the bulk motion of solid particles with non-negligible liquid effects.