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Theoretical Model for Normal Impact between Dry Sphere and Liquid Layer with Considerable Thickness

Category: Aerosol Physics and Instrumentation

Volume: 16 | Issue: 7 | Pages: 1533-1540
DOI: 10.4209/aaqr.2015.08.0527
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Jiliang Ma, Daoyin Liu , Xiaoping Chen

  • Key Laboratory of Energy Thermal Conversion and Control of Ministry of Education, School of Energy and Environment, Southeast University, Nanjing 210096, China


The normal impact can be divided into three stages: penetration, contact and rebound.

Three critical Stokes numbers are developed corresponding to different sub-stages.

The energy dissipation in the penetration stage is dominant for thick-layer impact.

An equation is proposed to predict the restitution coefficient of normal impact.


Detailed understanding on the impact mechanism with presence of liquid is helpful for elucidating complex behaviors of wet particle flows. This paper has extended elastohydrodynamic theory by coupling the physical force models for the wet normal impact with a liquid layer of considerable thickness. The contact is divided into penetration, contact, and rebound stages. Three critical Stokes numbers are developed for each stage to predict the sphere rebound behavior. The dependence of the critical Stokes numbers on the layer thickness, sphere radius and the liquid viscosity is also studied. When the layer thickness and liquid viscosity ranges within a low level, most of the kinetic energy is dissipated in the contact stage. With further increase of these two parameters, the energy dissipation in the penetration stage becomes predominant. Finally, we developed an equation to predict the restitution coefficient of the wet normal impact with acceptable accuracy.


Wet impact Restitution coefficient Stokes number Theoretical modeling

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