The coefficient of normal restitution for the Hertzian contact of two rough spheres colliding in a viscous fluid |
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Affiliation: | 1. State Key Laboratory of Clean Energy Utilization, Zhejiang University, Hangzhou 310027, PR China;2. School of Aeronautics and Astronautics, Zhejiang University, Hangzhou 310027, PR China |
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Abstract: | We use previous theoretical results for the added mass, history and lubrication forces between two spheres colliding in a fluid with viscosity ν to investigate the effect of viscous dissipation on the coefficient of restitution during contact. We assume that the mechanical interaction is governed by Hertzian mechanical contact of small duration τ and that the minimum approach distance between particles is approximately equal to the height σ of surface micro-asperities. A non-dimensionalization of the equation of motion indicates that the contact dynamics is governed by two parameters – the ratio ϵ of the surface roughness σ and the sphere radius a, and a contact Stokes number defined as Stc = σ2/ντ. An asymptotic solution of the equation of motion in the limit of small ϵ/Stc is used to obtain an explicit expression for the coefficient of restitution during contact and the latter is compared with estimates based on numerical solutions of the non-linear equation of motion. |
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Keywords: | Particle collisions Coefficient of restitution Hertzian contact Lubrication force |
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