Elastohydrodynamic collisions of solid spheres

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Abstract
Recent developments in solving the problem of the elastohydrodynamic collision between two solid elastic bodies involved elaborate numerical procedures in order to simultaneously account for the elastic deformation of the solid surfaces and viscous fluid pressure. This paper describes a simple analytical approximation based upon a Hertzian-like profile for the elastic deformation of the two solid elastic spheres. By introducing a scaling coefficient, a closed-form solution has been developed which is capable of predicting the evolution of the relative particle velocity, force and restitution coefficient to an accuracy that is comparable with the exact numerical solutions.