화학공학소재연구정보센터
Chemical Engineering Science, Vol.62, No.23, 6914-6926, 2007
An analytical solution of different configurations of the linear viscoelastic normal and frictional-elastic tangential contact model
In the current study an analytical solution describing the impact of a spherical particle on a rigid wall is derived. The contact is linear viscoelastic in normal and frictional-elastic in tangential direction. Due to its simplicity, the model combination considered is one of the most common in the framework of the Discrete Element Method especially for large-scale simulations. The linear viscoelastic normal model is realized according to Zhang and Whiten [1996. The calculation of contact forces between particles using spring and damping models. Powder Technology 88, 59-64,] assuming a contact to be ceased when the normal force attains a value of zero. In literature the frictional elastic tangential model is employed in three different configurations following Cundall and Strack [1979. A discrete numerical model for granular assemblies. Geotechnique 29, 47-65], Di Maio and Di Renzo [2004. Analytical solution for the problem of frictional-elastic collisions of spherical particles using the linear model. Chemical Engineering Science 59 (16), 3461-3475] and Brendel and Dippel [1998. Lasting contacts in molecular dynamics simulations. In: Herrmann, H.J., Hovi, J.-P, Luding, S. (Eds.), Physics of Dry Granular Media. Kluwer Academic Publishers, Dordrecht, 1998, p. 313]. The differences among these configurations are briefly explained, whereas the focus is set on the two most accurate model formulations given in the first two papers. All important final collision properties as positions and velocities are derived in an analytical form. Based on these results a comparison with experimental data of particle/wall and particle/particle collisions by Foerster et al. [1994. Measurements of the collision properties of small spheres. Physics of Fluids 6(3), 1108-1115], Lorenz et al. [1997. Measurements of impact properties of small, nearly spherical particles. Experimental Mechanics 37(3), 292-298] and Gorham and Kharaz [2000. The measurement of particle rebound characteristics. Powder Technology 112(3), 193-202] is performed, showing very good agreement especially for the model configuration of Di Maio and Di Renzo. The analytical solution as derived here helps understanding the complex collision process and can be applied for the evaluation of integration methods or in the context of an event-driven discrete element method. (C) 2007 Elsevier Ltd. All rights reserved.