4 research outputs found
A model for collisions in granular gases
We propose a model for collisions between particles of a granular material
and calculate the restitution coefficients for the normal and tangential motion
as functions of the impact velocity from considerations of dissipative
viscoelastic collisions. Existing models of impact with dissipation as well as
the classical Hertz impact theory are included in the present model as special
cases. We find that the type of collision (smooth, reflecting or sticky) is
determined by the impact velocity and by the surface properties of the
colliding grains. We observe a rather nontrivial dependence of the tangential
restitution coefficient on the impact velocity.Comment: 11 pages, 2 figure
On Low-Velocity Collisions of Viscoelastic Particles
The theory of the elastic contact of two bodies developed by Hertz [1] is generalized including the contribution of viscous effects to the total stress. A nonlinear differential equation for the compression is derived for particles with arbitrary curvature of their surfaces and is solved numerically for spherical particles. The resulting dependence of the normal restitution coefficient on the impact velocity is calculated and compared with experimental data for ice at low temperatures [2, 3]. A good agreement is found which allows to estimate unknown material constants in certain cases. An astrophysical application of the results is briefly discussed for the especially interesting case of icy particles in planetary rings.La thĂ©orie du contact Ă©lastique de deux corps developpĂ©e par Hertz [1] est gĂ©nĂ©ralisĂ©e tenant compte de la contribution des effects visqueux Ă la tension totale. Une Ă©quation diffĂ©rentielle nonlinĂ©aire est derivĂ©e pour des particles dont les surfaces ont une courbure arbitraire. Elle est rĂ©solue numĂ©riquement dans le cas des particles sphĂ©riques. La dĂ©pendence du coefficient de restitution normale de la vitesse d'impact est calculĂ©e et comparĂ©e avec des donnĂ©es expĂ©rimentales obtenues pour la glace aux tempĂ©ratures basses [2, 3]. Un bon accord est trouvĂ© qui permet l'estimation des constantes du matĂ©riel dans certains cas. Une application astrophysique de nos rĂ©sultats est discutĂ©e brĂšvement dans un cas d'intĂ©rĂȘt particulier: des particles de glace dans des anneaux planĂ©taires