Scaling of the normal coefficient of restitution for wet impacts

Abstract

Abstract.A thorough understanding of the energy dissipation in the dynamics of wet granular matter is essential for a continuum description of natural phenomena such as debris flow, and the development of various industrial applications such as the granulation process. The coefficient of restitution (COR), defined as the ratio between the relative rebound and impact velocities of a binary impact, is frequently used to characterize the amount of energy dissipation associated. We measure the COR by tracing a freely falling sphere bouncing on a wet surface with the liquid film thickness monitored optically. For fixed ratio between the film thickness and the particle size, the dependence of the COR on the impact velocity and various properties of the liquid film can be characterized with the Stokes number, defined as the ratio between the inertia of the particle and the viscosity of the liquid. Moreover, the COR for infinitely large impact velocities derived from the scaling can be analyzed by a model considering the energy dissipation from the inertia of the liquid film.Keywords: coefficient of restitution, impact, wetting, particle-laden flow, granular flow PACS: 45.50.Tn, 47.55.Kf Understanding the energy dissipation associated with particle-particle interactions is crucial for describing the collective behavior of granular matter [1], i.e., large agglomerations of macroscopic particles. The coefficient of restitution (COR), firstly introduced by Newton as the ratio between relative rebound and impact velocities [2], can be used to characterize the energy dissipation at the particle level. This number provides one of the basic ingredients of computer assisted modeling, such as molecular dynamics (MD) simulation, which has been developed into a powerful tool to describe the large scale collective behavior of granular matter in the past decades [3,4]. Besides the energy dissipation from particle-particle interactions, the dissipation arising from the interstitial air or liquid has to be considered when coping with natural phenomena such as dune migration [5] or debris flow [6], as well as with various industrial applications such as granulation process [7,8].The experience of building sand sculptures tells us that the rigidity of a granular material increases as a small amount of a wetting liquid is added. This is largely due to the cohesion arising from the formation of capillary bridges between adjacent particles [9]. The so-called wet granular matter behaves dramatically different from noncohesive dry granular matter while agitated, with emerging critical behavior, such as phase transitions [10] and pattern formations [11], being traceable to the energy or force scale of a single capillary bridge. In order to gain insights into the dynamical behavior of wet granular matter, it is essential to explore the COR and the associated energy dissipation of wet impacts. A recent investigation reveals that the dependence of the COR on various particle and liquid properties can be scaled with two dimensionless numbers:...

Numerical investigation of collision dynamics of wet particles via force balance

“…When increasing the impact velocity further, the slope decreases until a constant value is reached asymptotically, which always stays smaller than the dry coefficient of restitution. This typical trend was also observed for example by Kantak et al (2005), Gollwitzer et al (2012), Müller et al (2013) and Müller and Huang (2016). In accordance to previous experimental works (Antonyuk et al, 2009;Gollwitzer et al, 2012;Crüger et al, 2016a;Ma et al, 2016), an increase in layer thickness, leads to a decrease of the normal coefficient of restitution, because the particle penetrates deeper into the higher liquid layer, resulting in a longer time, the dissipative forces have time to act.…”

Dynamics of wet particle–wall collisions: Influence of wetting condition

“…3 the (normal) coefficient of restitution in dependence of the collision velocity during normal collisions is compared for the cases "wet wall" (lines) and "wet particle" (circles). As was already described by several authors (Antonyuk et al, 2009;Kantak et al, 2005;Gollwitzer et al, 2012;Müller and Huang, 2016) as well as in our previous work (Crüger et al, 2016a), for small collision velocities a dry particle sticks to a wet wall, leading to a normal coefficient of restitution of zero (e n = 0). After reaching a critical "sticking" velocity the particle is able to rebound (including rupture of the liquid bridge forming during rebound), resulting in a steep increase of the normal coefficient of restitution with increasing collision velocity.…”

“…Other authors prefer studying collision dynamics not via non-dimensional parameters, which always incorporate several influencing parameters, but instead investigate each effect individually. Thereby, for example Kantak et al (2005), Gollwitzer et al (2012), Müller et al (2013), Huang (2016), andCrüger et al (2016a) found a characteristic trend of the normal coefficient of restitution with (normal) impact velocity. Additionally, the influence of layer thickness and viscosity were studied for example by Antonyuk et al (2009), Sutkar et al (2015), Crüger et al (2016a,b) as well as Gollwitzer et al (2012).…”

Interface‐resolved simulations of normal collisions of spheres on a wet surface

“…Then increases sharply with increasing St M and finally evens out. The observed trend is similar to the findings by many previous studies, among which a few models or correlations have been proposed to predict with the Stokes number. We have compared all the existing models (to the knowledge of the authors) with our simulation data.…”