@article{BodrovaSchmidtSpahnetal.2012,
  author    = {Bodrova, Anna and Schmidt, J{\"u}rgen and Spahn, Frank and Brilliantov, Nikolai V.},
  title     = {Adhesion and collisional release of particles in dense planetary rings},
  series = {Icarus : international journal of solar system studies},
  volume    = {218},
  journal   = {Icarus : international journal of solar system studies},
  number    = {1},
  publisher = {Elsevier},
  address   = {San Diego},
  issn      = {0019-1035},
  doi       = {10.1016/j.icarus.2011.11.011},
  pages     = {60 -- 68},
  year      = {2012},
  abstract  = {We propose a simple theoretical model for aggregative and fragmentative collisions in Saturn's dense rings. In this model the ring matter consists of a bimodal size distribution: large (meter sized) boulders and a population of smaller particles (tens of centimeters down to dust). The small particles can adhesively stick to the boulders and can be released as debris in binary collisions of their carriers. To quantify the adhesion force we use the JKR theory (Johnson, K., Kendall, K., Roberts, A. [1971]. Proc. R. Soc. Lond. A 324, 301-313). The rates of release and adsorption of particles are calculated, depending on material parameters, sizes, and plausible velocity dispersions of carriers and debris particles. In steady state we obtain an expression for the amount of free debris relative to the fraction still attached to the carriers. In terms of this conceptually simple model a paucity of subcentimeter particles in Saturn's rings (French, R.G., Nicholson, P.D. [2000]. Icarus 145, 502-523; Marouf, E. et al. [2008]. Abstracts for "Saturn after Cassini-Huygens" Symposium, Imperial College London, UK, July 28 to August 1, p. 113) can be understood as a consequence of the increasing strength of adhesion (relative to inertial forces) for decreasing particle size. In this case particles smaller than a certain critical radius remain tightly attached to the surfaces of larger boulders, even when the boulders collide at their typical speed. Furthermore, we find that already a mildly increased velocity dispersion of the carrier-particles may significantly enhance the fraction of free debris particles, in this way increasing the optical depth of the system.},
  language  = {en}
}
@article{GuimaraesAlbersSpahnetal.2012,
  author    = {Guimaraes, Ana H. F. and Albers, Nicole and Spahn, Frank and Seiss, Martin and Vieira-Neto, Ernesto and Brilliantov, Nikolai V.},
  title     = {Aggregates in the strength and gravity regime Particles sizes in Saturn's rings},
  series = {Icarus : international journal of solar system studies},
  volume    = {220},
  journal   = {Icarus : international journal of solar system studies},
  number    = {2},
  publisher = {Elsevier},
  address   = {San Diego},
  issn      = {0019-1035},
  doi       = {10.1016/j.icarus.2012.06.005},
  pages     = {660 -- 678},
  year      = {2012},
  abstract  = {Particles in Saturn's main rings range in size from dust to kilometer-sized objects. Their size distribution is thought to be a result of competing accretion and fragmentation processes. While growth is naturally limited in tidal environments, frequent collisions among these objects may contribute to both accretion and fragmentation. As ring particles are primarily made of water ice attractive surface forces like adhesion could significantly influence these processes, finally determining the resulting size distribution. Here, we derive analytic expressions for the specific self-energy Q and related specific break-up energy Q(star) of aggregates. These expressions can be used for any aggregate type composed of monomeric constituents. We compare these expressions to numerical experiments where we create aggregates of various types including: regular packings like the face-centered cubic (fcc), Ballistic Particle Cluster Aggregates (BPCA), and modified BPCAs including e.g. different constituent size distributions. We show that accounting for attractive surface forces such as adhesion a simple approach is able to: (a) generally account for the size dependence of the specific break-up energy for fragmentation to occur reported in the literature, namely the division into "strength" and "gravity" regimes and (b) estimate the maximum aggregate size in a collisional ensemble to be on the order of a few tens of meters, consistent with the maximum particle size observed in Saturn's rings of about 10 m.},
  language  = {en}
}