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One of the most intriguing facets of Saturn's rings are the sharp edges of gaps in the rings where the surface density abruptly drops to zero. This is despite of the fact that the range over which a moon transfers angular momentum onto the ring material is much larger. Recent UVIS-scans of the edges of the Encke and Keeler gap show that this drop occurs over a range approximately equal to the rings' thickness. Borderies et al. show that this striking feature is likely related to the local reversal of the usually outward directed viscous transport of angular momentum in strongly perturbed regions. In this article we revise the Borderies et al. model using a granular flow model to define the shear and bulk viscosities, ν and ζ, and incorporate the angular momentum flux reversal effect into the axisymmetric diffusion model we developed for gaps in dense planetary rings. Finally, we apply our model to the Encke and Keeler division in order to estimate the shear and bulk viscosities in the vicinity of both gaps
Many solar wind observations at 1 au indicate that the proton (as well as electron) temperature anisotropy is limited. The data distribution in the (A(a), beta(a),(parallel to))-plane have a rhombic-shaped form around beta(a),(parallel to) similar to 1. The boundaries of the temperature anisotropy at beta(a),(parallel to) > 1 can be well explained by the threshold conditions of the mirror (whistler) and oblique proton (electron) firehose instabilities in a bi-Maxwellian plasma, whereas the physical mechanism of the similar restriction at beta(a),(parallel to) < 1 is still under debate. One possible option is Coulomb collisions, which we revisit in the current work. We derive the relaxation rate nu(A)(aa) of the temperature anisotropy in a bi-Maxwellian plasma that we then study analytically and by observed proton data from WIND. We found that nu(A)(pp) increases toward small beta(p),(parallel to) < 1. We matched the data distribution in the (A(p), beta(p),(parallel to))-plane with the constant contour nu(A)(pp) = 2.8 . 10(-6) s(-1), corresponding to the minimum value for collisions to play a role. This contour fits rather well the left boundary of the rhombic-shaped data distribution in the (A(p), beta(p),(parallel to))-plane. Thus, Coulomb collisions are an interesting candidate for explaining the limitations of the temperature anisotropy in the solar wind with small beta(a),(parallel to) < 1 at 1 au.