Polydisperse streaming instability – I. Tightly coupled particles and the terminal velocity approximation

We introduce a polydisperse version of the streaming instability, where the dust component is treated as a continuum of sizes. We show that its behaviour is remarkably different from the monodisperse streaming instability. We focus on tightly coupled particles in the terminal velocity approximation and show that unstable modes that grow exponentially on a dynamical time scale exist. However, for dust to gas ratios much smaller than unity they are confined to radial wave numbers that are a factor $\sim 1/\overline{\rm St}$ larger than where the monodisperse streaming instability growth rates peak. Here $\overline{\rm St} \ll 1$ is a suitable average Stokes number for the dust size distribution. For dust to gas ratios larger than unity, polydisperse modes that grow on a dynamical time scale are found as well, similar as for the monodisperse streaming instability and at similarly large wave numbers. At smaller wave numbers, where the classical monodisperse streaming instability shows secular growth, no growing polydisperse modes are found under the terminal velocity approximation. Outside the region of validity for the terminal velocity approximation, we have found unstable epicyclic modes that grow on $\sim 10^4$ dynamical time scales.Comment: 17 pages, 10 figures, 1 table. Submitte

Dynamics of dusty vortices - I. Extensions and limitations of the terminal velocity approximation

Motivated by the stability of dust laden vortices, in this paper we study the terminal velocity approximation equations for a gas coupled to a pressureless dust fluid and present a numerical solver for the equations embedded in the FARGO3D hydrodynamics code. We show that for protoplanetary discs it is possible to use the barycentre velocity in the viscous stress tensor, making it trivial to simulate viscous dusty protoplanetary discs with this model. We also show that the terminal velocity model breaks down around shocks, becoming incompatible with the two-fluid model it is derived from. Finally we produce a set of test cases for numerical schemes and demonstrate the performance of our code on these tests. Our implementation embedded in FARGO3D using an unconditionally stable explicit integrator is fast, and exhibits the desired second-order spatial convergence for smooth problems

Polydisperse Streaming Instability III. Dust evolution encourages fast instability

Planet formation via core accretion requires the production of kilometre-sized planetesimals from cosmic dust. This process must overcome barriers to simple collisional growth, for which the streaming instability (SI) is often invoked. Dust evolution is still required to create particles large enough to undergo vigorous instability. The SI has been studied primarily with single-size dust, and the role of the full evolved dust distribution is largely unexplored. We survey the polydisperse streaming instability (PSI) with physical parameters corresponding to plausible conditions in protoplanetary discs. We consider a full range of particle stopping times, generalized dust size distributions, and the effect of turbulence. We find that while the PSI grows in many cases more slowly with an interstellar power-law dust distribution than with a single size, reasonable collisional dust evolution, producing an enhancement of the largest dust sizes, produces instability behaviour similar to the monodisperse case. Considering turbulent diffusion, the trend is similar. We conclude that if fast linear growth of PSI is required for planet formation, then dust evolution producing a distribution with peak stopping times on the order of 0.1 orbits and an enhancement of the largest dust significantly above the single power-law distribution produced by a fragmentation cascade is sufficient, along with local enhancement of the dust to gas volume mass density ratio to order unity

Polydisperse Streaming Instability II. Methods for solving the linear stability problem

Occurring in protoplanetary discs composed of dust and gas, streaming instabilities are a favoured mechanism to drive the formation of planetesimals. The polydispserse streaming instability is a generalization of the streaming instability to a continuum of dust sizes. This second paper in the series provides a more in-depth derivation of the governing equations and presents novel numerical methods for solving the associated linear stability problem. In addition to the direct discretization of the eigenproblem at second order introduced in the previous paper, a new technique based on numerically reducing the system of integral equations to a complex polynomial combined with root finding is found to yield accurate results at much lower computational cost. A related method for counting roots of the dispersion relation inside a contour without locating those roots is also demonstrated. Applications of these methods show they can reproduce and exceed the accuracy of previous results in the literature, and new benchmark results are provided. Implementations of the methods described are made available in an accompanying PYTHON package psitools

Insights into the Atmospheric Pressure Plasma-Enhanced Chemical Vapor Deposition of Thin Films from Methyldisiloxane Precursors

This work describes the plasma-enhanced chemical vapor deposition of thin films at atmospheric pressure using dielectric barrier discharges fed with argon, oxygen and different methyldisiloxanes, i.e., hexamethyldisiloxane, pentamethyldisiloxane, and 1,1,3,3-tetramethyldisiloxane. The influence of the methyldisiloxane chemical structure and of the oxygen/methyldisiloxane feed ratio is investigated in order to provide insights into the organosilicon plasma chemistry at atmospheric pressure. As expected the FT-IR and XPS analyses show that the carbon content of the coatings depends on the number of methyl groups in the precursor molecule; in the case of coatings obtained with PMDSO and TMDSO carbon removal seems to be further enhanced by the presence of Si-H bonds. Gaschromatography-mass spectrometry analyses of the exhaust gas allow to assess the precursor depletion and to perform the quali-quantitative determination of by-products (e.g., silanes, siloxanes, silanols) formed by plasma activation. The results are exploited to rise hypotheses on the contribution of the different reaction pathways on the deposition mechanism

Bibliografia cartesiana (1997 - 2012)

Bibliografia cartesiana (1997-2012) è un repertorio bibliografico digitale consultabile on line su http://www.cartesius.net/bibliografia-cartesiana/bibliografia-cartesiana-1997-201