The stability of a rising droplet: an inertialess nonmodal growth mechanism

Prior modal stability analysis (Kojima et al., Phys. Fluids, vol. 27, 1984) predicted that a rising or sedimenting droplet in a viscous fluid is stable in the presence of surface tension no matter how small, in contrast to experimental and numerical results. By performing a non-modal stability analysis, we demonstrate the potential for transient growth of the interfacial energy of a rising droplet in the limit of inertialess Stokes equations. The predicted critical capillary numbers for transient growth agree well with those for unstable shape evolution of droplets found in the direct numerical simulations of Koh & Leal (Phys. Fluids, vol. 1, 1989). Boundary integral simulations are used to delineate the critical amplitude of the most destabilizing perturbations. The critical amplitude is negatively correlated with the linear optimal energy growth, implying that the transient growth is responsible for reducing the necessary perturbation amplitude required to escape the basin of attraction of the spherical solution.Comment: 11pages, 7 figure

Edge states control droplet break-up in sub-critical extensional flows

A fluid droplet suspended in an extensional flow of moderate intensity may break into pieces, depending on the amplitude of the initial droplet deformation. In subcritical uniaxial extensional flow the non-breaking base state is linearly stable, implying that only a finite amplitude perturbation can trigger break-up. Consequently, the stable base solution is surrounded by its finite basin of attraction. The basin boundary, which separates initial droplet shapes returning to the non-breaking base state from those becoming unstable and breaking up, is characterized using edge tracking techniques. We numerically construct the edge state, a dynamically unstable equilibrium whose stable manifold forms the basin boundary. The edge state equilibrium controls if the droplet breaks and selects a unique path towards break-up. This path physically corresponds to the well-known end-pinching mechanism. Our results thereby rationalize the dynamics observed experimentally [Stone & Leal, J. Fluid Mech. 206, 223 (1989)

Nucleosynthesis in asymptotic giant branch stars: Relevance for galactic enrichment and solar system formation

We present a review of nucleosynthesis in AGB stars outlining the development of theoretical models and their relationship to observations. We focus on the new high resolution codes with improved opacities, which recently succeeded in accounting for the third dredge-up. This opens the possibility of understanding low luminosity C stars (enriched in s-elements) as the normal outcome of AGB evolution, characterized by production of 12C and neutron-rich nuclei in the He intershell and by mass loss from strong stellar winds. Neutron captures in AGB stars are driven by two reactions: 13C(α,n)16O, which provides the bulk of the neutron flux at low neutron densities (Nn ≤ 107 n/cm3), and 22Ne(α,n)25Mg, which is mildly activated at higher temperatures and mainly affects the production of s-nuclei depending on reaction branchings. The first reaction is now known to occur in the radiative interpulse phase, immediately below the region previously homogenized by third dredge-up. The second reaction occurs during the convective thermal pulses. The resulting nucleosynthesis phenomena are rather complex and rule out any analytical approximation (exponential distribution of neutron fluences). Nucleosynthesis in AGB stars, modeled at different metallicities, account for several observational constraints, coming from a wide spectrum of sources: evolved red giants rich in s-elements, unevolved stars at different metallicities, presolar grains recovered from meteorites, and the abundances of s-process isotopes in the solar system. In particular, a good reproduction of the solar system main component is obtained as a result of Galactic chemical evolution that mixes the outputs of AGB stars of different stellar generations, born with different metallicities and producing different patterns of s-process nuclei. The main solar s-process pattern is thus not considered to be the result of a standard archetypal s-process occurring in all stars. Concerning the 13C neutron source, its synthesis requires penetration of small amounts of protons below the convective envelope, where they are captured by the abundant 12C forming a 13C-rich pocket. This penetration cannot be modeled in current evolutionary codes, but is treated as a free parameter. Future hydrodynamical studies of time dependent mixing will be required to attack this problem. Evidence of other insufficiencies in the current mixing algorithms is common throughout the evolution of low and intermediate mass stars, as is shown by the inadequacy of stellar models in reproducing the observations of CNO isotopes in red giants and in circumstellar dust grains. These observations require some circulation of matter between the bottom of convective envelopes and regions close to the H-burning shell (cool bottom processing). AGB stars are also discussed in the light of their possible contribution to the inventory of short-lived radioactivities that were found to be alive in the early solar system. We show that the pollution of the protosolar nebula by a close-by AGB star may account for concordant abundances of 26Al, 41Ca, 60Fe, and 107Pd. The AGB star must have undergone a very small neutron exposure, and be of small initial mass (M <= 1.5 [sols]). There is a shortage of 26Al in such models, that however remains within the large uncertainties of crucial reaction rates. The net 26Al production problem requires further investigation

Si Isotopic Ratios in Mainstream Presolar SiC Grains Revisited

Although mainstream SiC grains, the major group of presolar SiC grains found in meteorites, are believed to have originated in the expanding envelope of asymptotic giant branch (AGB) stars during their late carbon-rich phases, their Si isotopic ratios show a distribution that cannot be explained by nucleosynthesis in this kind of stars. Previously, this distribution has been interpreted to be the result of contributions from many AGB stars of different ages whose initial Si isotopic ratios vary due to the Galactic chemical evolution of the Si isotopes. This paper presents a new interpretation based on local heterogeneities of the Si isotopes in the interstellar medium at the time the parent stars of the mainstream grains were born. Recently, several authors have presented inhomogeneous chemical evolution models of the Galactic disk in order to account for the well known evidence that F and G dwarfs of similar age show an intrinsic scatter in their elemental abundances.Comment: Accepted for publication by ApJ. 19 pages of text + 17 figures and 4 table

On the Fragility of Bulk Metallic Glass Forming Liquids

In contrast to pure metals and most non-glass forming alloys, metallic glass-formers are moderately strong liquids in terms of fragility. The notion of fragility of an undercooling liquid reflects the sensitivity of the viscosity of the liquid to temperature changes and describes the degree of departure of the liquid kinetics from the Arrhenius equation. In general, the fragility of metallic glass-formers increases with the complexity of the alloy with differences between the alloy families, e.g., Pd-based alloys being more fragile than Zr-based alloys, which are more fragile than Mg-based alloys. Here, experimental data are assessed for 15 bulk metallic glasses-formers including the novel and technologically important systems based on Ni-Cr-Nb-P-B, Fe-Mo-Ni-Cr-P-C-B, and Au-Ag-Pd-Cu-Si. The data for the equilibrium viscosity are analyzed using the Vogel–Fulcher–Tammann (VFT) equation, the Mauro–Yue–Ellison–Gupta–Allan (MYEGA) equation, and the Adam–Gibbs approach based on specific heat capacity data. An overall larger trend of the excess specific heat for the more fragile supercooled liquids is experimentally observed than for the stronger liquids. Moreover, the stronger the glass, the higher the free enthalpy barrier to cooperative rearrangements is, suggesting the same microscopic origin and rigorously connecting the kinetic and thermodynamic aspects of fragility

s-Process in Low Metallicity Stars. I. Theoretical Predictions

A large sample of carbon enhanced metal-poor stars enriched in s-process elements (CEMP-s) have been observed in the Galactic halo. These stars of low mass (M ~ 0.9 Msun) are located on the main-sequence or the red giant phase, and do not undergo third dredge-up (TDU) episodes. The s-process enhancement is most plausibly due to accretion in a binary system from a more massive companion when on the asymptotic giant branch (AGB) phase (now a white dwarf). In order to interpret the spectroscopic observations, updated AGB models are needed to follow in detail the s-process nucleosynthesis. We present nucleosynthesis calculations based on AGB stellar models obtained with FRANEC (Frascati Raphson-Newton Evolutionary Code) for low initial stellar masses and low metallicities. For a given metallicity, a wide spread in the abundances of the s-process elements is obtained by varying the amount of 13C and its profile in the pocket, where the 13C(a, n)16O reaction is the major neutron source, releasing neutrons in radiative conditions during the interpulse phase. We account also for the second neutron source 22Ne(a, n)25Mg, partially activated during convective thermal pulses. We discuss the surface abundance of elements from carbon to bismuth, for AGB models of initial masses M = 1.3 -- 2 Msun, low metallicities ([Fe/H] from -1 down to -3.6) and for different 13C-pockets efficiencies. In particular we analyse the relative behaviour of the three s-process peaks: light-s (ls at magic neutron number N = 50), heavy-s (hs at N = 82) and lead (N = 126). Two s-process indicators, [hs/ls] and [Pb/hs], are needed in order to characterise the s-process distribution. In the online material, we provide a set of data tables with surface predictions. ...Comment: 31 pages, 15 figures + 6 online material, 10 table