Fingering instability down the outside of a vertical cylinder

We present an experimental and numerical study examining the dynamics of a gravity-driven contact line of a thin viscous film traveling down the outside of a vertical cylinder of radius R. Experiments on cylinders with radii ranging between 0.159 and 3.81 cm show that the contact line is unstable to a fingering pattern for two fluids with differing viscosities, surface tensions, and wetting properties. The dynamics of the contact line is studied and results are compared to previous studies of inclined plane experiments in order to understand the influence substrate curvature plays on the fingering pattern. A lubrication model is derived for the film height in the limit that ε = H/R≪1, where H is the upstream film thickness, and in terms of a Bond number ρgR3/(γH), and the linear stability of the contact line is analyzed using traveling wave solutions. Curvature controls the capillary ridge height of the traveling wave and the range of unstable wavelength when ε = O(10-1), whereas the shape and stability of the contact line converge to the behavior one observes on a vertical plane when ε ≤ O(10-2). The most unstable wave mode, cutoff wave mode for neutral stability, and maximum growth rate scale as 0.45 where = ρgR2/γ ≥ 1.3, and the contact line is unstable to fingering when ≥ 0.56. Using the experimental data to extrapolate outside the range of validity of the thin film model, we estimate the contact line is stable when <0.56. Agreement is excellent between the model and the experimental data for the wave number (i.e., number of fingers) and wavelength of the fingering pattern that forms along the contact line.

Doubly-charged ethane ions: Solution to the dilemma of stability predicted by theory and instability observed in experiment

Potential energy curves have been computed for [C2H6]2+ ions and the results used to interpret the conspicuous absence of these ions in 2E mass spectra and in charge-stripping experiments. The energies and structures of geometry-optimized ground-state singlet and excited-state triplet [C2H6]2+ ions have been determined along with energies for different decomposition barriers and dissociation asymptotes. Although singlet and triplet [C2H6]2+ ions can exist as stable entities, they possess low energy barriers to decomposition. Vertical Franck-Condon transitions, involving electron impact ionization of ethane as well as charge-stripping collisions of [C2H6]+ ions, produce [C2H6]2+ ions which promptly dissociate since they are formed with energies in excess of various decomposition barriers. Appearance energies computed for doubly-charged ethane fragment ions are in accordance with experimental values.

Hydrodynamic correlation functions of a driven granular fluid in steady state

We study a homogeneously driven granular fluid of hard spheres at intermediate volume fractions and focus on time-delayed correlation functions in the stationary state. Inelastic collisions are modeled by incomplete normal restitution, allowing for efficient simulations with an event-driven algorithm. The incoherent scattering function Fincoh(q,t ) is seen to follow time-density superposition with a relaxation time that increases significantly as the volume fraction increases. The statistics of particle displacements is approximately Gaussian. For the coherent scattering function S(q,ω), we compare our results to the predictions of generalized fluctuating hydrodynamics, which takes into account that temperature fluctuations decay either diffusively or with a finite relaxation rate, depending on wave number and inelasticity. For sufficiently small wave number q we observe sound waves in the coherent scattering function S(q,ω) and the longitudinal current correlation function Cl(q,ω). We determine the speed of sound and the transport coefficients and compare them to the results of kinetic theory.

Finite Element Modeling of Shell Shape in the Freshwater Turtle Pseudemys concinna Reveals a Trade-Off between Mechanical Strength and Hydrodynamic Efficiency

Aquatic species can experience different selective pressures on morphology in different flow regimes. Species inhabiting lotic regimes often adapt to these conditions by evolving low-drag (i.e., streamlined) morphologies that reduce the likelihood of dislodgment or displacement. However, hydrodynamic factors are not the only selective pressures influencing organismal morphology and shapes well suited to flow conditions may compromise performance in other roles. We investigated the possibility of morphological trade-offs in the turtle Pseudemys concinna. Individuals living in lotic environments have flatter, more streamlined shells than those living in lentic environments; however, this flatter shape may also make the shells less capable of resisting predator-induced loads. We tested the idea that ‘‘lotic’’ shell shapes are weaker than ‘‘lentic’’ shell shapes, concomitantly examining effects of sex. Geometric morphometric data were used to transform an existing finite element shell model into a series of models corresponding to the shapes of individual turtles. Models were assigned identical material properties and loaded under identical conditions, and the stresses produced by a series of eight loads were extracted to describe the strength of the shells. ‘‘Lotic’’ shell shapes produced significantly higher stresses than ‘‘lentic’’ shell shapes, indicating that the former is weaker than the latter. Females had significantly stronger shell shapes than males, although these differences were less consistent than differences between flow regimes. We conclude that, despite the potential for many-to-one mapping of shell shape onto strength, P. concinna experiences a trade-off in shell shape between hydrodynamic and mechanical performance. This trade-off may be evident in many other turtle species or any other aquatic species that also depend on a shell for defense. However, evolution of body size may provide an avenue of escape from this trade-off in some cases, as changes in size can drastically affect mechanical performance while having little effect on hydrodynamic performance.

Hydrodynamic Characterization of Bile Salt Host-Guest Complexes by Pulsed Field Gradient NMR Spectroscopy

The work described herein is aimed at understanding primary and secondary aggregation of bile salt micelles and how micelles can perform chiral recognition of binapthyl analytes. Previous work with cholate and deoxycholate using micellar electrokinetic chromatography (MEKC) and nuclear magnetic resonance (NMR) has provided insightinto cholate and deoxycholate micelle formation, especially with respect to the critical micelle concentration (CMC). Chiral separations of the model analyte, 1,1â??-binaphthyl-2,2â??-diyl hydrogen phosphate (BNDHP), via cholate (C) and deoxycholate (DC) mediated MEKC separataions previously have shown the DC CMC to be 7-10 mM andthe cholate CMC at 14 mM at ph 12. A second model analyte,1,1â??-binaphthol (BN), was also previously investigated to probe micellar structure, but the MEKC data for this analyte implied a higher CMC, which may be interpreted as secondary aggregation. Thiswork extends the investigation of bile salts to include pulsed field gradient spin echo (PFGSE) NMR experiments being used to gain information about the size and degree of polydispersity of cholate and deoxycholate micelles. Concentrations of cholate below 10mM show a large variation in effective radius likely due to the existence of transient preliminary aggregates. The onset of the primary micelle shows a dramatic increase in effective radius of the micelle in cholate and deoxycholate. In the region of expectedsecondary aggregation a gradual increase of effective radius was observed with cholate; deoxycholate showed a persistent aggregate size in the secondary micelle region that is modulated by the presence of an analyte molecule. Effective radii of cholate anddeoxycholate (individually) were compared with and without R- and S-BNDHP in order to observe the effective radius difference of micelles with and without analyte present. The presence of S-BNDHP consistently resulted in a larger effective aggregate radius incholate and deoxycholate, confirming previous data of the S-BNDHP interacting more with the micelle than R-BNDHP. In total, various NMR techniques, like diffusion NMR can be used to gain a greater understanding of the bile salt micellization process and chiral resolution.