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.

Study of the Compressive Strength of Aluminum Curved Elements

Currently, the Specification for Aluminum Structures (Aluminum Association, 2010) shows thin-walled aluminum plate sections with radii greater than eight inches have a lower compressive strength capacity than a flat plate with the same width and thickness. This inconsistency with intuition, which suggests any degree of folding a plate should increase its elastic buckling strength, inspired this study. A wide range of curvatures are studied—from a nearly flat plate to semi-circular. To quantify the curvature, a single non-dimensional parameter is used to represent all combinations of width, thickness and radius. Using the finite strip method (CU-FSM), elastic local buckling stresses are investigated. Using the ratio of stress values of curved plates compared to flat plates of the same size, equivalent plate-buckling coefficients are calculated. Using this data, nonlinear regression analyses are performed to develop closed form equations for five different edge support conditions. These equations can be used to calculate the elastic critical buckling stress for any curved aluminum section when the geometric properties (width, thickness, and radius) and the material properties (elastic modulus and Poisson’s ratio) are known. This procedure is illustrated in examples, each showing the applicability of the derived equations to geometries other than those investigated in this study and also providing comparisons with theoretically exact numerical analysis results.

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.