Orthogonal collocation for a nonlinear integro-differential equation

This paper is concerned with the numerical solution using orthogonalcollocation of a nonlinear integro-differential equation whichexhibits certain features arising in the modelling of catalyticcombustion in a cylindrical reactor taking account of radiation.These features imply that the available convergence theory oforthogonal collocation cannot be applied directly. Optimal convergenceresults of the orthogonal collocation approximation are provedfor our equation, and these are illustrated by numerical experiments.In addition superconvergence results for the iterated collocationsolution are obtained.     

Methanol electrochemical oxidation at nanometer-scale PtRu materials

The electrochemical oxidation of CH₃OH at nanometer-scale PtRu catalyst materials is reported. Comparisons are made between the properties of a Johnson Matthey (JM) PtRu black sample (50 at.% Ru (X_Ru ≈ 0.5)) and PtRu particles (2-6 nm, nominally X_Ru ≈ 0.5) prepared by sonication under anhydrous conditions. Cyclic voltammetry and in situ infrared spectroscopy measurements show the catalysts are active for the oxidation of 0.5 M CH₃OH in 0.1 M HClO₄ at temperatures between ambient and 70 °C. The sonochemically prepared PtRu sample displayed properties characteristic of bulk PtRu alloys with X_Ru ≈ 0.5. Evidence for phase separation of Pt and Ru was observed in CO stripping voltammetry from the JM catalyst adsorbed at low metal loadings (20 μg/cm²) on bulk Au electrodes. Per gram of catalyst, the JM material was more active toward CO₂ formation and displayed greater resistance to poisoning by adsorbed CO than the sonochemically prepared material during ambient temperature oxidation of 0.5 M CH₃OH in 0.1 M HClO₄.     

Accurate numerical estimation of interphase momentum transfer in Lagrangian–Eulerian simulations of dispersed two-phase flows

The Lagrangian–Eulerian (LE) approach is used in many computational methods to simulate two-way coupled dispersed two-phase flows. These include averaged equation solvers, as well as direct numerical simulations (DNS) and large-eddy simulations (LES) that approximate the dispersed-phase particles (or droplets or bubbles) as point sources. Accurate calculation of the interphase momentum transfer term in LE simulations is crucial for predicting qualitatively correct physical behavior, as well as for quantitative comparison with experiments. Numerical error in the interphase momentum transfer calculation arises from both forward interpolation/approximation of fluid velocity at grid nodes to particle locations, and from backward estimation of the interphase momentum transfer term at particle locations to grid nodes. A novel test that admits an analytical form for the interphase momentum transfer term is devised to test the accuracy of the following numerical schemes: (1) fourth-order Lagrange Polynomial Interpolation (LPI-4), (3) Piecewise Cubic Approximation (PCA), (3) second-order Lagrange Polynomial Interpolation (LPI-2) which is basically linear interpolation, and (4) a Two-Stage Estimation algorithm (TSE). A number of tests are performed to systematically characterize the effects of varying the particle velocity variance, the distribution of particle positions, and fluid velocity field spectrum on estimation of the mean interphase momentum transfer term. Numerical error resulting from backward estimation is decomposed into statistical and deterministic (bias and discretization) components, and their convergence with number of particles and grid resolution is characterized. It is found that when the interphase momentum transfer is computed using values for these numerical parameters typically encountered in the literature, it can incur errors as high as 80% for the LPI-4 scheme, whereas TSE incurs a maximum error of 20%. The tests reveal that using multiple independent simulations and higher number of particles per cell are required for accurate estimation using current algorithms. The study motivates further testing of LE numerical methods, and the development of better algorithms for computing interphase transfer terms.     

Ultrafast Electron Transfer Kinetics of Graphene Grown by Chemical Vapor Deposition

High electrochemical reactivity is required for various energy and sensing applications of graphene grown by chemical vapor deposition (CVD). Herein, we report that heterogeneous electron transfer can be remarkably fast at CVD‐grown graphene electrodes that are fabricated without using the conventional poly(methyl methacrylate) (PMMA) for graphene transfer from a growth substrate. We use nanogap voltammetry based on scanning electrochemical microscopy to obtain very high standard rate constants k⁰≥25 cm s^?1 for ferrocenemethanol oxidation at polystyrene‐supported graphene. The rate constants are at least 2–3 orders of magnitude higher than those at PMMA‐transferred graphene, which demonstrates an anomalously weak dependence of electron‐transfer rates on the potential. Slow kinetics at PMMA‐transferred graphene is attributed to the presence of residual PMMA. This unprecedentedly high reactivity of PMMA‐free CVD‐grown graphene electrodes is fundamentally and practically important.     

Modeling droplet dispersion and interphase turbulent kinetic energy transfer using a new dual-timescale Langevin model

Dispersion of spray droplets and the modulation of turbulence in the ambient gas by the dispersing droplets are two coupled phenomena that are closely linked to the evolution of global spray characteristics, such as the spreading rate of the spray and the spray cone angle. Direct numerical simulations (DNS) of turbulent gas flows laden with sub-Kolmogorov size particles, in the absence of gravity, report that dispersion statistics and turbulent kinetic energy (TKE) evolve on different timescales. Furthermore, each timescale behaves differently with Stokes number, a non-dimensional flow parameter (defined in this context as the ratio of the particle response time to the Kolmogorov timescale of turbulence) that characterizes how quickly a particle responds to turbulent fluctuations in the carrier or gas phase. A new dual-timescale Langevin model (DLM) composed of two coupled Langevin equations for the fluctuating velocities, one for each phase, is proposed. This model possesses a unique feature that the implied TKE and velocity autocorrelation in each phase evolve on different timescales. Consequently, this model has the capability of simultaneously predicting the disparate Stokes number trends in the evolution of dispersion statistics, such as velocity autocorrelations, and TKE in each phase. Predictions of dispersion statistics and TKE from the new model show good agreement with published DNS of non-evaporating and evaporating droplet-laden turbulent flow.     

Design and fabrication of teflon-coated tungsten nanorods for tunable hydrophobicity

The nature of water interaction with tungsten nanorods (WNRs) fabricated by the glancing-angle deposition technique (GLAD)-using RF magnetron sputtering under various Ar pressures and substrate tilting angles and then subsequent coating with Teflon-has been studied and reported. Such nanostructured surfaces have shown strong water repellency properties with apparent water contact angles (AWCA) of as high as 160°, which were found to depend strongly upon the fabrication conditions. Variations in Ar pressure and the substrate tilting angle resulted in the generation of WNRs with different surface roughness and porosity properties. A theoretical model has been proposed to predict the observed high AWCAs measured at the nanostructure interfaces. The unique pyramidal tip geometry of WNRs generated at low Ar pressure with a high oblique angle reduced the solid fraction at the water interface, explaining the high AWCA measured on such surfaces. It was also found that the top geometrical morphologies controlling the total solid fraction of the WNRs are dependent upon and controlled by both the Ar pressure and substrate tilting angle. The water repellency of the tungsten nanorods with contact angles as high as 160° suggests that these coatings have enormous potential for robust superhydrophobic and anti-icing applications in harsh environments.