An image system and surface singularity solutions for potential flow past an elliptical cylinder

The Milne-Thomson circle theorem is extended to give a simplegeneral expression for the image system in an elliptical cylinderintroduced into an otherwise specified unbounded potential flowwhich contains no singularities in the region to be occupiedby the ellipse. This image system is used to obtain an expressionfor the corresponding source-sink surface singularity distributionon the ellipse, thus providing new benchmark test cases forsource-sink solutions as obtained numerically by a panel method.Several typical examples are given to illustrate the generaltheoretical approach.     

Solvent Effect and Reactivity Trend in the Aerobic Oxidation of 1,3‐Propanediols over Gold Supported on Titania: NMR Diffusion and Relaxation Studies

In recent work, it was reported that changes in solvent composition, precisely the addition of water, significantly inhibits the catalytic activity of Au/TiO₂ catalyst in the aerobic oxidation of 1,4‐butanediol in methanol due to changes in diffusion and adsorption properties of the reactant. In order to understand whether the inhibition mechanism of water on diol oxidation in methanol is generally valid, the solvent effect on the aerobic catalytic oxidation of 1,3‐propanediol and its two methyl‐substituted homologues, 2‐methyl‐1,3‐propanediol and 2,2‐dimethyl‐1,3‐propanediol, over a Au/TiO₂ catalyst has been studied here using conventional catalytic reaction monitoring in combination with pulsed‐field gradient nuclear magnetic resonance (PFG‐NMR) diffusion and NMR relaxation time measurements. Diol conversion is significantly lower when water is present in the initial diol/methanol mixture. A reactivity trend within the group of diols was also observed. Combined NMR diffusion and relaxation time measurements suggest that molecular diffusion and, in particular, the relative strength of diol adsorption, are important factors in determining the conversion. These results highlight NMR diffusion and relaxation techniques as novel, non‐invasive characterisation tools for catalytic materials, which complement conventional reaction data.     

Interpretation of NMR Relaxation as a Tool for Characterising the Adsorption Strength of Liquids inside Porous Materials

Nuclear magnetic resonance (NMR) relaxation times are shown to provide a unique probe of adsorbate–adsorbent interactions in liquid‐saturated porous materials. A short theoretical analysis is presented, which shows that the ratio of the longitudinal to transverse relaxation times (T₁/T₂) is related to an adsorbate–adsorbent interaction energy, and we introduce a quantitative metric e_surf (based on the relaxation time ratio) characterising the strength of this surface interaction. We then consider the interaction of water with a range of oxide surfaces (TiO₂ anatase, TiO₂ rutile, γ‐Al₂O₃, SiO₂, θ‐Al₂O₃ and ZrO₂) and show that e_surf correlates with the strongest adsorption sites present, as determined by temperature programmed desorption (TPD). Thus we demonstrate that NMR relaxation measurements have a direct physical interpretation in terms of the characterisation of activation energy of desorption from the surface. Further, for a series of chemically similar solid materials, in this case a range of oxide materials, for which at least two calibration values are obtainable by TPD, the e_surf parameter yields a direct estimate of the maximum activation energy of desorption from the surface. The results suggest that T₁/T₂ measurements may become a useful addition to the methods available to characterise liquid‐phase adsorption in porous materials. The particular motivation for this work is to characterise adsorbate–surface interactions in liquid‐phase catalysis.