Three-dimensional temporally resolved measurements of turbulence–flame interactions using orthogonal-plane cinema-stereoscopic PIV

A new orthogonal-plane cinema-stereoscopic particle image velocimetry (OPCS-PIV) diagnostic has been used to measure the dynamics of three-dimensional turbulence–flame interactions. The diagnostic employed two orthogonal PIV planes, with one aligned perpendicular and one aligned parallel to the streamwise flow direction. In the plane normal to the flow, temporally resolved slices of the nine-component velocity gradient tensor were determined using Taylor’s hypothesis. Volumetric reconstruction of the 3D turbulence was performed using these slices. The PIV plane parallel to the streamwise flow direction was then used to measure the evolution of the turbulence; the path and strength of 3D turbulent structures as they interacted with the flame were determined from their image in this second plane. Structures of both vorticity and strain-rate magnitude were extracted from the flow. The geometry of these structures agreed well with predictions from direct numerical simulations. The interaction of turbulent structures with the flame also was observed. In three dimensions, these interactions had complex geometries that could not be reflected in either planar measurements or simple flame–vortex configurations.     

Correction: Suppressing carboxylate nucleophilicity with inorganic salts enables selective electrocarboxylation without sacrificial anodes

Correction for ‘Suppressing carboxylate nucleophilicity with inorganic salts enables selective electrocarboxylation without sacrificial anodes’ by Nathan Corbin et al., Chem. Sci., 2021, DOI: 10.1039/D1SC02413B.

We regret that there was a minor error in the structure of the benzyl chloride in Scheme 2, Fig. 2 and the ESI. The structure of the benzyl chloride should be 4-methyl benzyl chloride but was instead given as 3-methyl benzyl. The correct figure and scheme are shown below, and the ESI has been updated.Open in a separate windowFig. 2(A) Comparison of acid yields for non-sacrificial-anode and sacrificial-anode carboxylation of various substrates. (B) Ratio of carboxylic acid to nucleophilic side products (ester + carbonate + alcohol) for various systems and substrates. Effect of adding MgBr₂ to the sacrificial-anode system on the (C) acid yield and (D) ratio of acid to S_N2 side products for benzyl bromide. Acid yields are tabulated in Table S6.† ND: acid not detected (acid-to-S_N2 ratio <0.1).Open in a separate windowScheme 2Substrate scope for the sacrificial-anode-free electrochemical carboxylation of organic halides. ^aStandard reaction conditions: 100 mM electrolyte, 100 mM substrate, 100 mM MgBr₂, silver cathode, platinum anode, 20 sccm CO₂, 2.2 mL DMF, −20 mA cm⁻² for 3.5 h. TBA-Br was used for chlorinated substrates because bromide oxidizes more readily than chloride, and only a small amount of chloride was replaced by bromide (<1% for the alkyl chloride, ∼4% for the benzylic chloride). Yields are referenced to the initial amount of substrate and were calculated from ¹H NMR spectroscopy using either 1,3,5-trimethoxybenzene or ethylene carbonate as internal standards. ^b−15 mA cm⁻² instead of −20 mA cm⁻². ^c150 mM MgBr₂ instead of 100 mM MgBr₂.The Royal Society of Chemistry apologises for these errors and any consequent inconvenience to authors and readers.     

Suppressing carboxylate nucleophilicity with inorganic salts enables selective electrocarboxylation without sacrificial anodes

Although electrocarboxylation reactions use CO₂ as a renewable synthon and can incorporate renewable electricity as a driving force, the overall sustainability and practicality of this process is limited by the use of sacrificial anodes such as magnesium and aluminum. Replacing these anodes for the carboxylation of organic halides is not trivial because the cations produced from their oxidation inhibit a variety of undesired nucleophilic reactions that form esters, carbonates, and alcohols. Herein, a strategy to maintain selectivity without a sacrificial anode is developed by adding a salt with an inorganic cation that blocks nucleophilic reactions. Using anhydrous MgBr₂ as a low-cost, soluble source of Mg²⁺ cations, carboxylation of a variety of aliphatic, benzylic, and aromatic halides was achieved with moderate to good (34–78%) yields without a sacrificial anode. Moreover, the yields from the sacrificial-anode-free process were often comparable or better than those from a traditional sacrificial-anode process. Examining a wide variety of substrates shows a correlation between known nucleophilic susceptibilities of carbon–halide bonds and selectivity loss in the absence of a Mg²⁺ source. The carboxylate anion product was also discovered to mitigate cathodic passivation by insoluble carbonates produced as byproducts from concomitant CO₂ reduction to CO, although this protection can eventually become insufficient when sacrificial anodes are used. These results are a key step toward sustainable and practical carboxylation by providing an electrolyte design guideline to obviate the need for sacrificial anodes.

Selective electrocarboxylation of nucleophilically susceptible organic halides without sacrificial anodes is enabled by inorganic salt additives, which suppress the nucleophilicity of anions in the electrolyte.     

Construction of lattice orders on the semigroup ring of a positive rooted monoid

Lattice orders on the semigroup ring of a positive rooted monoid are constructed, and it is shown how to make the monoid ring into a lattice-ordered ring with squares positive in various ways. It is proved that under certain conditions these are all of the lattice orders that make the monoid ring into a lattice-ordered ring. In particular, all of the partial orders on the polynomial ring A[x] in one positive variable are determined for which the ring is not totally ordered but is a lattice-ordered ring with the property that the square of every element is positive. In the last section some basic properties of d-elements are considered, and they are used to characterize lattice-ordered division rings that are quadratic extensions of totally ordered division rings.     

Application of the symmetry principle for biharmonic functions to a problem in fracture mechanics

It is shown that a well-known series expansion of the stress function around a tip of a crack in an elastic plate, converges on a two-sheet Riemann surface. Explicit expressions for its coefficients, the stress intensity factors, are obtained. More generally, a new series expansion around the whole crack is found and investigated.     

Inverse spectral problems for inhomogeneous elastic cylinders

The goal of the paper is to formulate the inverse spectral problems for a determination of elastic moduli and to develop a method of their solution. These types of problems always arise when one tries to determine moduli in inhomogeneous materials using spectral data which are received from an experiment of excitation of free oscillations. Our treatment of the problems is within the framework of linear elasticity and is based on the Levitan and Marchenko's theory of Sturm-Liouville inverse problems.     

Sol-Gel Synthesis of Nanocrystalline PZT Using a Novel System

A simple system has been developed for the preparation of lead zirconate titanate, Pb(Zr _x Ti_{1 – x} )O₃ powders by sol-gel process. To achieve stable and homogeneous precursor solutions, chelating ligands such as acetic acid and acetylacetone have been used for the chemical modification of titanium and zirconium starting precursors. Phase-pure PZT powders were obtained, through a pyrochlore-free pathway, from the amorphous xerogel after heat treatment at 600°C. The formation of the crystalline phase, compositional homogeneity, sinterability, dielectric and piezoelectric characteristics of PZT are reported.