Propagation of a pre-existing turbulent fluid fracture

The propagation of rough and smooth wall pre-existing turbulent fluid fractures is investigated. The laminar fluid fracture is included as a special case for comparison. Lubrication theory is assumed to apply in the fracture and turbulence is introduced through the wall shear stress. The Perkins–Kern–Nordgren approximation is made in which the fluid pressure is proportional to the half-width of the fracture. The fracture half-width satisfies a non-linear diffusion equation. By using a linear combination of the Lie point symmetries of the non-linear diffusion equation a group invariant solution for the fracture length, volume and half-width is derived. The evolution of the length, half-width and mean flow velocity is analysed for a range of working conditions at the fracture entry. It is found that the mean flow velocity increases approximately linearly along the fracture.     

Controlled Activity Polymers. IV. Copolymers of 2-(1-Naphthylacetyl)Ethyl Acrylate With Hydrophilic Comonomers: Synthesis and Characterization

2-(1-Naphthylacetyl)ethyl acrylate (NAEA) was synthesized by esterification of 1-naphthylacetic acid (NAA) and 2-hydroxyethyl acrylate (HEA) and then polymerized to obtain the polymer-bound auxin NAA. The resulting polymer is potentially useful as a plant growth regulator through hydrolytic release of NAA. Copolymers of NAEA with hydrophilic comonomers were prepared by solution polymerization. The copolymer compositions were determined from elemental analysis, ¹³C-NMR, and UV spectroscopy. The copolymer microstructure was predicted from the reactivity ratios in order to investigate the influence on the behavior of controlled release. These model structures will be utilized for assessment of structure/hydrolysis relationships in a subsequent paper.     

Nanocomposite Hydrogel of Pd@ZIF-8 and Laponite®: Size-Selective Hydrogenation Catalyst under Mild Conditions

The composite hydrogel of a nanoscale metal–organic framework (NMOF) and nanoclay has emerged as a new soft-material with advanced properties and applications. Herein, we report a facile synthesis of a hydrogel nanocomposite by charge-assisted self-assembly of Pd@ZIF-8 nanoparticles with Laponite^® nanoclay which coat the surface of Pd@ZIF-8 nanoparticles. Such surface coating significantly enhanced the thermal stability of the ZIF-8 compared to the pristine framework. Further, the Pd@ZIF-8+LP hydrogel nanocomposite shows better size-selective catalytic hydrogenation of olefins than Pd@ZIF-8 nanoparticles based on selective diffusion of the substrate.     

Microwave Assisted Rupture of Furoxans to Nitrile Oxides and Intermolecular Capture by Dipolarophiles

3,4-Diaroylfuroxans 1 react with various dipolarophiles 3 under microwave activation to afford the cycloadduct 4 instead of the expected isoxazole 5 in good yields in the absence of solvent.     

Corrigendum on ‘investigation on molecular interaction studies of binary mixture of Dehpa and Petrofin at 298.15 K’

Expressions of Redlich–Kister (RK) excess function using polynomials on difference of molar composition are used. Calculated values of excess properties from experimental values are well presented in some curves as a function of mole fraction (x₂) of the second pure component of the studied binary liquid mixture. Nevertheless, the authors presented values of adjustable parameters, not for the polynomial of the popular RK equation (i.e. vs. x₂–x₁), but for globally the excess property Y^E as an overall three degree polynomial on (x₂) including implicitly the molar fraction product (x₁·x₂) in their nonlinear regression, which can then induces some readers to probable confusion.     

Click Chemistry on Polymer Support: Synthesis of 1-Vinyl- and 1-Allyl-1,2,3-triazoles via Selenium Linker

Polystyrene-supported 2-azidoethyl phenyl selenide and 3-azidopropyl phenyl selenide reagents have been developed and applied to the traceless solid-phase organic synthesis of 1-vinyl- and 1-allyl-1,2,3-triazoles by CuI-mediated azide–alkyne cycloadditions and subsequent cleavage from the polymer support through oxidation–elimination reaction with 30% hydrogen peroxide. The advantages of this method include straightforward operation, good yield and purity of the products, and good stability and lack of odor for the reagents.     

On weak–strong uniqueness for the compressible Navier–Stokes system with non-monotone pressure law

We show the weak–strong uniqueness property for the compressible Navier–Stokes system with general non-monotone pressure law. A weak solution coincides with the strong solution emanating from the same initial data as long as the latter solution exists.     

Analysis of F-53B,Gen-X,ADONA, and emerging fluoroalkylether substances in environmental and biomonitoring samples: A review

The persistent, bioaccumulative, and toxic properties of certain per- and polyfluoroalkyl substances (PFAS) raise concerns for environmental and human health. This has led to the gradual phase-out from production and commerce of some legacy PFAS. Fluoroalkylether compounds (ether-PFAS) are among the fluorinated alternative chemicals that are beginning to be reported in impacted and background environments. Extensive monitoring activities were conducted since 2015–2019 to bridge knowledge gaps on the environmental fate and effects of ether-PFAS including F-53B (6:2 chlorinated polyfluoroalkyl ether sulfonate [6:2 Cl-PFAES] and 8:2 Cl-PFAES), Gen-X (hexafluoropropylene oxide dimer acid [HFPO-DA]), and ADONA (dodecafluoro-3H-4,8-dioxanonanoate). In recent years, advances in nontarget screening using high-resolution mass spectrometry have revealed the identities of other infrequently monitored ether-PFAS. In this critical review, we provide an up-to-date inventory of the structures of ether-PFAS discovered in the recent literature. Their environmental occurrence, fate, and effects are discussed on a comparative perspective with some legacy PFAS such as perfluorooctanoic acid (PFOA) and perfluorooctane sulfonic acid (PFOS). Information on the methods employed for the quantitative and semi-quantitative analysis of ether-PFAS is also provided, including sample preparation and mass spectrometry analysis, analytical performance, and limitations. In particular, the compiled database of MS/MS fragment ions (n = 111) can be useful in spectrum interpretation of novel ether-PFAS. The concluding remarks open on possible research avenues and the challenges that remain to be addressed.     

Euler–MacLaurin formulas via differential operators

Recently there has been a renewed interest in asymptotic Euler–MacLaurin formulas, because of their applications to spectral theory of differential operators. Using elementary means, we recover such formulas for compactly supported smooth functions on intervals, polygons, and three-dimensional polytopes, where the coefficients in the asymptotic expansion are sums of differential operators involving only derivatives of the function in directions normal to the faces of the polytope. Our formulas apply to wedges of any dimension.