Alternative subcell discretisations for viscoelastic flow: Velocity-gradient approximation

Under subcell discretisation for viscoelastic flow, we have given further consideration to the compatibility of function spaces for stress/velocity-gradient approximation [see F. Belblidia, H. Matallah, B. Puangkird, M.F. Webster, Alternative subcell discretisations for viscoelastic flow: stress interpolation, J. Non-Newtonian Fluid Mech. 146 (2007) 59–78]. This has been conducted through the three scheme discretisations (quad-fe(par), fe(sc) and fe/fv(sc)). In this companion study, we have extended the application of an original implementation for velocity-gradient approximation, being of localised superconvergent recovered form, continuous and quadratic on the parent fe-triangular element. This has led to the consideration of both localised (pointwise) and global (Galerkin weighted-residual) approximations for velocity-gradient, highlighting some of their advantages and disadvantages. The global form is equivalent to the discontinuous elastico–viscous stress splitting (DEVSS-type) technique of Fortin and co-workers. Each representation, local or global, is based on linear/quadratic order upon parent or subcell element stencils. We consider Oldroyd modelling and the contraction flow benchmark, covering abrupt and rounded-corner planar geometries. The localised superconvergent quadratic velocity-gradient treatment affords strong stability and accuracy properties for the three scheme discretisations considered. Through associated analysis and iterative solution processes, we have successfully linked global approximations to their localised counterparts, depicting the inadequacy of inaccurate but stable versions through their corresponding solution features. These issues pervade all formulations, coupled or pressure-correction, and in focusing on velocity-gradient approximation, also apply universally to all discrete representations of stress. The inaccuracy of the global treatment can be somewhat repaired through an increase in (mass) iteration number. The efficiency of localised schemes (and associated properties) is particularly attractive over their global alternatives, being less restrictive to choice of spatial-order (higher-order). Conversely, global implementations are more restrictive in satisfaction of the space inclusion principle. Localised schemes come into their own when chosen to represent strongly localised solution features, such as arise in non-smooth flows. Analysis has also proved helpful in clarifying that space inclusion (extended LBB-condition) is a non-necessary convergence condition in the viscoelastic context.Overall, the localised-quadratic velocity-gradient treatment for both linear (subcell) and quadratic (parent) stress interpolation has achieved both stability and accuracy. Under DEVSS-type approximations (global), once function spaces for stress and velocity-gradients have been selected, this choice dictates the state of system consistency. Additionally, stability gains are recognised through the further application of strain-rate-stabilisation procedures.     

Synthesis,spectroscopic and structural characterisation of vanadium(IV) and oxovanadium(IV) complexes with arsenic donor ligands

The reaction of o-C₆H₄(AsMe₂)₂ with VCl₄ in anhydrous CCl₄ produces orange eight-coordinate [VCl₄{o-C₆H₄(AsMe₂)₂}₂], whilst in CH₂Cl₂ the product is the brown, six-coordinate [VCl₄{o-C₆H₄(AsMe₂)₂}]. In dilute CH₂Cl₂ solution slow decomposition occurs to form the V^III complex [V₂Cl₆{o-C₆H₄(AsMe₂)₂}₂]. Six-coordination is also found in [VCl₄{MeC(CH₂AsMe₂)₃}] and [VCl₄{Et₃As)₂]. Hydrolysis of these complexes occurs readily to form vanadyl (VO²⁺) species, pure samples of which are obtained by reaction of [VOCl₂(thf)₂(H₂O)] with the arsines to form green [VOCl₂{o-C₆H₄(AsMe₂)₂}], [VOCl₂{MeC(CH₂AsMe₂)₃}(H₂O)] and [VOCl₂(Et₃As)₂]. Green [VOCl₂(o-C₆H₄(PMe₂)₂}] is formed from [VOCl₂(thf)₂(H₂O)] and the ligand. The [VOCl₂{o-C₆H₄(PMe₂)₂}] decomposes in thf solution open to air to form the diphosphine dioxide complex [VO{o-C₆H₄(P(O)Me₂)₂}₂(H₂O)]Cl₂, but in contrast, the products formed from similar treatment of [VCl₄{o-C₆H₄(AsMe₂)₂}_x] or [VOCl₂{o-C₆H₄(AsMe₂)₂}] contain the novel arsenic(V) cation [o-C₆H₄(AsMe₂Cl)(μ-O)(AsMe₂)]⁺. X-ray crystal structures are reported for [V₂Cl₆{o-C₆H₄(AsMe₂)₂}₂], [VO(H₂O){o-C₆H₄(P(O)Me₂)₂}₂]Cl₂, [o-C₆H₄(AsMe₂Cl)(μ-O)(AsMe₂)]Cl·[VO(H₂O)₃Cl₂] and powder neutron diffraction data for [VCl₄{o-C₆H₄(AsMe₂)₂}₂].     

The Effect of the Buffering Capacity of the Supporting Electrolyte on the Electrochemical Oxidation of Dopamine and 4‐Methylcatechol in Aqueous and Nonaqueous Solvents

Dopamine was electrochemically oxidized in aqueous solutions and in the organic solvents N,N‐dimethyl‐formamide and dimethylsulfoxide containing varying amounts of supporting electrolyte and water, to form dopamine ortho‐quinone. It was found that the electrochemical oxidation mechanism in water and in organic solvents was strongly influenced by the buffering properties of the supporting electrolyte. In aqueous solutions close to pH 7, where buffers were not used, the protons released during the oxidation process were able to sufficiently change the localized pH at the electrode surface to reduce the deprotonation rate of dopamine ortho‐quinone, thereby slowing the conversion into leucoaminochrome. In N,N‐dimethylformamide and dimethylsulfoxide solutions, in the absence of buffers, dopamine was oxidized to dopamine ortho‐quinone that survived without further reaction for several minutes at 25 °C. The voltammetric data obtained in the organic solvents were made more complicated by the presence of HCl in commercial sources of dopamine, which also underwent an oxidation process.     

Facile Hydrolysis and Alcoholysis of Palladium Acetate

Palladium(II) acetate is readily converted into [Pd₃(μ²‐OH)(OAc)₅] ( 1 ) in the presence of water in a range of organic solvents and is also slowly converted in the solid state. Complex 1 can also be formed in nominally anhydrous solvents. Similarly, the analogous alkoxide complexes [Pd₃(μ²‐OR)(OAc)₅] ( 3 ) are easily formed in solutions of palladium(II) acetate containing a range of alcohols. An examination of a representative Wacker‐type oxidation shows that the Pd‐OH complex 1 and a related Pd‐oxo complex 4 can be excluded as potential catalytic intermediates in the absence of exogenous water.