Efficient computation of non-isothermal highly viscous incompressible flow

We consider the numerical solution of the non–isothermal incompressible Navier–Stokes equations using a discrete projection method. The computation of velocity and temperature subproblems is carried out on different meshes chosen with respect to the physical behavior of these quantities. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Rheological modeling of the diffusion process and the interphase of symmetrical bilayers based on PVDF and PMMA with varying molecular weights

The diffusion process in the molten state at a polymer/polymer interface of symmetrical and model bilayers has been investigated using a small-amplitude oscillatory shear measurement. The polymers employed in this study were poly (vinylidene fluoride) (PVDF) and poly (methyl methacrylate) (PMMA) of varying molecular weights and polydispersities. The measurements were conducted in the linear viscoelastic regime (small deformations) so as to decouple the effect of flow from the diffusion. The focus of this paper has been to investigate the effects of healing time, angular frequency (ω), temperature, and molecular weight on the inter-diffusion and the triggered interphase between the neighboring layers. The kinetics of diffusion, based on the evolution of the apparent diffusion coefficient (D _a) versus the healing time, was experimentally obtained. The transition from the non-Fickian to the normal Fickian region for the inter-diffusion at the interface was clearly observed, qualitatively consistent with the reptation model, but it occurred at a critical time greater than the reptation time (τ _rep). In non-Fickian region, effects of frequency and temperature were studied with regard to the ratio of the apparent diffusion coefficient to the self-diffusion coefficient (D _a/D _s). The D _s determined in the Fickian region was found to be consistent with Graessley’s model as well as with the literatures. And the dependence of the D_s on the frequency agreed well with the Doi–Edwards theory, in particular, scaling as $D_{\rm s} \sim \omega^{1/2}$ at ω?>?1/τ _e and $D_{\rm s} \sim \omega^{0}$ at ω?<?1/τ _rep. Our experimental results also confirmed that the dependence of the D _s on the temperature for PMMA and PVDF can be well described by the Arrhenius law. Moreover, blends of PMMAs have been proposed in order to be able to change the $\overline M_\emph{w} $ . The rheological investigations of these corresponding bilayers rendered it possible to monitor the effect of $\overline M_\emph{w} $ on the diffusion process. The obtained results gave $D_{\rm s} \sim \overline M_\emph{w}^{-1}$ , thus corroborating some earlier studies and some experimental results recently reported by Time-Resolved Neutron Reflectivity Measurements. Lastly, the thickness of the interphase and its corresponding viscoelastic properties could be theoretically determined as a function of the healing?time.     

Aryl Radical‐Mediated Alkenylation of Alkyl Halides

The free‐radical alkenylation of a range of alkyl iodides with a vinyldisulfones has been carried out, leading to the desired vinylsulfones in moderate to good yields under mild conditions. The process is initiated by an aryl radical which abstracts the iodine atom from the alkyl iodide to form a C‐centered radical intermediate, the addition of which onto the vinyldisulfone providing the final vinylsulfone. The aryl radical is generated in situ through a single‐electron transfer from an electron donor‐acceptor complex (EDA) formed between a diaryliodonium salt (Ph₂I⁺ PF₆^?) and triethylamine.     

Synthesis of new molecules containing head,spacer, and label moieties

We describe the synthesis and characterization of novel molecules containing head with precise shape, spacer, and label moieties. The protocol is based on a Pd(0)-catalyzed cross-coupling reaction between ethynylphenyl/bromide to obtain a rigid head followed by the attachment of a flexible spacer possessing two reactive functional groups on the termini. The final step consists of forming a covalent bond between spacer and label. In addition, monosubstituted soluble labels were synthesized in good yields.     

Silver(I) oxide mediated highly selective monotosylation of symmetrical diols. Application to the synthesis of polysubstituted cyclic ethers

[reaction: see text] The reaction of symmetrical diols and oligo(ethylene glycol)s with a stoichiometric amount of p-toluenesulfonyl chloride in the presence of silver(I) oxide and a catalytic amount of potassium iodide led selectively to the monotosylate derivatives in high yields. Polysubstituted cyclic ethers were obtained readily upon treatment of the corresponding diols with an excess of silver oxide. The high selectivity was explained on the basis of the difference in acidity between the two hydroxy groups, which undergo an intramolecular hydrogen bonding.     

Lyapunov Stability of Differential Inclusions with Lipschitz Cusco Perturbations of Maximal Monotone Operators

Set-Valued and Variational Analysis - We give new criteria for weak and strong invariant closed sets for differential inclusions in $\mathbb {R}^{n}$ , and which are simultaneously governed by...     

On Brøndsted–Rockafellar’s Theorem for convex lower semicontinuous epi-pointed functions in locally convex spaces

Mathematical Programming - In this work we give an extension of the Brøndsted–Rockafellar Theorem, and some of its important consequences, to proper convex lower-semicontinuous...     

New Formulas for the Fenchel Subdifferential of the Conjugate Function

Following (López and Volle, J Convex Anal 17, 2010) we provide new formulas for the Fenchel subdifferential of the conjugate of functions defined on locally convex spaces. In particular, this allows deriving expressions for the minimizers set of the lower semicontinuous convex hull of such functions. These formulas are written by means of primal objects related to the subdifferential of the initial function, namely a new enlargement of the Fenchel subdifferential operator.     

Viscosity and Rheological Properties of Graphene Nanopowders Nanofluids

The dynamic viscosity and rheological properties of two different non-aqueous graphene nano-plates-based nanofluids are experimentally investigated in this paper, focusing on the effects of solid volume fraction and shear rate. For each nanofluid, four solid volume fractions have been considered ranging from 0.1% to 1%. The rheological characterization of the suspensions was performed at 20 ∘C, with shear rates ranging from 10−1s−1 to 103s−1, using a cone-plate rheometer. The Carreau–Yasuda model has been successfully applied to fit most of the rheological measurements. Although it is very common to observe an increase of the viscosity with the solid volume fraction, we still found here that the addition of nanoparticles produces lubrication effects in some cases. Such a result could be very helpful in the domain of heat extraction applications. The dependence of dynamic viscosity with graphene volume fraction was analyzed using the model of Vallejo et al.