Flow of a mixture of a viscous fluid and a granular solid in an orthogonal rheometer

In this paper, we study the flow of a linearly viscous fluid and a granular solid, consisting of many particles, situated between two parallel plates rotating about different axes. Flow in orthogonal rheometers has been studied for many viscoelastic fluids so that their rheological properties can be measured. The mixture is modeled using the theory of interacting continua, and constitutive relations for the fluid phase, the granular phase, and the interaction forces are provided. For a very special case, an analytical solution to the equations of motion is also provided.     

Constitutive relations for the interaction force in multicomponent particulate flows

In the mechanics of multiphase (or multicomponent) mixtures, one of the outstanding issues is the formulation of constitutive relations for the interaction force. In this paper, we give a brief review of the various relations proposed for this interaction force. The review is tilted toward presenting the works of those who have used the mixture theory (or the theory of interacting continua) to derive or to propose a relationship for the interaction (or diffusive) force. We propose a constitutive relation which is general and frame-indifferent and thus suitable for use in many flow conditions. At the end, we provide an alternative approach for finding the drag force on a particle in a particulate mixture. This approach has been used in the non-Newtonian fluid mechanics to find the drag force on surfaces.     

Adsorption of Metanil Yellow Azoic Dye from Aqueous Solution onto Mg‐Fe‐NO3 Layered Double Hydroxide

We report the preparation and characterization of a layered double hydroxide (LDH) adsorbent for azoic dye, metanil yellow (yellow GX; YGX) removal. The nanoparticles of Mg‐Fe‐LDH‐NO₃ adsorbent were prepared with Mg/Fe molar ratio of 3:1 by a hydrothermal process and coprecipitation method at pH 9.5 and were characterized by X‐ray powder diffraction (XRPD), thermal gravimetric analysis (TGA), elemental analysis, and Fourier transform infrared spectroscopy (FT‐IR). The size and morphology of nanoparticles were examined by scanning electron microscopy (SEM). The XRD patterns indicate that the intercalation of YGX between the LDH layers has not occurred and surface adsorption has happened. In the adsorption experiments, the Gibbs free energy ΔG⁰ values, the enthalpy ΔH⁰, and entropy ΔS⁰ was determined. The isotherms showed that the adsorption of YGX by Mg‐Fe‐LDH‐NO₃ was both consistent with Langmuir and Freundlich equations.     

Different orientations of C=O versus P=O in P(O)NHC(O) skeleton: the first study on an aliphatic diazaphosphorinane with a gauche orientation

Different orientations of P(O) versus C(O) in P(O)NHC(O) skeleton have been discussed in two new phosphorus(V)-nitrogen compounds with formula XP(O)Y and XP(O)Z₂ where X = NHC(O)C₆H₄(4-F) and Y = NHCH₂C(CH₃)₂CH₂NH (1), Z = NHC₆H₄(4-CH₃) (2). Compound 1 is the first example of an aliphatic diazaphosphorinane with a gauche orientation which has been studied by X-ray crystallography; the P=O bond is in the equatorial position of the ring. Both compounds show ⁿ J(F,C) and ^m J(F,H) coupling constants (n = 1, 2, 3 and 4; m = 3 and 4) and ³ J(P,C) > ² J(P,C). Quantum chemical calculations were performed with HF and Density Functional Theory (DFT) methods using 6−31+G(d,p) basis set. A tentative assignment of the observed vibrational bands for these molecules is discussed. Compound 1 shows a deshielded C atom of the carbonyl moiety (in ¹³C NMR spectrum) relative to that of 2, which is supported by IR spectroscopy in which the considerably lower C=O frequency is observed for 1. Comparing the X-ray crystallography and IR spectra of 1 and 2 shows that the acyclic compound 2, containing P=O and C=O bonds in an anti position, are involving in a stronger N–H···O=P hydrogen bond in crystal network. This leads to a weaker P=O and N_C(O)NHP(O)–H bonds and stronger N···O interaction. The N_amide–H is involved in an intramolecular N–H···O hydrogen bond.     

Temporary shape development in shape memory nanocomposites using magnetic force

Direct mechanical force is used to create a temporary shape in shape memory polymers. This can become difficult in situations where the sample is not directly accessible such as interior in the body. In these cases it is not possible to use a direct mechanical force to deform the sample into temporary shape; therefore other alternative routes should be proposed. The magnetic force is a good candidate for inducing remote deformation. The ability of magnetic field to cause deformation in soft matters has already been revealed. To prove the hypothesis of using magnetic force to create temporary shape, magnetic field active shape memory polymeric nanocomposites were manufactured by incorporation of NdFeB ferromagnetic micro particles in a nanocomposite based on crosslinked low density polyethylene loaded with 2 wt.% of organoclay. The results indicate that as the NdFeB content increases, the reversible temporary deformation induced in the samples by the magnetic force increases. The effect of NdFeB concentration on the shape recovery progress and the possibility of heat induction in NdFeB filled samples through the application of an alternating magnetic field were also examined.     

Accurate and approximate integrations of Drucker–Prager plasticity with linear isotropic and kinematic hardening

Up to now, some explicit approximate integration schemes based on exponential maps, for non-hardening material obeying Drucker–Prager’s criterion, have been presented. Two new exponential-based approximate formulations, for associative Drucker–Prager plasticity are developed in this article. Both are consistent and explicit algorithms. The linear isotropic and Prager’s kinematic hardening behavior are assumed. Furthermore, an accurate solution for the constitutive equations is derived. The accuracies of the suggested approximate algorithms are assessed by creating related iso-error maps. In addition, by using piecewise strain load histories, and calculating computation times, the robustness and efficiency of the formulations are demonstrated.     

In situ vinylindole synthesis. Diels-alder reactions with maleimides to give tetrahydrocarbazoles

Tetrahydrocarbazoles have been prepared in one-flask syntheses from indoles, ketones or aldehydes, and maleimides, with acid catalysis. The reactions involve a condensation of the indole with the ketone or aldehyde, followed by an in situ trapping of the vinylindole in a Diels-Alder addition with a maleimide. Isomerization of the double bond into the indole nucleus gave the tetrahydrocarbazoles which were isolated ( 6, 9 , and 10 ). Variation of the indole, carbonyl compound, and maleimide has been explored. The predominant stereochemistry of the tetrahydro ring in the products is all-cis, although a second stereoisomer has been isolated. Two regioisomers were generated from all unsymmetrical 2-alkanones, except 2-butanone, which gave the single isomer 9a . Aromatization of tetrahydrocarbazoles 6 to carbazoles 7 was accomplished with 2,3-dichloro-5,6-dicyano-1,4-benzoquinone.     

Material symmetry and the evolution of anisotropies in a simple material—I. Change of reference configuration

Noll's rule is used to determine the structure of a material symmetry group written with respect to one reference configuration when the representation of the symmetry with respect to another configuration is the traditional material symmetry group associated with isotropy, transverse isotropy or orthotropy, and for an arbitrary deformation gradient relating the two configurations. It is shown that the former symmetry group can contain an orthogonal subgroup. It is determined whether this subgroup is that for isotropic, transversely isotropic, orthotropic, monoclinic, or triclinic response, and the preferred directions of the symmetry are determined.     

The use of Chebyshev cardinal functions for the solution of a partial differential equation with an unknown time-dependent coefficient subject to an extra measurement

A numerical technique is presented for the solution of a parabolic partial differential equation with a time-dependent coefficient subject to an extra measurement. The method is derived by expanding the required approximate solution as the elements of Chebyshev cardinal functions. Using the operational matrix of derivative, the problem can be reduced to a set of algebraic equations. From the computational point of view, the solution obtained by this method is in excellent agreement with those obtained by previous works and also it is efficient to use.     

Structure and Mechanical Properties of 50/50 NR/SBR Blend/Pristine Clay Nanocomposites

A blend/clay nanocomposites of 50/50 (wt%) NR/SBR was prepared via mixing the latex of a 50/50 NR/SBR blend with an aqueous clay dispersion and co‐coagulating the mixture. The structure of the nanocomposite was characterized by transmission electron microscopy (TEM) and X-ray diffraction (XRD). Nanocomposites containing less than 10 phr clay showed a fully exfoliated structure. After increasing the clay content to 10 phr, both nonexfoliated (stacked layers) and exfoliated structures were observed in the nanocomposites. The results of mechanical tests showed that the nanocomposites presented better mechanical properties than clay‐free NR/SBR blend vulcanizate. Furthermore, tensile strength, tensile strain at break, and hardness (shore A) increased with increasing clay content, up to 6 phr, and then remained almost constant.