Analysis of plane and axisymmetric flows of incompressible fluids with the stream tube method: Numerical simulation by trust-region optimization algorithm

New concepts for the study of incompressible plane or axisymmetric flows are analysed by the stream tube method. Flows without eddies and pure vortex flows are considered in a transformed domain where the mapped streamlines are rectilinear or circular. The transformation between the physical domain and the computational domain is an unknown of the problem. In order to solve the non-linear set of relevant equations, we present a new algorithm based on a trust region technique which is effective for non-convex optimization problems. Experimental results show that the new algorithm is more robust compared to the Newton-Raphson method.     

Water-soluble cellulose derivatives prepared by the action of solutions of nitrogen dioxide in dimethylformamide

Cellulose derivatives soluble in water and in dilute alkali were prepared by dissolving a bleached sulfite pulp in solutions of nitrogen dioxide in dimethylformamide (DMF) and heating at 70–90°C for 1–3 hr. No cellulose oxidation was detected. Nitrite esters and apparently also, nitrate esters, were formed with degrees of substitution (DS) ranging from 0.18 to 0.55 and with nitrogen contents ranging from 1.47 to 4.32%. Solution viscosities in water increased with increasing nitrogen content. The degree of polymerization (DP) decreased rapidly in the initial stages of the reaction followed by a slow, gradual decrease with increasing reaction times.     

Theoretical analysis of non-uniform extensional flows in relation to processing rheology and predictions of some constitutive equations

In this paper, a characteristic equation involving the stream function, already given by one of the authors in a previous work for classifying axisymmetric incompressible flows, is re-considered. Non-uniform nearly extensional flows are derived as particular solutions from this equation. Using experimental data in the literature for polymer solutions and melts, it is proved that particular solutions of the characteristic equation lead to kinematics very close to those encountered in the fiber-spinning process. The kinematic equations satisfactorily correlating the fiber-spinning data are used in order to determine the ability of constitutive equations to predict realistic stresses in the flow domain. The rheological parameters of the fluids, obtained from experiments, are used for computation of differential and integral constitutive equations in the spinning conditions. Comparisons with the stress response of adequate constitutive equations are given and discussed.Also affiliated to: Université Joseph Fourier Grenoble I and Institut National Polytechnique de Grenoble, Associé au CNRS (URA 1510)     

A finite-element approach in stream-tube method for solving fluid and solid mechanics problems

This paper presents a theoretical formulation in which the stream-tube method (STM) is examined through a variational approach for solving solid strain and fluid flow problems with finite elements. The analysis considers a reference domain, used as computational domain, related to the physical domain by an unknown transformation function to be determined numerically. Mass conservation is automatically verified by STM. The variational approach leads to eliminate the pressure in fluid problems and avoids to set up a mixed displacement–pressure procedure in the case of incompressible solids. Examples are given for fluid flows, applications and comparisons are also provided in the bending problem in elasticity.     

The reaction of hexamethyl phosphoric triamide (HMPT) with phosphoryl chloride : A reexamination. Application to a novel preparation of BOP reagent for peptide coupling

The reaction of hexamethyl phosphoric triamide with phosphoryl chloride at R.T. gave actually a chlorophosphonium salt. This reaction is illustrated in a novel preparation of BOP reagent for peptide coupling in good conditions.     

Numerical simulation of complex flows of non-Newtonian fluids using the stream tube method and memory integral constitutive equations

In this paper a memory integral viscoelastic equation is considered for simulating complex flows of non-Newtonian fluids by stream tube analysis. A formalism is developed to take into account co-deformational memory equations in a mapped computational domain where the transformed streamlines are parallel and straight. The particle-tracking problem is avoided. Evolution in time and related kinematic quantities involved with a K-BKZ integral constitutive model are easily taken into account in evaluating the stresses. Successive subdomains, the stream tubes, may be considered for computing the main flow in abrupt axisymmetric contractions from the wall to the central flow region. The ‘peripheral stream tube’ close to the duct wall is determined by developing a non-conventional modified Hermite element. A mixed formulation is adopted and the relevant non-linear equations are solved numerically by the Levenberg-Marquardt algorithm. Although the singularity at the section of contraction is not involved explicitly, the results obtained for the peripheral stream tube clearly show the singularity effects and the extent of the recirculating zone near the salient corner. The algorithm is stable even at high flow rates and provides satisfactory solutions when compared with similar calculations in the literature.     

Vibrational Spectra of Anhydrous Lanthanum,Europium, Gadolinium,and Dysprosium Nitrates and Oxinitrates

IR. and Raman spectra of LnONO₃ (50–4,000 cm^?1, Ln?La, Gd, Eu, and Dy) are reported and discussed. The low frequency region of the spectra reflects the cubic structure of these compounds. The dimensions of the cubic unit cells determined by X-Ray powder diagrams are: 12.81 ± 0.05 Å for EuONO₃, 12.69 ± 0.05 Å for GdONO₃, and 12.67 ± 0.05 Å for DyONO₃. The vibrational frequencies of the nitrato group are consistent with a bidentate nitrate of C_2v symmetry. The synthesis of anhydrous Ln (NO₃)₃ (Ln?La, Gd, Eu, and Dy) by dehydration of the corresponding penta- or hexahydrates is described. The IR. and Raman spectra (50-4,000 cm^?1) are analysed. Splitting of the bands point to a complex structure of these compounds. All six vibrational modes of the nitrato group are observed and the data are again consistent with bidentate NO^?₃ moieties. Finally, an analytical control of the purity of Ln (NO₃)₃ is suggested.