Gas solubility of carbon dioxide in poly(lactic acid) at high pressures: Thermal treatment effect

The sorption of carbon dioxide in glassy Poly(lactic acid) (PLA) films was studied by quartz crystal microbalance (QCM) at high pressures. Two thermal treatments, melted and quenched, were performed in PLA with two different L:D contents, 80:20 and 98:2, films and compared with a third thermal protocol, annealed, and used in a previous work. The results obtained show that for pressures higher than 2 MPa, the carbon dioxide solubility is larger in PLA 80:20 than in PLA 98:2, indicating that the L:D plays a dominant role on this property. The thermal treatments only affect the gas solubility in PLA 98:2. Sorption isotherms at temperatures 303, 313, and 323 K, below the glass transition temperature of the polymer, and pressures up to 5 MPa were measured and analyzed with three different models, the dual‐mode sorption model, the Flory–Huggins equation, and a modified dual‐mode sorption model where the Henry's law term was substituted by the Flory–Huggins equation. This last model performs especially well for CO₂ in PLA 80:20, due to the convex upward curvature of the solubility isotherms for that system. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 616–625, 2007     

OPTIMAL INSTAR PARASITIZATION IN A STAGE STRUCTURED HOST-PARASITOID MODEL

A stage structured host-parasitoid model is derived and the equilibria studied. It is shown under what conditions the parasitoid controls an exponentially growing host in the sense that a coexistence equilibrium exists. Furthermore, for host populations whose inherent growth rate is not too large it is proved that in order to minimize the adult host equilibrium level it is necessary that the parasitoids attack only one of the larval stages. It is also proved in this case that the minimum adult host equilibrium level is attained when the parasitoids attack that larval stage which also maximizes the expected number of emerging adult parasitoid per larva at equilibrium. Numerical simulations tentatively indicate that the first conclusion remains in general valid for the model. However, numerical studies also show that it is not true in general that the optimal strategy will maximize the number of emerging adult parasitoid per larva at equilibrium.     

Dynamics of liquid membranes. II: Adaptive finite difference methods

Two domain-adaptive finite difference methods are presented and applied to study the dynamic response of incompressible, inviscid, axisymmetric liquid membranes subject to imposed sinusoidal pressure oscillations. Both finite difference methods map the time-dependent physical domain whose downstream boundary is unknown onto a fixed computational domain. The location of the unknown time-dependent downstream boundary of the physical domain is determined from the continuity equation and results in an integrodifferential equation which is non-linearly coupled with the partial differential equations which govern the conservation of mass and linear momentum and the radius of the liquid membrane. One of the finite difference methods solves the non-conservative form of the governing equations by means of a block implicit iterative method. This method possesses the property that the Jacobian matrix of the convection fluxes has an eigenvalue of algebraic multiplicity equal to four and of geometric multiplicity equal to one. The second finite difference procedure also uses a block implicit iterative method, but the governing equations are written in conservation law form and contain an axial velocity which is the difference between the physical axial velocity and the grid speed. It is shown that these methods yield almost identical results and are more accurate than the non-adaptive techniques presented in Part I. It is also shown that the actual value of the pressure coefficient determined from linear analyses can be exceeded without affecting the stability and convergence of liquid membranes if the liquid membranes are subjected to sinusoidal pressure variations of sufficiently high frequencies.     

Interfacial dynamics‐based modelling of turbulent cavitating flows,Part‐2: Time‐dependent computations

The interfacial dynamics‐based cavitation model, developed in Part‐1, is further employed for unsteady flow computations. The pressure‐based operator‐splitting algorithm (PISO) is extended to handle the time‐dependent cavitating flows with particular focus on the coupling of the cavitation and turbulence models, and the large density ratio associated with cavitation. Furthermore, the compressibility effect is important for unsteady cavitating flows because in a water–vapour mixture, depending on the composition, the speed of sound inside the cavity can vary by an order of magnitude. The implications of the issue of the speed of the sound are assessed with alternative modelling approaches. Depending on the geometric confinement of the nozzle, compressibility model and cavitation numbers, either auto‐oscillation or quasi‐steady behaviour is observed. The adverse pressure gradient in the closure region is stronger at the maximum cavity size. One can also observe that the mass transfer process contributes to the cavitation dynamics. Compared to the steady flow computations, the velocity and vapour volume fraction distributions within the cavity are noticeably improved with time‐dependent computations. Copyright © 2004 John Wiley & Sons, Ltd.     

Calculation of impulsively started incompressible viscous flows

The paper's focus is the calculation of unsteady incompressible 2D flows past airfoils. In the framework of the primitive variable Navier–Stokes equations, the initial and boundary conditions must be assigned so as to be compatible, to assure the correct prediction of the flow evolution. This requirement, typical of all incompressible flows, viscous or inviscid, is often violated when modelling the flow past immersed bodies impulsively started from rest. Its fulfillment can however be restored by means of a procedure enforcing compatibility, consisting in a pre‐processing of the initial velocity field, here described in detail. Numerical solutions for an impulsively started multiple airfoil have been obtained using a finite element incremental projection method. The spatial discretization chosen for the velocity and pressure are of different order to satisfy the inf–sup condition and obtain a smooth pressure field. Results are provided to illustrate the effect of employing or not the compatibility procedure, and are found in good agreement with those obtained with a non‐primitive variable solver. In addition, we introduce a post‐processing procedure to evaluate an alternative pressure field which is found to be more accurate than the one resulting from the projection method. This is achieved by considering an appropriate ‘unsplit’ version of the momentum equation, where the velocity solution of the projection method is substituted. Copyright © 2004 John Wiley & Sons, Ltd.     

Efficient discretization of pressure‐correction equations on non‐orthogonal grids

An alternative discretization of pressure‐correction equations within pressure‐correction schemes for the solution of the incompressible Navier–Stokes equations is introduced, which improves the convergence and robustness properties of such schemes for non‐orthogonal grids. As against standard approaches, where the non‐orthogonal terms usually are just neglected, the approach allows for a simplification of the pressure‐correction equation to correspond to 5‐point or 7‐point computational molecules in two or three dimensions, respectively, but still incorporates the effects of non‐orthogonality. As a result a wide range (including rather high values) of underrelaxation factors can be used, resulting in an increased overall performance of the underlying pressure‐correction schemes. Within this context, a second issue of the paper is the investigation of the accuracy to which the pressure‐correction equation should be solved in each pressure‐correction iteration. The scheme is investigated for standard test cases and, in order to show its applicability to practical flow problems, for a more complex configuration of a micro heat exchanger. Copyright © 2003 John Wiley & Sons, Ltd.     

GOLDEN AGES OR MAGIC MOMENTS?

ABSTRACT. The paper is an attempt to refute Quinn's ‘the Golden Age of fisheries population models has ended “hypothesis. The approach is to show it is possible to provide simple matrix based theory for use with delay difference equations applied to products of the 0th to 4th powers of length and numbers at length (Alias” proto‐moments“). It compares these to models just based upon numbers and biomass. It also shows examples (of comparatively little moment) indicating how using multiple proto‐moments could improve the ability of delay difference equations to handle the size dependent processes of maturity, selection, natural mortality rates and predation rates and thus improving the biological reality of these models.     

Synthesis and characterization of novel polyimides with 2,2‐bis[4(4‐aminophenoxy)phenyl]phthalein‐3′,5′‐bis(trifluoromethyl)anilide

2,2‐Bis[4(4‐aminophenoxy)phenyl]phthalein‐3′,5′‐bis(trifluoromethyl)anilide (6FADAP), containing fluorine and phthalimide moieties, was synthesized via the Williamson ether condensation reaction from 1‐chloro‐4‐nitrobenzene and phenolphthalein‐3′,5′‐bis(trifluoromethyl)anilide, which was followed by hydrogenation. Monomers such as 2,2‐bis[4(4‐aminophenoxy)phenyl]phthalein‐anilide containing phthalimide groups and 2,2‐bis[4(4‐aminophenoxy)phenyl]phthalein containing only phthalein moieties were also synthesized for comparison. The monomers were first characterized by Fourier transform infrared (FTIR), ¹H NMR, ¹⁹F NMR, elemental analysis, and titration and were then used to prepare polyimides with 2,2‐bis(3,4‐dicarboxyphenyl)hexafluoropropane dianhydride. The polyimides were designed to have molecular weights of 20,000 g/mol via off‐stoichiometry and were characterized by FTIR, NMR, gel permeation chromatography (GPC), differential scanning calorimetry, and thermogravimetric analysis. Their solubility, water absorption, dielectric constant, and refractive index were also evaluated. The polyimides prepared with 6FADAP, containing fluorine and phthalimide moieties, had excellent solubility in N‐methylpyrrolidinone, N,N‐dimethylacetamide, tetrahydrofuran, CHCl₃, tetrachloroethane, and acetone, and GPC analysis showed a molecular weight of 18,700 g/mol. The polyimides also exhibited a high glass‐transition temperature (290 °C), good thermal stability (～500 °C in air), low water absorption (1.9 wt %), a low dielectric constant (2.81), a low refractive index, and low birefringence (0.0041). © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 3361–3374, 2003     

The modified characteristic finite difference fractional steps method for the coupled system of fluid dynamics in porous media and its analysis

For the coupled system of multilayer fluid dynamics in porous media, the modified characteristic finite difference fractional steps method applicable to parallel arithmetic is put forward and two‐dimensional and three‐dimensional schemes are used to form a complete set. Some techniques, such as calculus of variations, energy method, piecewise biquadratic interpolation, multiplicative commutation rule of difference operators, decomposition of high order difference operators and prior estimates are adopted. Optimal order estimates in L² norm are derived to determine the error in the approximate solution. This method has already been applied to the numerical simulation of multilayer fluid dynamics in porous media. © 2003 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 19: 665–681, 2003.     

Protonation constant of salicylidene (N-benzoyl)glycyl hydrazone and its coordination behaviour towards some bivalent metal ions

Protonation constant of an unsymmetrical Schiff base, salicylidene(N-benzoyl)glycyl hydrazone (SalBzGH), and formation constants of its complexes have been determined potentiometrically at different temperatures in aqueous dioxane medium. Complexes of SalBzGH with VO(IV), Mn(II), Co(II), Ni(II), Cu(II), Zn(II), Cd(II) and Hg(II) have been prepared. Elemental analyses, pH-metric, molar conductance, magnetic susceptibility, electronic, IR, ESR, XRD (powder) and NMR studies have been carried out to study the coordination behaviour of SalBzGH toward these metal ions. pH-metric and 1H NMR studies show the presence of two dissociable protons in the ligand. IR and NMR spectra suggest the tridentate nature of the ligand, coordinating as a uninegative species in the Mn(II) complex and as a dinegative species in all the other complexes. Presence of two different conformers of the ligand at room temperature and stabilization of a single conformer upon complex formation have been established from¹H NMR spectra of the metal-free ligand, Zn(II) and Hg(II) complexes recorded at 296 K. Electronic and ESR spectra indicate highly distorted tetragonal geometry for VO(IV) and Cu(II) complexes. XRD powder patterns of the Zn(II) complexes are indexed for an orthorhombic crystal system.