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  • Engineering General  (15)
  • FLUID MECHANICS AND HEAT TRANSFER  (4)
  • Polymer and Materials Science  (4)
  • Magnetism  (2)
  • 1
    Electronic Resource
    Electronic Resource
    Adaptive finite difference methods for liquid membranes (1992)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 34 (1992), S. 823-836 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A domain-adaptive technique and an iterative, block bidiagonal method are used to analyse the unsteady dynamics of annular liquid membranes subject to fluctuations in the mass injected into the volume enclosed by the membranes. The domain-adaptive technique maps the unknown, time-dependent, curvilinear geometry of the liquid membrane into a unit interval. The condition that the membrane's radius is zero at the convergence point is used to determine the convergence length, which is governed by an ordinary differential equation. This equation is solved iteratively together with those which govern the fluid dynamics equations. A block bidiagonal technique is used to determine the mass per unit length, radius, and axial and radial velocity components of the membrane. It is shown that the pressure of the gases enclosed by the liquid membrane responds instantaneously to changes in and exhibits the same periodic behaviour as the mass injection rate. The convergence length takes a delay time to respond to the mass injection rate fluctuations. The magnitude of this delay time increases as the Froude and Weber numbers and the nozzle exit angle are increased. The amplitude of the oscillations of both the convergence length and the pressure coefficient increases as the pressure difference across the membrane and the amplitude of the mass injection rate fluctuations are increased.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620340309
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  • 2
    Electronic Resource
    Electronic Resource
    Kinetics of thermal degradation of semi-stiff macromolecules II. Poly-N-vinyl-carbazolPresented at the International Symposium on Degradation and Stabilization of Polymers held in Brussels (Belgium), 11-13 September, 1974. (1975)
    Weinheim : Wiley-Blackwell
    Angewandte Makromolekulare Chemie 43 (1975), S. 105-123 
    Details
    ISSN: 0003-3146
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Description / Table of Contents: Der thermische Abbau von Poly-N-vinyl-carbazol (PVK) wurde mittels „flash“-Pyrolyse, kontrollierter Pyrolyse und dynamisch-thermogravimetrischer Analyse untersucht. Die Analyse der Abbauprodukte erfolgte über Gas-Flüssig-Chromatographie sowie Massenspektrometrie als Trennungs- und Identifizierungsverfahren. Das untersuchte PVK wurde durch radikalische Polymerisation in Benzol mit AIBN als Katalysator dargestellt.Aus den Versuchsergebnissen ergibt sich, daß PVK fast vollkommen über einen stufenweisen „unzipping“ Mechanismus in das Monomere zerfällt. Die Zusammensetzung der Pyrolysate ermöglicht eine Formulierung des Abbaumechanismus des Polymeren. Mit Hilfe des Verfahrens der multiplen Aufheizgeschwindigkeiten wurde die Kinetik des thermischen Abbaus untersucht. Die Bruttoaktivierungsenergie der Depolymerisation wurde zu 40 kcal/mol gemessen und für die Reaktionsordnung wurde ungefähŕ 1 gefunden.Es werden einige thermodynamische Betrachtungen aufgeführt, um den Wert der Aktivierungsenergie des gesamten Prozesses zu erklären. Es wird ein Mechanismus vorgeschlagen.
    Notes: The thermal degradation of poly-N-vinyl-carbazol (PVK) has been studied using flash pyrolysis, controlled pyrolysis and programmed thermogravimetry analysis techniques. The degradation products have been analyzed using gas-liquid chromatography and mass spectrometry as separation and characterization techniques. The examined PVK has been prepared by free radical polymerization in benzene using AIBN as catalyst.It is shown from experimental results that PVK breaks up almost completely into the monomer through a stepwise unzipping mechanism. The composition of the pyrolyzate allows to propose a mechanism for the polymer degradation. Thermal degradation rates have been analyzed using a multiple heating rates procedure. A value of 40 kcal/mol has been found for the overall activation energy of depolymerization and a value approximately equal to one for the order of reaction.Some thermodynamic considerations have been made in order to explain the value of the activation energy of the whole process. A mechanism is suggested.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/apmc.1975.050430108
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  • 3
    Electronic Resource
    Electronic Resource
    Molecular dynamics of a smectic liquid-crystalline side-chain polymer. The dielectric properties of aligned and nonaligned material studied over a wide range of frequency and temperature (1987)
    Bognor Regis [u.a.] : Wiley-Blackwell
    Journal of Polymer Science Part B: Polymer Physics 25 (1987), S. 1099-1111 
    Details
    ISSN: 0887-6266
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The dielectric relaxation behavior of a nonaligned and an aligned liquid-crystalline (LC) polymer are reported for the ranges 10-3.5 to 105 Hz and 274-363 K. Multiple processes (δ and α) are observed that follow a Vogel equation for the temperature dependence related to the apparent glass transition temperature. The occurrence of these processes and the variation in their relaxation strengths as sample alignment is changed is interpreted in terms of a molecular theory for the dielectric behavior of a LC polymer that involves the director order parameter Sd, the mesophase order parameter S, the dipole moment components of the mesogenic head groups, and their associated relaxation functions.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/polb.1987.090250511
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  • 4
    Electronic Resource
    Electronic Resource
    Polymerization of N-(fluoro phenyl) maleimidesPaper presented in part before the IUPAC, International Symposium on Macromolecules (SIM) held in Rio de Janeiro, Brazil, 26-31 July 1974. (1979)
    New York : Wiley-Blackwell
    Journal of Polymer Science: Polymer Chemistry Edition 17 (1979), S. 81-96 
    Details
    ISSN: 0360-6376
    Keywords: Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Poly(N-aryl maleimide)s of characteristic structures have been synthesized and some of their physical properties studied. These include N-(2-fluoro phenyl), N-(3-fluoro phenyl), N-(4-fluoro phenyl), N-(2,4-difluoro phenyl), N-(2,5-difluoro phenyl), N-(2,3,5,6-tetrafluoro phenyl), and N-(pentafluoro phenyl). The polymerization of N-(fluoro phenyl) maleimides by free-radical initiation in bulk or in solution and by anionic catalyst have been studied to compare the characteristics of polymerization by γ-ray irradiation with that by free-radical initiation. The polymers were characterized by elemental analysis, intrinsic viscosity, spectroscopy (IR and NMR), programmed thermogravimetric analysis, and x-ray diffraction. Spectra of polymers prepared by radiation and anionic polymerization were nearly identical with those of polymers prepared by free-radical polymerization initiated by AIBN in bulk or in solution and by the self-initiated thermal polymerization. A variety of reaction conditions were tried, but all attempts to change the molecular structure of the polymers were unsuccessful. Rates of thermal degradation for poly[N-(fluoro phenyl) maleimide]s have been analyzed by using a multiple-heating-rate procedure. Overall activation energy, order of reaction, and frequency factor have been evaluated. On the basis of the comparison between the overall activation energy of the thermal degradation of poly[N-(fluoro phenyl) maleimide]s and NMR spectra of their corresponding monomers, it can be concluded that the 1H shifts due to ethylenic protons are so characteristic in sign and magnitude as to be useful in thermal stability elucidation. Some qualitative explanations were given on the stability of these polymers as affected by the type and size of the substituent. The x-ray diffractograms of all samples show two rather broad peaks indicative of noncrystalline structures. The location of the peaks does not depend upon preparation conditions and temperature. Poly(N-maleimide)s of fluoroanilines have not been hitherto described.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/pol.1979.170170109
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  • 5
    Electronic Resource
    Electronic Resource
    Dynamics of liquid membranes. II: Adaptive finite difference methods (1991)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 12 (1991), S. 881-894 
    Details
    ISSN: 0271-2091
    Keywords: Liquid membranes ; Adaptive finite difference methods ; Integrodifferential equations ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: 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.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650120906
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  • 6
    Electronic Resource
    Electronic Resource
    Hopf bifurcation in annular liquid jets with mass transfer (1995)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 20 (1995), S. 1293-1314 
    Details
    ISSN: 0271-2091
    Keywords: chemical reactors ; annular liquid jets ; grid generation ; mass absorption ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A numerical study of Hopf bifuractions in annular liquid jets with mass transfer is presented. The study is based on the asymptotic equations which govern the dynamics of inviscid, incompressible, thin, annular liquid jets and on equilibrium conditions for mass transfer at the jet's inner and outer interfaces. It is shown that the amplitude of the time-periodic motion that results from the Hopf bifurcation increases whereas its frequency decreases as the solubility ratio is increased.
    Additional Material: 19 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650201202
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  • 7
    Electronic Resource
    Electronic Resource
    PLANAR LIQUID SHEETS AT LOW REYNOLDS NUMBERS (1996)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 22 (1996), S. 961-978 
    Details
    ISSN: 0271-2091
    Keywords: planar liquid sheets ; perturbation methods ; film casting ; film coating ; plane stagnation flows ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Asymptotic methods are employed to derive the leading-order equations which govern the fluid dynamics of time-dependent, incompressible, planar liquid sheets at low Reynolds numbers using as small parameter the slenderness ratio. Analytical and numerical solutions of relevance to both steady film casting processes and plane stagnation flows are obtained with the leading-order equations. It is shown that for steady film casting processes the model which accounts for both gravity and low-Reynolds-number effects predicts thicker and slower planar liquid sheets than those which neglect a surface curvature term or assume that Reynolds number is zero, because the neglect of the curvature term and the assumption of zero Reynolds number are not justified at high take-up velocities owing to the large velocity gradients that occur at the take-up point. It is also shown that for Reynolds number/Froude number ratios larger than one, models which neglect the surface curvature or assume a zero Reynolds number predict velocity profiles which are either concave or exhibit an inflection point, whereas the model which accounts for both curvature and low-Reynolds-number effects predicts convex velocity profiles. For plane stagnation flows it is shown that models which account for both low-Reynolds-number and curvature effects predict nearly identical results to those of models which assume zero Reynolds number. These two models also predict a faster thickening of the planar liquid sheet than models which account for low- Reynolds-number effects but neglect the surface curvature. This curvature term is very large near the stagnation point and cannot be neglected there. It is also shown that the thickening of the sheet occurs closer to the stagnation point as the Reynolds number/Froude number ratio is increased, i.e. as the magnitude of the gravitational acceleration is increased. In addition it is shown that large surface tension introduces a third-order spatial derivative in the axial momentum equation at leading order.
    Additional Material: 11 Ill.
    Type of Medium: Electronic Resource
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  • 8
    Electronic Resource
    Electronic Resource
    A PIECEWISE-LINEARIZED METHOD FOR ORDINARY DIFFERENTIAL EQUATIONS: TWO-POINT BOUNDARY-VALUE PROBLEMS (1996)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 22 (1996), S. 1089-1102 
    Details
    ISSN: 0271-2091
    Keywords: piecewise-linearized methods ; two-point boundary value problems ; singular perturbations ; finite differences ; finite elements ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Piecewise-linearized methods for the solution of two-point boundary value problems in ordinary differential equations are presented. These problems are approximated by piecewise linear ones which have analytical solutions and reduced to finding the slope of the solution at the left boundary so that the boundary conditions at the right end of the interval are satisfied. This results in a rather complex system of non-linear algebraic equations which may be reduced to a single non-linear equation whose unknown is the slope of the solution at the left boundary of the interval and whose solution may be obtained by means of the Newton-Raphson method. This is equivalent to solving the boundary value problem as an initial value one using the piecewise-linearized technique and a shooting method. It is shown that for problems characterized by a linear operator a technique based on the superposition principle and the piecewise-linearized method may be employed. For these problems the accuracy of piecewise-linearized methods is of second order. It is also shown that for linear problems the accuracy of the piecewise-linearized method is superior to that of fourth-order-accurate techniques. For the linear singular perturbation problems considered in this paper the accuracy of global piecewise linearizat ion is higher than that of finite difference and finite element methods. For non-linear problems the accuracy of piecewise-linearized methods is in most cases lower than that of fourth-order methods but comparable with that of second-order techniques owing to the linearization of the non-linear terms.
    Additional Material: 7 Ill.
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  • 9
    Electronic Resource
    Electronic Resource
    Numerical solution of reaction-diffusion equations by compact operators and modified equation methods (1987)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 7 (1987), S. 337-351 
    Details
    ISSN: 0271-2091
    Keywords: Compact Differences ; Modified Equation Methods ; Reaction-Diffusion Equations ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A system of reaction-diffusion equations which governs the propagation of an ozone decomposition laminar flame in Lagrangian co-ordinates is analysed by means of compact operators and modified equation methods. It is shown that the use of fourth-order accurate compact operators yields very accurate solutions if sufficient numbers of grid points are located at the flame front, where very steep gradients of temperature and species concentrations exist. Modified equation methods are shown to impose a restriction on the time step under certain conditions. The solutions obtained by means of compact operators and modified equation methods are compared with solutions obtained by other methods; good agreement is obtained.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650070404
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  • 10
    Electronic Resource
    Electronic Resource
    Finite element methods for one-dimensional combustion problems (1990)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 11 (1990), S. 893-906 
    Details
    ISSN: 0271-2091
    Keywords: Adaptive ; Characteristic ; Flux-corrected Transport ; Petrov-Galerkin ; Finite Elements ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Three adaptive finite element methods based on equidistribution, elliptic grid generation and hybrid techniques are used to study a system of reaction-diffusion equations. It is shown that these techniques must employ sub-equidistributing meshes in order to avoid ill-conditioned matrices and ensure the convergence of the Newton method. It is also shown that elliptic grid generation methods require much longer computer times than hybrid and static rezoning procedures. The paper also includes characteristic, Petrov-Galerkin and flux-corrected transport algorithms which are used to study a linear convection-reaction-diffusion equation that has an analytical solution. The flux-corrected transport technique yields monotonic solutions in good agreement with the analytical solution, whereas the Petrov-Galerkin method with quadratic upstream-weighted functions results in very diffused temperature profiles. The characteristic finite element method which uses a Lagrangian-Eulerian formulation overpredicts the flame front location and exhibits overshoots and undershoots near the temperature discontinuity. These overshoots and undershoots are due to the interpolation of the results of the Lagrangian operator onto the fixed Eulerian grid used to solve the reaction-diffusion operator, and indicate that characteristic finite element methods are not able to eliminate numerical diffusion entirely.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650110613
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