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  • 1995-1999  (3,508)
  • 1996  (3,508)
  • General Chemistry  (1,786)
  • Engineering  (847)
  • Industrial Chemistry  (438)
  • Chemical Engineering  (437)
  • Nuclear reactions
  • 1
    Electronic Resource
    Electronic Resource
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996) 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 481-505 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper we provide a theory of the asymptotic expansion for an abstract kinetic equation. We show that the modified Chapman-Enskog procedure, introduced in [19], gives the error of order of ε2, uniformly in time, on the second level of approximation and in particular that the zeroth moment of the solution (the spatial density of particles) can be approximated by the solution of the diffusion-type equation with the same accuracy. The theory is applied to several types of kinetic equations with the Fokker-Planck collision operator.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 555-569 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A mathematical approach to the concept of shape of a submanifold M of a Euclidean space had previously been given by means of ‘measuring functions’ (e.g. diameter or volume) and of the derived ‘size functions’. This paper relates the study and the computation of any such size function to the structure of critical points of the associated measuring function.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 593-605 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We present a Riesz-like hyperholomorphic functional calculus for a set of non-commuting operators based on Clifford analysis. Applications to the quantum field theory are described.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996) 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 699-716 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider the system of elastic waves in three dimensions under the presence of an impurity of the medium which we represent by a real-valued function q(x) (or q(x,t)). The medium is assumed to be isotropic and occupies the whole space Ω = ∝3. We study the location of the scattering frequencies associated with such phenomenon. We conclude that there is a large region on the complex plane which is free of scattering frequencies. In the remaining region they are discrete provided that q satisfies suitable assumptions concerning its behaviour at infinity.
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 717-736 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider parabolic systems defined on cylindrical domains close to the threshold of instability, in which the Fourier modes with positive growth rates are concentrated at a non-zero critical wave number. In particular, we consider systems for which a so-called Ginzburg-Landau equation can be derived. Due to the presence of continuous spectrum, classical bifurcation theory is not available to describe bifurcating solutions. Thus, we consider a modified system with artificial spectral gap, which possesses an infinite-dimensional centre manifold. The amplitude equation on this manifold is called a generalized Ginzburg-Landau equation. From previous work [18] it is known that the Fourier modes are exponentially concentrated at integer multiples of the critical wave number. Hence, the error made by this modification is exponentially small in powers of the bifurcation parameter. The approximations obtained via the generalized Ginzburg-Landau equation are valid on a much longer time scale than those obtained by using the classical Ginzburg-Landau equation as an amplitude equation.
    Additional Material: 2 Ill.
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  • 8
    Electronic Resource
    Electronic Resource
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 825-845 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A review of exact solutions of discrete velocity models is given. Different methods of constructing the solutions are discussed. New methods are proposed for the stationary Broadwell model, and new class of solutions is obtained. Two-dimensional flows in channel are studied on the basis of exact solutions and analogy with the Carleman model. Explicit example of non-unique solution to a boundary value problem is given. Exact hydrodynamic equations are derived for the stationary Broadwell model. A role of the Navier-Stokes approximation is discussed in detail by comparison with these exact equations.
    Additional Material: 2 Ill.
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  • 9
    Electronic Resource
    Electronic Resource
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 1-13 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The albedo and scattering operators are central objects in the time-dependent transport theory. Their mutual relationship has recently been established by Arianfar and Emamirad for the case of transparent boundaries. In this paper, we extend the result to general boundary conditions. To allow for this extension, the scattering theory for a transport-like equation is generalized to include partially reflecting boundary conditions. The existence of the wave and scattering operators is directly inferred from the properties of the evolution operators that are determined, in turn, by the physics of collisions within and at the boundaries of the scattering domain.
    Type of Medium: Electronic Resource
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  • 10
    Electronic Resource
    Electronic Resource
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 257-285 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The problem of determining bilinear combinations of holomorphic and antiholomorphic generalized hypergeometric type integrals left invariant under the action of the monodromy groups of the integrals is studied. In the special cases of simple Pochhammer type integrals and of twofold hypergeometric type integrals the existence and uniqueness of the bilinear invariants are proved, and the bilinear invariants are explicitly computed. Preparing the tools it is shown how to linearize and iterate representations of the braid group Bn as automorphism groups of certain free subgroups of the braid group Bn+1, and how the resulting iterated linear representations of the braid group in a natural way provide an algorithm to compute the monodromy group of generalized hypergeometric type integrals. Explicit formulae for different types of integration contours are given in the case of simple and twofold integrals.
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  • 11
    Electronic Resource
    Electronic Resource
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 255-255 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
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  • 12
    Electronic Resource
    Electronic Resource
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 363-374 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Periodic solutions of arbitrary period to semilinear partial differential equations of Zabusky or Boussinesq type are obtained. More generally, for a linear differential operator A(y,∂), the equation A(y,∂)u = (-1)∣γ∣∂γf(y,∂γu), y = (t,x)∊∝k×G is studied, where homogeneous boundary conditions on ∂G and periodicity conditions on t are imposed. The solutions are obtained by variational methods in anisotropic Sobolev spaces.
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  • 13
    Electronic Resource
    Electronic Resource
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 401-424 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The quasi-hydrodynamic carrier transport equations for semiconductors extended to Fermi-Dirac statistics are considered. It is shown that in the high injection case, these equations reduce to a drift-diffusion model with non-linear diffusion terms. The limiting procedure is proved rigorously and error estimates are shown. We compute numerically static voltage-current characteristics of a forward biased pn-junction diode and compare the curves with the corresponding characteristics obtained from the standard drift-diffusion model based on Boltzmann statistics. It turns out that there exists a so-called threshold voltage at which the behaviour of the characteristic changes. Under high injection conditions, the dependence of the current on the bias appears to be approximately polynomial. The characteristics are studied analytically for a unipolar device.
    Additional Material: 6 Ill.
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  • 14
    Electronic Resource
    Electronic Resource
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 529-554 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: No Abstract
    Additional Material: 3 Ill.
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  • 15
    Electronic Resource
    Electronic Resource
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996) 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
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  • 16
    Electronic Resource
    Electronic Resource
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 639-649 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider the Cauchy problem for the damped Boussinesq equation governing long wave propagation in a viscous fluid of small depth. For the cases of one, two, and three space dimensions local in time existence and uniqueness of a solution is proved. We show that for discontinuous initial perturbations this solution is infinitely differentiable with respect to time t and space co-ordinates for t〉0 on a bounded time interval.
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  • 17
    Electronic Resource
    Electronic Resource
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 679-697 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We study a non-linear generalized initial-boundary value problem of a scalar conservation law which models the sedimentation of an ideal suspension.
    Additional Material: 7 Ill.
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  • 18
    Electronic Resource
    Electronic Resource
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996) 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
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  • 19
    Electronic Resource
    Electronic Resource
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 761-772 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: For a linear coagulation kernel and a constant fragmentation kernel we prove the existence of equilibrium solutions and examine asymptotic properties for time-dependent solutions which are proved to converge to the equilibria. The rate of the convergence is estimated. It is shown also that all time-dependent solutions with the same density can tend to only one particular steady-state solution. In this sense the equilibrium solution is proved to be unique. Existence, uniqueness and mass conservation of time-dependent solutions has been proved in a previous paper by the authors [10].
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  • 20
    Electronic Resource
    Electronic Resource
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 847-856 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Using the invariance principle in a Banach space with less restriction, we discuss the asymptotic behaviour of an integro-differential equation with infinite delay which is an infection disease model. It is proved that the equilibria are globally asymptotic stable if the parameters fit some relation and the integral kern satisfies a convergence condition.
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  • 21
    Electronic Resource
    Electronic Resource
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 897-907 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider a non-linear plate equation of Bernoulli-Euler type with a locally distributed damping term. Our main result asserts that if the damping is effective in a neighbourhood of the boundary then the energy decays exponentially. The method we use is a combination of multiplier techniques and of a compactness-uniqueness argument.
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  • 22
    Electronic Resource
    Electronic Resource
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 287-312 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The Child-Langmuir asymptotics of the Vlasov-Poisson system provides a model for vacuum diodes which operate under large biases. In these conditions the energy of the injected particles at the cathode is very small compared with the applied external bias. From the mathematical view point, this leads to an interesting and non-standard asymptotic problem for the Vlasov-Poisson equation, which has already been investigated in the one-dimensional Cartesian case, in [7]. The purpose of this paper is to extend the analysis to the cylindrically or spherically symmetric case. Surprisingly, the behaviour of the solutions of the model is somehow different than in the Cartesian case. This feature had not been noticed by the physicists before. Furthermore, the mathematical analysis is much more involved than in [7] because of the geometrical effects, and the techniques that are used are quite different. They mainly rely on the use of supersolutions in the spirit of [18, 19]. This work is divided in two parts. In this first part, we state the problem and establish the basic estimates which are needed for the asymptotic analysis.
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  • 23
    Electronic Resource
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    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 375-380 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper an asymptotic result concerning the interface for some problems connected with radially symmetric non-linear diffusion is presented.
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  • 24
    Electronic Resource
    Electronic Resource
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996) 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
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  • 25
    Electronic Resource
    Electronic Resource
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 425-450 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Van Roosbroeck's bipolar drift diffusion equations cover the qualitative behaviour of many semiconductor devices. The complexity of the model equations however prevents efficient implementations needed in circuit simulations. Under close-to-thermal-equilibrium biasing conditions (zero space charge assumption, low injection limit) the van Roosbroeck system can be replaced by a system of coupled non-linear Volterra integral equations of the second kind. Involving only the macroscopic quantities current, applied voltage and serial resistance this Volterra system can be handled with comparably little effort. Volterra integral equations models are formulated for a large class of semiconductor devices with abrupt pn-junctions. The model equations are made explicit for diodes, transistors and thyristors. A survey on various results concerning Volterra models describing the switching behaviour of pn-diodes is given. The integral equation model allows to recover all relevant properties of the voltage-current characteristics.
    Additional Material: 4 Ill.
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  • 26
    Electronic Resource
    Electronic Resource
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 1317-1333 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We give new finite time blow-up results for the non-linear parabolic equations ut-Δu = up and ut-Δu+μ∣∇u∣q = up. We first establish an a priori bound in Lp+1 for the positive non-decreasing global solutions. As a consequence, we prove in particular that for the second equation on ∝N, with q = 2p/(p+1) and small μ〉0, blow-up can occur for any N≥1, p〉1, (N-2)p〈N+2 and without energy restriction on the initial data. Incidentally, we present a simple model in population dynamics involving this equation.
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  • 27
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    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 1397-1407 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: No Abstract
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  • 28
    Electronic Resource
    Electronic Resource
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 15-31 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We analyse the time decay of solutions to the Cauchy problem for the linear hyperbolic system of elasticity for anisotropic media. As an example, we will consider media with hexagonal symmetry. First we derive decay estimates for special initial data using the method of stationary phase in several variables and degenerate phase function based on the Malgrange preparation theorem. Asymptotic expansions are given to prove the sharpness of the weaker time decay found for zinc and beryl than in the isotropic case. A method using Besov spaces leads to Lp-Lq-estimates.
    Additional Material: 4 Ill.
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  • 29
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    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 63-85 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: This paper is concerned with the effective numerical treatment of elliptic boundary value problems when the solutions contain singularities. The paper deals first with the theory of problems of this type in the context of weighted Sobolev spaces and covers problems in domains with conical vertices and non-intersecting edges, as well as polyhedral domains with Lipschitz boundaries. Finite element schemes on graded meshes for second-order problems in polygonal/polyhedral domains are then proposed for problems with the above singularities. These schemes exhibit optimal convergence rates with decreasing mesh size. Finally, we describe numerical experiments which demonstrate the efficiency of our technique in terms of ‘actual’ errors for specific (finite) mesh sizes in addition to the asymptotic rates of convergence.
    Additional Material: 12 Ill.
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  • 30
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    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 171-185 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: It is shown that the non-linear coagulation-fragmentation equation with constant kernels has a unique equilibrium solution. This equilibrium solution is given explicitly in terms of the initial data and the kernels. Weak L1 convergence of time-dependent solutions to the unique equilibrium is demonstrated via an invariance principle employing a suitable lower semicontinuous Lyapunov functional.
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  • 31
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    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 217-233 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The mixed-Neumann problem for the non-linear wave equation □u-a(u)(∣∂tu)∣2-∣∇u∣2 = fε(z) is studied. The function fε(z) = ∑k∊Kfk(z,ε-1φk(z),ε), ε∊[0,1], K is finite, fk(z,θk,ε) are 2π-periodic with respect to θk. The existence of solution uε on a domain z = (t,x,y)∊[0,T]×∝+×∝d, d = 1 or 2, is proved when ε is sufficiently small; T does not depend on ε. By the non-linear geometric optics method the asymptotic (with respect to ε→0) solution ũ ε is constructed. The estimation for the rest ε2rε = uε-ũε is derived and the limit rε, ε→0, is studied.
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  • 32
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    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996) 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
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  • 33
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: This paper analyses the Child-Langmuir asymptotics of the Vlasov-Poisson problem in cylindrical or spherical symmetry. The problem was stated in the first part of this paper [2]. We recall that the Child-Langmuir asymptotics concerns the boundary value problem for the Vlasov-Poisson system in the situation where the thermal energy of the injected particles at the boundary is small compared with the external applied bias.In the first part, we derived the set of estimates which allow us to pass to the limit in the asymptotic problem. In the present part, we analyse the limit (or ‘reduced’) problem, which leads us to a characterization of the limit or ‘Child-Langmuir’ current which flows through the system.
    Additional Material: 8 Ill.
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  • 34
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    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 341-361 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The Lyapunov stability is analysed for a class of integro-differential equations with unbounded operator coefficients. These equations arise in the study of non-conservative stability problems for viscoelastic thin-walled elements of structures. Some sufficient stability conditions are derived by using the direct Lyapunov method. These conditions are formulated for arbitrary kernels of the Volterra integral operator in terms of norms of the operator coefficients. Employing these conditions the supersonic flutter of a viscoelastic panel is studied and explicit expressions for the critical gas velocity are derived. Dependence of the critical flow velocity on the material characteristics and compressive load is analysed numerically.
    Additional Material: 5 Ill.
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  • 35
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    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 381-400 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The equations describing the dynamics and steady states of a tubular reactor are studied in the region where an arbitrary number of steady-state solutions exist. The stability of these solutions is examined and their persistence for increases in the parameter values is determined. The physical implications of these solutions are examined.
    Additional Material: 3 Ill.
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  • 36
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    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 451-461 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We use the implicit function theorem to prove an existence of a heteroclinic orbit to a system of two non-linear second-order ODEs. The perturbation is carried out around infinite value of a ‘coupling parameter’. The form of the system which is considered in this paper is related to the system defining travelling wave solutions in a two temperature model of the laser sustained plasma.
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  • 37
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    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 33-51 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper we generalize the abstract results of Mock and Marcowich [13, 12] for convergence of discrete Van Roosbroeck systems [12, 13, 17], to the case when the solutions are typically in W1,4-ε and not in H2. These conditions are verified on finite element discretizations. Error estimates are derived when the solution is unique. Due to the singularity at the flat angles, these estimates in the H1 norm are only O(h1/2). The techniques that are presented are broad and may be applied to other type of discretizations.
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  • 38
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    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996) 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
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  • 39
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    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996) 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
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  • 40
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    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 1335-1347 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Explicit a priori continuous dependence estimates are derived for the Brinkman equations for non-isothermal flow in porous media. Continuous dependence on the cooling coefficient is shown when a boundary condition of Newton cooling type is employed. Continuous dependence on the model itself is proved when the Boussinesq model is allowed to change to one appropriate to penetrative convection. The final result derives an a priori continuous dependence estimate for the heat supply and body force.
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  • 41
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    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 1349-1395 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Lie's theory in its current formulation is linear, local and canonical. As such, it is not applicable to a growing number of non-linear, non-local and non-canonical systems which have recently emerged in particle physics, superconductivity, astrophysics and other fields. In this paper, which is written by a physicist for mathematicians, we review and develop a generalization of Lie's theory proposed by the Italian-American physicist R. M. Santilli back in 1978 when at the Department of Mathematics of Harvard University and today called Lie-Santilli isotheory. The latter theory is based on the so-called isotopies which are non-linear, non-local and non-canonical maps of any given linear, local and canonical theory capable of reconstructing linearity, locality and canonicity in certain generalized spaces and fields. The emerging Lie-Santilli isotheory is remarkable because it preserves the abstract axioms of Lie's theory while being applicable to non-linear, non-local and non-canonical systems. After reviewing the foundations of the Lie-Santilli isoalgebras and isogroups, and introducing seemingly novel advances in their interconnections, we show that the Lie-Santilli isotheory provides the invariance of all infinitely possible (well-behaved), non-linear, non-local and non-canonical deformations of conventional Euclidean, Minkowskian or Riemannian invariants. We also show that the non-linear, non-local and non-canonical symmetry transformations of deformed invariants are easily computable from the linear, local and canonical symmetry transforms of the original invariants and the given deformation. We then briefly indicate a number of applications of the isotheory in various fields. Numerous rather fundamental and intriguing, open mathematical and physical problems are indicated during the course of our analysis.
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  • 42
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    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 42 (1996), S. 767-776 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Identification of low-order linear multiinput/multiouput models can lead to accurate descriptions of the dynamic behavior of a continuous crystallization process. While open-loop experiments exhibit an oscillating crystal size distribution, improved experimental conditions can be established through stabilization of the process with a simple single-loop feedback controller. The resulting closed-loop identification problem is studied using low-order linear multivariable input-output models. Two closed-loop identification methods are applied, one of which was recently introduced to provide accurate approximate models in general closed-loop process configurations. Identification and validation data are obtained from an evaporative pilot crystallizer, and the identified models are validated in terms of time- and frequency-domain responses. A fourth-order, three-input three-output model is shown to describe accurately the process dynamics. The results are compared with a linearized and reduced first-principles model.
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  • 43
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    AIChE Journal 42 (1996), S. 2582-2593 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: A model-predictive control (MPC) design methodology for processes with more manipulated inputs than outputs is developed. Essential features of the proposed approach are the following: the on-line optimization minimizes an objective function based on the l2 norm; an end-condition equation is utilized; model uncertainty is considered as upper and lower bounds on the pulse-response-model coefficients; hard constraints on the input and move-size variables and soft constraints on the output variables are posed. A major difference between square and nonsquare MPC is that in the former the end-condition can be used directly, while in the latter a nonlinear programming problem needs to be solved during the design phase to select values for the input move suppression coefficients. This technique is illustrated through a number of simulations and application to a real industrial process.
    Additional Material: 10 Ill.
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  • 44
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    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 42 (1996), S. 2627-2634 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: A comprehensive experimental study of gas holdup in bubble columns of varying diameters, fitted with different distributor types, using several liquids is presented. Air was used as the gas phase. Experiments to test the influence of gas density were also carried out with He, Ar, and SF6. A generalization of the two-phase model for gas-solid fluidized beds was used to interpret the experimental data where the “dilute” phase is identified with the “large” bubble population and the “dense” phase with the liquid phase where the “small” bubble population is entrained. Gas holdups in dilute and dense phases were determined from dynamic gas disengagement experiments.In the churn-turbulent regime of operation, voidage of the gas in the dense phase was independent of the superficial gas velocity. Reilly et al.'s correlations for the gas holdup and superficial gas velocity at the regime transition point estimate the gas voidage of the dense phase and the superficial gas velocity well through this phase. Corresponding correlations of Wilkinson et al. significantly underpredict dense-phase parameters. The experiment showed that the dilute phase or large bubble holdup in bubble columns, operating at superficial gas velocities 〉 0.1 m/s, is independent of liquid properties, how the gas is distributed and the density of the gas phase. But it is affected significantly by the column diameter. Relying on hydrodynamic analogies with a gas-solid-fluid bed, a simple correlation was developed that is considerably more accurate than the Wilkinson correlation that significantly overpredicts large bubble holdup.
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  • 45
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    AIChE Journal 42 (1996), S. 1569-1582 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Complex hydrodynamic behavior of circulating fluidized beds makes their scale-up very complicated. In particular, large-scale lateral solids segregation causes a complex two-phase flow pattern which influences significantly their performance. Lateral solids segregation has been attributed to direct collisional interactions between particles as well as to interaction between gas-phase eddies and dispersed particles. However, these phenomena have not been investigated thoroughly.This article discusses an advanced 2-D hydrodynamic model developed for circulating fluidized beds based on the two-fluid concept. Because theory to model the interaction between gas-phase eddies and dispersed particles is not available, turbulence was modeled on a macroscopic scale using a modified Prandtl mixing length model. To model the influence of direct particle-particle collisions the kinetic theory for granular flow was applied based on the Chapman-Enskog theory of dense gases. For model validation purposes, a cold flow circulating fluidized bed was employed in which sand was transported with air as fluidizing agent. The column is equipped with pressure transducers to measure the axial pressure profile and with a reflective optical fiber probe to measure the local solids concentration and axial solids velocity. Theoretically calculated solids concentration and axial solids velocity agree satisfactorily with experiment, especially when one realizes that the model contains no adjustable parameters. In general, however, the model slightly underpredicted the experimentally observed lateral solids segregation and yielded a more peaked velocity profile compared to its experimental counterpart.
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  • 46
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    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 42 (1996), S. 1590-1599 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Cohesive (Group C) particles have been widely used in various industries. To handle and process such fine particles, a clear understanding of the flow behavior and interparticle force, is needed. To achieve that objective, a Laser Doppler Anemometer system was used to measure particle velocity, fluctuating velocity, and size and extent of agglomeration or cluster formation of particles in a dilute gas/fine oil shale particle flow system with particle density of 2,082 kg/m3, average particle volumetric concentration of 1.5%, and average particle mass flux of about 100 kg/m2·s in a controlled-moisture environment. The flow behavior of the particles was also studied for a mixture of 99% shale particles and 1% antistatic agent (Larostat powder, a quaternary ammonium compound) to examine the role of electrostatic force in gas/cohesive particle flow behavior. The addition of Larostat powder significantly reduced the electrostatic force and, in turn, made Group C particles behave similar to Group A or in some cases to Group B particles. In addition, our experimental data showed that the Maxwellian distribution function is a reasonable assumption to describe the velocity probability density function of the shale particles with or without antistatic agents.
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  • 47
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    AIChE Journal 42 (1996), S. 1621-1626 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Flow visualization of flowing particles around a tube of various types of tube arrangements in a moving bed was studied using X-ray video films to obtain a relation between particles behavior and local heat-transfer coefficients. A stagnant part of solid particles was observed on the tube in the case of a staggered arrangement. This part did not appear in the case of the single tube and the single row of tubes. The measured local heat-transfer coefficients around a tube was decreased in this stagnant part. Furthermore, influences of different tube arrangements both on flow patterns of particles and on local heat-transfer coefficients between tubes and bed were examined.
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  • 48
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    AIChE Journal 42 (1996), S. 1600-1611 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: A method for generating theoretical breakage distribution functions for multiple particle breakage is presented. It starts with the joint probability function that accounts for all the child particles; it is then reduced to the marginal probability function commonly used in the breakage equation. This method is flexible enough to allow the user to choose the number of child particles and the functional form to be used. The method is demonstrated with both product and summation functions with a power-law form. To facilitate the use of these theoretical functions for statistical analyses, a companion discretized breakage equation is developed. The new equation guarantees the conservation of mass and correct prediction of the total number of particles despite discretization. It is easy to use because it is a set of ordinary differential equations and applicable to both equal-size and geometric-size intervals. Simulation results show that different breakage distribution functions coupled with different breakage rates can produce almost indistinguishable particle-size distributions, signifying the need for further work in this area.
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  • 49
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    AIChE Journal 42 (1996), S. 2607-2615 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: A mathematical model has been developed that predicts the effects of design parameters, operating variables and physical properties on the performance of a membrane reactor with a permeselective wall. The model consists of the full set of partial differential equations that describe the conservation of mass, momentum and chemical species, coupled with chemical kinetics and appropriate boundary conditions for the physical problem. The solution of this system is obtained by a finite-volume technique. The model was applied to study the dehydrogenation of cyclohexane. Two membrane types in tubular form were studied: a selective porous glass with low gas permeabilities and a porous alumina with very high gas permeabilities. It is concluded that gas separation and reactor performance are strongly influenced by dispersion effects only in the latter membrane reactor, while in both cases radial concentration profiles do not correspond to those obtained with plug flow. Therefore, simulations of this type of problem should be based on complex dispersion models rather than the existing ideal plug-flow ones.
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  • 50
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    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 42 (1996), S. 1627-1632 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: A new approach for the determination of concentrations in the case of nonequilibrium washing stages is presented. Each washing stage is assumed to consist of series of mixing cells, and the conservation of solute mass is solved by Laplace transformation. The simplicity of the resulting equations makes this approach more practical than the existing one.
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  • 51
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    AIChE Journal 42 (1996), S. 1633-1641 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: The graphical construction called an energy-utilization diagram (EUD) is adopted for analyses of energy transformation and exergy losses in a distillation column. The overall exergy loss on one plate of a column can be decomposed into six kinds of exergy losses and are represented graphically. Two of them are caused by mixing and cooling in the vapor phase, and the other two by mixing and heating in the liquid phase. To display the remaining two yielded by condensation and evaporation of each component, the concept of the individual energy level is applied. The relationship between the individual energy level and the xy diagram is presented as well as effects of the reflux ratio and the feed location on the EUD for the whole column. Separation of n-hexane and n-octane is used to illustrate the methodology.
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  • 52
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    AIChE Journal 42 (1996), S. 1642-1647 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Based on the UBET, a new strategy for identifying faulty equipment for dynamic chemical processes under automatic control is presented. The strategy is designed to distinguish between measurement biases, controller biases, and process leaks. For illustration purposes, application is given to a level control process under pseudo-steady state. This approach was inspired by the work of Rollins and Devanathan to identify biased measurements under dynamic conditions. Advantages of this method are that it is not computationally intensive, can accurately detect and specifically identify the type of fault, and can accurately determine the time when the fault occurs.
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  • 53
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    AIChE Journal 42 (1996), S. 1662-1672 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Stricter emission control legislation for diesel use has been increasing interest in highly efficient wall-flow particulate filters. The mathematical modeling of the filter regeneration process is indispensable in developing reliable and durable trap systems for various applications. Although modeling of wall-flow filters has been investigated extensively, significant problems still exist in the correlation of modeling results with measurements. This article describes an improved modeling and model tuning approach. A classical zero-dimensional regeneration model, modified to account for incomplete soot oxidation effects, is discussed, and existing and novel methods of estimating trap loading, crucial in all modeling applications, are compared. The design of a model tuning approach based on full-scale experiments is highlighted with examples of model predictions during trap failure that show capabilities of supporting the design of trap protection techniques. Applications to regeneration rate control, filter sizing and the development of on-board diagnostics are demonstrated with examples. Dimensional analysis is used for the concise quantitative evaluation of the parameters affecting the evolution of the regeneration process.
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  • 54
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    AIChE Journal 42 (1996), S. 3202-3211 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Increased demand for cryocoolers for aerospace and terrestrial applications has served as an incentive over the past decade to develop units with specific performance parameters. Since many of these units also require a high degree of reliability, considerable effort has been directed toward meeting this goal. The excellent progress that has been made is summarized, and there is every indication that the use of cryocoolers will expand greatly during the next decade, with a rapid transition from present aerospace/military applications to highly civilian uses in such areas as medicine, electronic transmission, environmental control, energy storage, and transportation.
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  • 55
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    AIChE Journal 42 (1996), S. 3241-3252 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: This article evaluates the effectiveness of a segregated model for prediction of growth and differentiation of Bacillus licheniformis in a submerged-culture fermentation system. The segregated model accounts for each of the three morphological forms of the Bacillus life cycle. The sporangium biomass was characterized using an age-population model to reflect the age-dependent progress toward spore formation. Constitutive relationships governing the rates of vegetative cell reproduction, spore germination, commitment to sporulation, and substrate consumption are proposed. Based on this model framework, the dynamic cell growth and differentiation equations were developed.Batch, steady-state and step-test fermentation data from a laboratory-scale fermentor were incorporated into a maximum likelihood parameter estimation scheme for model identification. Confident estimates of growth and differentiation parameters were obtained for the segregated model using biomass measurements. In addition, the model describes successfully growth and differentiation in batch and steady-state operating modes.
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  • 56
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    AIChE Journal 42 (1996), S. 3267-3282 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: A regenerative absorption-based process was developed for removing VOCs from N2 in an inert, nonvolatile, organic liquid flowing in compact hollow-fiber devices. The process eliminates flooding, loading, and entrainment, and can replace activated carbon adsorption. Two types of holow-fiber membranes were studied: one with a microporous wall and the other with a highly VOC-permeable nonporous coating on the outer surface of a microporous hollow fiber. Criteria for nondispersive operation were developed for each case. Experiments were conducted for the absorption of acetone, methylene chloride, toluene, and methanol from the respective VOC-N2 gas mixture using two absorbents: silicone oil and mineral oil. The highest mass-transfer coefficient was obtained for toluene followed by methylene chloride, acetone, and methanol. Different resistances making up the overall resistance in VOC absorption were characterized comprehensively to develop a predictive capability and compare the absorption performances of two types of fibers and the two absorbents. The absorbent-filled porous membrane contributed significantly to the total mass-transfer resistance. Numerical simulations of governing equations based on a cell model agree well with experimental results.
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  • 57
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    AIChE Journal 42 (1996), S. 3301-3309 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Two-dimensional chaotic mixing of similar Newtonian fluids in the presence of an advected dissimilar minor phase fluid body with specified size, interfacial tension, and viscosity ratio was numerically investigated. Interfacial tension was sufficiently high to allow only small deformations in the dissimilar minor phase body. Mixing was confined to a rectangular cavity with periodically driven upper and lower surfaces. Regions of regular motion (i.e., islands) of comparable size to the minor phase body were eventually destroyed or replaced by the minor phase body. Islands persisted for longer times when the initial separation distance between the minor phase body and island was large or when the viscosity ratio was small. When interfacial tension was small enough to deform the minor phase body more readily, islands showed little indication of instability. Results suggest opportunities for improving mixing uniformity in practical processes and disclose how interactions between dissimilar fluids affect mixing.
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  • 58
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    AIChE Journal 42 (1996), S. 3340-3350 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: A new spray technique, called ultrasound-modulated two-fluid (UMTF) atomization, is based on resonance between the liquid capillary waves generated by ultrasound and those generated by high-velocity air. The capillary waves generated by ultrasound on the cone of liquid film issuing from a coaxial two-fluid atomizer are magnified in amplitude by air blowing around them. Atomization occurs when the amplitude of the capillary waves is too great to maintain wave stability, and the resulting drop sizes are determined by the frequency of the ultrasound. Calculations of the relative amplitude growth for the capillary waves of various wavelengths yield predictions that agree remarkably well with experimental results of drop size and size distribution. Specifically, uniform drops with diameter determined by the third harmonic frequency of the ultrasound are obtained in UMTF atomization at high air velocity and large air-to-water mass ratio. In contrast, drop-size distributions with multiple peaks are obtained in UMTF atomization at low air velocity and small air-to-water mass ratio. The use of air also allows the liquid jet to atomize at ultrasonic power levels below and liquid flow rates above the threshold values for ultrasonic atomization without air. These new findings provide not only direct evidence of the capillary wave mechanism but also a means of controlling drop size and size distribution in two-fluid atomization.
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  • 59
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    AIChE Journal 42 (1996), S. 3434-3441 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Many nuclear facilities throughout the world must separate strontium-90 and cesium-137 from natural waters containing calcium, magnesium, and sodium. Our research showed that chabazite, a zeolite with a hexagonal ring structure, is cost-effective for this purpose. A batch kinetic uptake model for this five-component ion-exchange system was developed and tested against experimental data. The pore-diffusion model of Yao and Tien is used with the equilibrium model of Perona. The resulting model is fast and stable, and represents the experimental data well.
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  • 60
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Gray box models combine the short development time of data-driven black box models with extrapolation properties of knowledge-driven first principles models (white box), which in (bio)chemical engineering are always based on macroscopic balances. By modeling the inaccurately known terms in a macroscopic balance with a black box model, one naturally obtains a so-called serial gray box model configuration. The identification data must cover only the input-output space of the inaccurately known terms, and the accurately known terms can be used for reliable extrapolation. In this way, the serial gray box configuration results in accurate models with known extrapolation properties with a limited experimental effort. This strategy is demonstrated for the modeling and control of a pressure vessel using real-time experiments. For this case, the strategy is superior to a black box modeling approach that requires much more data and to a parallel gray box approach that results in a model with poor extrapolation properties. Moreover, neural networks are an accurate and convenient modeling tool for the black part in gray box model configurations, because a very fast noniterative training algorithm is used for training neural networks.
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  • 61
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    AIChE Journal 42 (1996), S. 3310-3317 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Short contact time circulating fluidized beds (CFBs) are high-performance reactors with great potential of application for fast endothermic reactions. Optimal kinetic conditions require high operating temperature and very short residence time (∼0.15 s), as well as plug flow in the reaction zone, and fast and efficient solid separation before quenching effluents. Hydrodynamics of dilute CFB operated at high gas velocity was simulated in isothermal condition. The gas-flow field is described using turbulence closure models developed for the single phase and modified to account for particle presence. Numerical computation was compared with experimental results of Arena et al. (1993) and Tinaburri et al. (1996) for two different riser configurations. A parametric analysis was performed to investigate inlet geometry influence on flow pattern along the riser. Internal tube and circumferential gas inlet produced the most promising configuration to realize optimal flow condition.
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  • 62
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    AIChE Journal 42 (1996), S. 3364-3372 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Three binary vapor-liquid equilibrium (VLE) data were measured: tertbutanolethanediol, tertbutanol-KAc, and ethanediol-KAc. Experimental data were correlated with the salt-containing local composition model (SCLCM). For the multicomponent system, VLE data predicted by SCLCM are in agreement with the data in the literature. An industrial plant (3500T/Y) of salt-containing extractive distillation for the tertbutanol/water/ethanediol/potassium acetate system was simulated by SCLCM and improved the Rose relaxation method. Simulation results agree well with industrial data.
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  • 63
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    AIChE Journal 42 (1996), S. 3388-3402 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: A method to analyze the closed-loop stability of a system composed of a nonlinear process and a discrete controller is developed. The closed-loop system is described by a set of difference equations resulting from the discretization of the continuous-time model. A commonly used method of discretization (forward difference) offers an incorrect relative order compared to exact discretization. The state and input sensitivity equations of the continuous-time model are used in computing the nominal closed-loop stability criteria. The nominal stability analysis is extended to the important cases of unmeasured states and uncertain model parameters. A numerical Lyapunov function is used to estimate closed-loop regions of attraction. A simulation example (a CSTR with input multiplicity) presented illustrates the analysis methods and closed-loop behavior.
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  • 64
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    AIChE Journal 42 (1996), S. 1938-1944 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: The cross-flow microfiltration flux is assumed to fall smoothly with a decreasing slope from startup to the steady state. Under actual operating conditions beyond a critical level, however, an anomalous decline pattern arises; initially cross-flow medium filtration occurs and then thin-cake filtration. At the earlier stage, fine particles in polydispersed suspensoids are filtered out on the surface of the membrane and/or captured within the latter, clogging the membrane pores gradually. After the membrane surface is covered by the deposit, further filtration occurs by the buildup of filter cake on the initial deposit. Among the many operating variables, three major controlling factors for the earlier stage are confirmed: solids concentration, relative size of solids and pores, and relative force of sweeping and capturing of suspensoids. Because suspended solids are separated by medium- and cake-law filtration in a series, a method for evaluating the time dependence of flux with the new pattern is derived. Reliable flux analysis is achieved for the transient flux of the dilute suspension forming a low compressibility fouling layer, which helps understand efficient flux performance.
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  • 65
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    AIChE Journal 42 (1996), S. 1945-1956 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: A hollow-fiber supported gas membrane process for the separation of NH3 from aqueous solutions containing both NH3 and CO2 was investigated theoretically and experimentally. A lumen laminar flow and radial diffusion model was applied to calculate the membrane wall transfer coefficient from the data stripping a single volatile component, NH3 or CO2, from their individual aqueous solutions. Influence of the type of membranes and operating conditions on mass-transfer rate were discussed, especially the influence of the membrane transfer coefficient on the film mass-transfer coefficient in the lumen. Appropriate configurations of the hollow-fiber modules for stripping of a single component were analyzed to optimize mass transfer. To predict the stripping of NH3 from a solution containing NH3 and CO2, a mathematical model incorporating local chemical equilibria and Nernst-Planck diffusion was developed to describe the mass transport. The models described the experimental data fairly well. The experimental results showed that the supported gas membrane process can be used to remove NH3 effectively from aqueous media containing NH3 and CO2.
    Additional Material: 12 Ill.
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  • 66
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    AIChE Journal 42 (1996), S. 2005-2013 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Thin liquid films stabilized by surfactants above the critical micelle concentration exhibit stratification or stepwise dynamic thinning. A continuum hydrodynamic model is outlined for stepwise film thinning that incorporates equilibrium micellar structuring through self-consistent oscillatory disjoining pressures and effective viscosities. Effective viscosities as functions of thickness are evaluated with an extension of the local average density model, considering dilute colloidal suspension shear viscosities and solvent effects. To establish local shear viscosities, structured DFT micellar profiles, coarse-grained densities, and disjoining pressure are used. Ionic micelles and other colloidal systems with repulsive interactions show structured effective viscosities that are generally less than the corresponding homogeneous solution shear viscosity, bounded by the pure solvent viscosity and that of the bulk micellar solution. For 0.1 and 0.2-M sodium dodecylsulfate micellar solutions, the effective viscosities are less than 5 and 10%, respectively, below the homogeneous fluid viscosity, except at small thicknesses, indicating that the micellar film thins faster than a pure water film of the same thickness.Calculated thinning curves closely resemble experimental observations in the stepwise thinning behavior, displaying decreasing slopes and increased step durations at later times. Despite the micellar structuring within the film, the ionic micelles do not contribute appreciably to the viscous resistance of the thinning film. Rather, Reynolds' film thinning is obeyed, with the equilibrium oscillatory disjoining pressures driving the stepwise dynamics. The shear viscosity of the ionic micellar film is well approximated by that of the bulk solution.
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  • 67
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    AIChE Journal 42 (1996), S. 2025-2035 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Thomas and Windle's model of Case II transport is analyzed for a semiinfinite medium by a singular perturbation technique. Two adjacent boundary layers separate equilibrated and dry regions. A thin boundary layer of width ∼ O(M-1/2/ln M), where M (≫1) dictates how rapidly the mixture's viscosity decays with liquid concentration, sits next to the equilibrated outer left region. Here, quasi-steady diffusion balances relaxation. A thicker intermediate layer of width ∼ O(M-1/2) separates the lefthand boundary layer and the dry outer region on the right, where both relaxation and unsteady diffusion participate in the transport. Matching the solutions at leading order specifies the moving front's speed, v: v ∼ M1/2. The analysis indicates that relaxation significantly affects the nearly dry region just ahead of the moving front. This disagrees with the widely accepted view that ordinary diffusion dominates in the nearly dry righthand region. Approximating that ordinary diffusion dominates in this region leads to a stepexponential concentration profile at the front and a simple analytical solution for the front speed, v with the correct M scaling. This approximate result accurately predicts the values of v determined by direct numerical solutions.
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  • 68
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    AIChE Journal 42 (1996), S. 2047-2056 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: The solvatochromic dye phenol blue (N, N-dimethylindoaniline) is used to characterize the solvent strength (polarity) of the saturated liquid phase in a series of solvent-carbon dioxide binary mixtures. Data were obtained at 35 and 55°C and at pressures up to ∼70 bar. Five solvents were investigated - acetone, cyclohexane, methanol, THF, and toluene. The polarity of the liquid phase decreases significantly with increasing pressure due to the increasing carbon dioxide content of this phase at equilibrium. For example, the polarity of acetone saturated with carbon dioxide at 35°C and ∼60 bar is equivalent to the polarity of pure cyclohexane at ambient pressure. The local environment about the dye is significantly richer in the polar liquid component than the bulk composition would indicate. The degree of enrichment reflects concentration effects at low pressure, and both concentration and pressure effects at high pressure where the mixtures are highly compressible. The NRTL model of Renon and Prausnitz is able to predict these local compositions with reasonable accuracy except at CO2-rich conditions where compressibility effects are important.
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  • 69
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    AIChE Journal 42 (1996), S. 2057-2068 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: A general theory is developed for the mechanical expression of agrofood, cellular materials. The so-called, Liquid-containing biporous particles expression model considers liquid transfer within a network of three different volumes: extraparticle, extracellular and intracellular volumes. The system of partial differential equations is solved for the expression under constant pressure, allowing calculation of the total layer settlement, as well as the deformation of extraparticle, extracellular and intracellular volumes. The model is able to predict the behavior of four different steps in the consolidation stage: the primary deformation and the creep deformation of extraparticle volume, and the deformation and deliquoring of both extracellular and intracellular volumes. The model is applied to the hydraulic pressing of rapeseeds. The theoretical model agrees well with experimental data for the overall range of pressing time.
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  • 70
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    AIChE Journal 42 (1996), S. 2036-2046 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: An improved set of all the thermodynamic and molecular properties required for the prediction of the existing 20 systems of Structure H (sH) hydrate phase equilibrium data is presented. The statistical thermodynamics model was based on the van der Waals and Platteeuw theory, and the spherical core Kihara potential was used for guest-water interactions. Optimized Kihara parameters and reference thermodynamic properties were derived from experimental data of over 20 sH hydrate forming systems. The model could fit all the existing sH hydrate data within an accuracy of ± 6%. Inhibitor predictions were also shown to fit recent data with no adjustable parameters. The feasibility of using hydrate cage occupancies to derive refined Kihara parameters of the guest molecules was investigated. Possible existence of sH hydrates at cryogenic temperatures was also established based on the model.
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    AIChE Journal 42 (1996), S. 2080-2083 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Additional Material: 11 Ill.
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    AIChE Journal 42 (1996), S. 2087-2089 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Additional Material: 3 Ill.
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    AIChE Journal 42 (1996), S. 2084-2086 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Additional Material: 2 Ill.
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    AIChE Journal 42 (1996), S. 2240-2250 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: A methodology is presented to obtain approximate models from input-output data, particularly oriented to implement a model-predictive control scheme. Causal, time-invariant nonlinear discrete systems with a certain type of continuity condition called fading memory are dealt with. To synthesize the nonlinear model a finite-dimensional linear dynamic part (discrete Laguerre polynomials) is used, followed by a nonlinear nonmemory map (single hidden-layer perceptron). Results of the application to approximate and control a binary distillation column are presented.
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    AIChE Journal 42 (1996) 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
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  • 76
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    AIChE Journal 42 (1996), S. 2692-2697 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Additional Material: 4 Ill.
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    AIChE Journal 42 (1996), S. 2699-2700 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
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  • 78
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    AIChE Journal 42 (1996), S. 2701-2712 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: A general computational approach is presented for numerical modeling of viscous flow in baffled, impeller-stirred-tank reactors. A multiblock, body-fitted grid structure facilitates modeling of various impeller and baffle designs, and a new procedure offers averaged velocity data from a complex 3-D CFD dataset. Impellers are modeled precisely, eliminating the need for inputting experimental velocity data for boundary conditions. The method can be used quickly to obtain extremely detailed flow computations at a fraction of the cost of computing unsteady moving grid solutions. A steady-state computational approach that neglects the relative motion between impeller and baffles yields numerical results comparably accurate to full unsteady computations for laminar flow at a fraction of the time and expense. The approximate steady-state method is used to predict power requirements of a Rushton turbine in laminar flow.An unsteady, moving grid technique provides time-accurate solutions for the flow inside an impeller-stirred reactor with side-wall baffles. These computed results are compared with those using the approximate steady-state method and with experimental measurements. The unsteady, moving grid method uses two different initial conditions: one starting from rest and the other starting from an approximate steady-state solution obtained at the starting position of the impeller relative to the baffles. For unsteady simulations of laminar flow in stirred vessels, the final operating condition can be achieved much more efficiently if the solution obtained from the steady-state procedure is used as an approximate initial condition.
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    AIChE Journal 42 (1996), S. 2721-2728 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: In this study, Multimode boiling on a straight pin is theoretically investigated. Axial steady-state temperature distributions along the fin are numerically evaluated, as well as their linear stability characteristics. When film and transition boiling coexist on the fin surface, or only the transition boiling covers the entire fin, the operation remains stable only if the fin length is less than some critical value. When transition and nucleate boiling coexist on a fin, or the fin is in the three-mode boiling (film + transition + nucleate boiling), the entry of nucleate boiling at the fin tip stabilizes the boiling process. This study on base heat flow and fin efficiency with the stability criteria also suggests a new fin design methodology.
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  • 80
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    AIChE Journal 42 (1996), S. 2761-2764 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: In this article, rigorous mathematical analysis is used to prove that the necessary condition for multiple steady-state solutions to exist in two-stage separation process problems involving ternary mixtures is the tendency of the mixture to exhibit a second liquid phase. The unrealistic solution multiplicity that exists in these problems, when phase splitting is not included in the model equations used to solve them, vanishes when phase splitting is included. The standard specification of reflux ratio and bottoms flow rate has been investigated.
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  • 81
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    AIChE Journal 42 (1996), S. 2743-2760 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: High-purity distillation columns are typically difficult to control because of their severely nonlinear behavior reflected by their sharp composition and temperature profiles. The dynamic behavior of such a column, as characterized by the movement of its sharp profile, was elucidated by a nonlinear wave theory established previously. With binary alcohol mixtures, this study provides an experimental observation of such wave-propagation dynamics of a 40-tray stripping column and a 50-tray fractionation column in response to step disturbances of feed composition, feed flow rate, and reboiler heat supply. Our experimental results have verified that the sharp profile in a high-purity column moves as a constant-pattern wave and that the nonlinear wave theory predicts its velocity satisfactorily with very simple mathematics. Our results also demonstrate the asymmetric dynamics of the transitions between two steady states.
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  • 82
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    AIChE Journal 42 (1996), S. 2765-2772 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: A process for carrying out simultaneous reaction and separation of desired products in a single unit operation is described. It uses a fixed packed column of an admixture of a catalyst and a sorbent that selectively removes a reaction by-product from the reaction zone. The sorbent is periodically regenerated by using the principles of pressure-swing adsorption. The process steps allow direct production of the desired product at high purity and at the reaction pressure. High conversion of the reactants to products in an endothermic, equilibrium-controlled reaction can be achieved while operating the reaction at a substantially lower temperature than would be necessary by a plug-flow reactor packed with the catalyst alone. The equilibrium-controlled reverse water-gas shift reaction for the production of carbon monoxide is experimentally evaluated as a proof of the concept.
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  • 83
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    AIChE Journal 42 (1996), S. 2729-2742 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: A theoretical investigation is presented of the convection-diffusion of model nonspherical solutes in shear flow over a plane wall. The analysis proceeds by formulating the underlying configuration-space Brownian transport equation for the distribution over accessible positions and orientations. Geometrical constraints are imposed via boundary conditions preventing wall penetration, and some of the calculations incorporate hydrodynamic interactions with the wall. The analysis is brought to fruition by regular perturbation expansion in the rotary Péclet number, and solution of the resultant boundary-value problems by a Galerkin technique. Three specific mechanistic conclusions result from the analysis. First, steric constraints imposed by the wall impedes the shear-induced solute alignment (producing a more nearly uniform distribution over orientations relative to the unbounded-fluid case) near the wall. Second, although the first effect of flow is to counteract the equilibrium depletion of solute centers near the wall, flow reinforces this depletion at higher order in the shear rate. Third, solute-wall hydrodynamic interactions act to strengthen the shear-induced solute alignment near the wall. This last phenomenon occurs because hydrodynamic wall effects significantly decrease the rotary diffusivity, but have little effect on the angular velocity, thereby locally increasing the effective rotary Péclet number (the effective flow strength). Correspondingly, solute-wall hydrodynamic interactions reinforce the flow effects on the near-wall depletion just noted. Steric and hydrodynamic wall effects typically are of order 15-20% near the wall.
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  • 84
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    AIChE Journal 42 (1996), S. 2911-2925 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: To study runaway behavior in autoclave low-density polyethylene (LDPE) reactors, a kinetic model for a perfectly stirred tank reactor is presented. The kinetic model not only includes the standard initiation, propagation, and termination reactions for polymerization, but it also has free radical reactions that describe the decomposition of ethylene ultimately leading to a runaway. Dynamic simulation of the model indicates runaway behavior for the following conditions: excess initiator in feed; feed impurity; feed temperature disturbance; controller failure; and poorly tuned controller. Operating strategies such as mixed initiator feeds and grade transitions are also explored from a dynamic view. Stability analysis indicates safe operating limits for certain variables at typical conditions. The model provides useful insights for preventing runaway reactions in LDPE autoclaves.
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    AIChE Journal 42 (1996), S. 2993-2994 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
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  • 86
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    AIChE Journal 42 (1996), S. 3020-3029 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: An oriented submicron silicalite membrane has been prepared by growing a layer of oriented silicalite crystals on a composite precursor nanocrystalline silicalite/alumina film using controlled secondary growth. The orientation of the crystals at the surface was such that both straight and sinusoidal channel networks run nearly parallel to the membrane surface. The membrane exhibits ideal selectivities for H2 over N2 as high as 60 at 150°C and O2 over N2 as high as 3.6 at 185°C. H2, N2 and O2 permeances are 2.13, 0.05 and 0.17 cm3(STP)/(cm2·min·atm) at 185°C, respectively, and the corresponding apparent activation energies are 11, 26 and 32 kJ/mol. The permeation characteristics are attributed to the preferred orientation of the molecular sieving layer.
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    AIChE Journal 42 (1996), S. 538-546 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Nuclear magnetic resonance (NMR) spin-lattice relaxation measurements are used to investigate pore structures and fluid phase distributions in porous media. A new method for estimating relaxation time distribution functions from measured relaxation data is presented using a B-spline basis to represent the distribution function and Tikhonov regularization to stabilize the estimation problem. Surface relaxivity, which is required to convert relaxation time distributions to pore-size distributions of fluid phase distributions at partial saturations, is determined using pore volume-to-surface-area ratios estimated by NMR diffusion measurements. This approach was validated by analyzing certain model porous media with known pore volume-to-surface-area ratios. The method is demonstrated by determining pore-size and fluid phase distributions of sandstone and carbonate samples, as well as by comparing the pore-size distributions of chalk samples obtained by this methodology with those estimated by mercury porosimetry.
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    AIChE Journal 42 (1996), S. 547-561 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Emulsion liquid membrane separation processes remain excessively vulnerable to one or more of four major problems. Difficulties lie in developing liquid membranes that combine high levels of both stability and permeability with acceptably low levels of swelling and ease of subsequent demulsification for membrane and solute recovery. This article provides a new technique for simultaneously overcoming the first three problems, while identifying physical indications that the proposed solution may have little adverse effect on the fourth problem (demulsification) and may even alleviate it. Numerous benefits of optimized conversion of the membrane phase into suitable non-Newtonian form are identified, their mechanisms outlined, and experimental verifications provided. These include increased stability, retained (or enhanced) permeability, reduced swelling, increased internal phase volume, and increased stirrer speeds. The highly favorable responsiveness of both aliphatic and aromatic membranes to the new technique is demonstrated.
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    AIChE Journal 42 (1996), S. 562-570 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: A generalized four-parameter quartic equation of state (EOS) proposed by Shah and coworkers (1992, 1994) was extended to polar fluids. To use the new generalized quartic EOS for polar fluids, only four characteristic properties of the pure compound are required - critical temperature, critical volume, acentric factor, and dipole moment. For nonpolar fluids, the previous equation is recovered and its superior performance for nonpolar fluids is retained. A new set of coefficients for polar fluids for the EOS was determined from multiproperty regressions using literature data for various physical and thermodynamic experimental properties of 30 pure compounds. These regressed coefficients, which are functions of the critical temperature, critical pressure, acentric factor, and the dipole moment of the fluid, were generalized. The accuracy of this equation of state is evaluated with the new set of regressed coefficients to predict thermodynamic properties of pure polar compounds, including vapor pressure, density, residual enthalpy, enthalpy of vaporization, and second virial coefficient. The capability and accuracy of this quartic equation of state are also compared with the well-known Peng-Robinson EOS.
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    AIChE Journal 42 (1996), S. 571-584 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: The recently developed formalism for describing the solute-induced effect in dilute near-critical mixtures is extended to fluids composed of anisotropic molecules through the statistical mechanical interpretation of the derivative (∂P/∂x2)T,p∞ whose critical value is the Krichevskii parameter.Rigorous expressions for Henry's constant and the solute distribution factor along the orthobaric curve are derived in terms of the volumetric and entropic solute-induced local effects, and the quasi-linear behavior of their orthobaric density dependence away from the solvent's critical point is rationalized.The formalism is illustrated with integral equation calculations of the orthobaric density dependence of several solvation thermodynamic quantities for an infinitely dilute volatile solute in near-critical solutions of hard-sphere Yukawa fluids.
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    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 42 (1996), S. 595-598 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
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  • 92
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    Electronic Resource
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 42 (1996), S. 638-648 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: The full Navier-Stokes equations were employed with a single-fluid model and a front tracking scheme to study a large cylindrical bubble in a free shear layer. A general formulation based on work by Auton et al. of the hydrodynamic forces on a finite Reynolds number large bubble in an unsteady, nonuniform and rotational flow was then used to investigate the effects of nonlinear spatial and temporal gradients on dispersion. The resulting bubble dispersion in the full Navier-Stokes solution significantly differ from that by a conventional bubble dynamic equation based on linear spatial gradients and quasi-steady flow. This was due to the adjunct forces not accounted for by such a formulation, which are related to regions of high nonuniformity and unsteadiness. These adjunct forces in the drag/lift direction were correlated with rapid variations of relative bubble velocity and high gradients of the liquid velocity.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
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  • 93
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    Electronic Resource
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 42 (1996), S. 623-637 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: The evolution of a film with insoluble surfactant on a wavy horizontal wall differs from flow without surfactant (the way it usually is studied) in that the film passes through different stages. The first stage is as if the surfactant were absent. Once the surface tension gradient - induced by the nonuniform surfactant concentration adsorbed at the free surface - starts resisting the flow effectively, the evolution enters a transitional stage. A final stage is reached once the free surface becomes rigid due to the surface-tension gradient (high elasticity limit) or becomes virtually leveled before the surface-tension gradient is released (low elasticity limit). The velocity profile through the film changes with time, sol fluid is depleted or accumulated at different strata in the film as the flow evolves. The velocity profile and resulting deformations throughout the film can be influenced significantly by the viscosity distribution or stratification, which occurs, for example, when multiple layers of different viscosity are coated simultaneously. A model and applications for the leveling of such a film are presented. The evolution is described in general terms for a film of uniform viscosity and for a film of two discrete layers of different viscosity. Then the three limiting cases are established. For two of these limits, the effect on the exponential decay rate of the flow and the deformation of the different strata or layers is examined when the viscosity is changed in an infinitesimally thin layer or stratum, and in a layer of finite thickness in films of two and three discrete layers.
    Additional Material: 9 Ill.
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  • 94
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    Electronic Resource
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 42 (1996), S. 613-622 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Deterministic cross-stream migration of FENE dumbbells, cyclic trimers and bicyclic tetramers in nonhomogeneous, nonrectilinear flows representative of tortuous pores is analyzed. Identifying the crucial feature of misalignment between a tumbling dumbbell and the surrounding streamlines, Brunn (1983) showed that the dumbbell model requires three reflections in the bead-bead hydrodynamic interaction (HI) for lateral migration to occur: lower-order approximations of the HI are insufficient because they lead only to alignment with the flow rather than tumbling. In any orientation the trimer (tetramer) has at least two (three) “bonds” out of alignment with the flow. Radial migration in rotary Couette flow between concentric cylinders occurs in the freely draining limit, and the simplest, first-order HI is sufficient to cause lateral migration in rectilinear tube flow. Flow through a sinusoidally corrugated pore brings a new convective timescale on which the bead-spring entity moves between converging and diverging flow environments. Since this process outpaces the dumbbell's alignment, even a freely draining dumbbell spends most of its time slightly misaligned with the surrounding streamlines, and migrates toward the walls (higher shear). Tumbling occurs on a much longer timescale, with the dumbbell traveling through many wavelengths of the wall corrugations (and fluctuating in orientation) between successive (rapid) end-for-end flips in the shear field. The flipping time seems to scale inversely with the length of the dumbbell. The trimer and tetramer rotate largely as in rectilinear shear, and exhibit somewhat stronger migration for the same bond length. As a simple model of pore entrance effects, net drift in an oscillatory Sampson flow through a thin orifice is also considered.
    Additional Material: 8 Ill.
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  • 95
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    Electronic Resource
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 42 (1996), S. 649-659 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Drop breakup mechanisms inside a cavity flow are presented for two immiscible fluids. Due to the nonuniform flow condition of the cavity, the breakup mechanism varied along the streamlines. The streamlines were characterized by stream zones A and B, where zone A possessed a methodical transient breakup governed by Tomotika's breakup via capillary instabilities, and the breakup mechanism of stream zone B consisted of tip streaming breakup, an inefficient breakup mechanism. The flow behavior near flight region had a significant role in the drop breakup mechanisms. The study of the evolution of drop dispersion showed that the matrix viscosity is critical in controlling the transient breakup process and that the shear rate increase had little or no effect on the drop breakup.
    Additional Material: 27 Ill.
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  • 96
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    Electronic Resource
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 42 (1996), S. 660-670 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: The expansion behavior and structural phenomena of fluid-particle systems was simulated using a method analogous to the Monte Carlo method for molecular systems. Individual particles are moved, and the resulting moves are accepted or declined based on the change in the system's potential energy and the average kinetic energy of the system. Several fluid-particle systems have been successfully predicted with the model including colloidal particle concentration profiles and random packing of uniform spheres. Additionally, predictions of steady-state fluidized-bed expansion characteristics for uniformly sized stainless-steel spheres and narrowly distributed nickel and glass spheres show excellent agreement with the theoretical model used in the simulation and satisfactory agreement with experimental data. Dynamic expansion predictions of both bed height and overall bed structure as a function of time also agree with the experimental data.
    Additional Material: 13 Ill.
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  • 97
    Electronic Resource
    Electronic Resource
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 42 (1996), S. 96-130 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Recent and ongoing research in the distillation of nonideal mixtures is reviewed focusing on advances in the methodologies for the synthesis, design, analysis and control of separation sequences involving homogeneous and heterogeneous azeotropic towers. Maps of residue curves and distillation lines are examined, as well as geometric methods for the synthesis and design of separation sequences, trends in the steady-state and dynamic analysis of homogeneous and heterogeneous towers, the nonlinear behavior of these towers, and strategies for their control.Emphasis is placed on the methods of computing all of the azeotropes associated with a multicomponent mixture, on the features that distinguish azeotropic distillations from their zeotropic counterparts, on the potential for steady-state multiplicity, and on the existence of maximum and minimum reflux bounds. Important considerations in the selection of entrainers are examined. For the synthesis of separation trains, when determining the feasible product compositions, the graphical methods are clarified, especially the conditions under which distillation boundaries can be crossed and bounding strategies under finite reflux. The application of geometric theory to locate the fixed points, at minimum reflux, is reviewed in connection with homotopy-continuation algorithms for this purpose. The use of homotopy-continuation algorithms, especially for the steady-state simulation of heterogeneous azeotropic distillations, is justified. Methods for phase stability analysis are reviewed in connection with the location of real bifurcation points at phase transitions, an important feature of algorithms for the dynamic simulation of heterogeneous azeotropic distillations.
    Additional Material: 47 Ill.
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  • 98
    Electronic Resource
    Electronic Resource
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 42 (1996), S. 777-790 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Most advanced control applications rely on good dynamic process models. The performance of the control system depends on the accuracy of the model used. Typically, such models are developed by conducting off-line identification experiments on the process. These identification experiments often result in input-output data with small output signal-to-noise ratio, and using these data results in inaccurate model parameter estimates. Prefilters are used to separate useful information from the noise in the input-output data and to improve parameter estimates. A systematic design procedure for selecting a prefilter using discrete wavelet transforms is presented. The design procedure provides explicit information on the compromises in prefilter design, interpreted in terms of parameter variance and bias. The prefilter design procedure is then applied to identify a second-order output error model.
    Additional Material: 10 Ill.
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  • 99
    Electronic Resource
    Electronic Resource
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 42 (1996), S. 301-318 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Experiments conducted quantify the macroscopic hydrodynamic characteristics of various scale 2-D bubble columns, which include dispersed and coalesced bubble regimes characterized by two flow conditions (4- and 3-region flow) with coherent flow structures. Hydrodynamic behavior is analyzed based on flow visualization and a particle image velocimetry (PIV) system. Columns operated in the 4-region flow condition comprise descending, vortical, fast bubble and central plume regions. The fast bubble flow region moves in a wavelike manner, and thus the flow in the vicinity of this region is characterized macroscopically in terms of wave properties. In columns greater than 20 cm in width, the transition from the dispersed bubble flow regime to the 4- and then to 3-region flow in the coalesced bubble regime occurs progressively with gas velocities at 1 and 3 cm/s, respectively. The demarcation of flow regimes is directly related to measurable coherent flow structures. The instantaneous and time-averaged liquid velocity and holdup profiles provided by the PIV system are presented in light of the macroscopic flow structure in various 2-D bubble columns. Numerical simulations demonstrate that the volume of fluid method can provide the time-dependent behavior of dispersed bubbling flows and account for the coupling effects of pressure field and the liquid velocity on the bubble motion. Comparison of computational results with PIV results for two different bubble injector arrangements is satisfactory.
    Additional Material: 27 Ill.
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  • 100
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    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 42 (1996), S. 1101-1107 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: The development of composites with self-diagnostic capabilities is based on the analysis of a mathematical model of the structure. The method is illustrated for a vibrating cantilevered plate and analyzed considering damping. Damage is modeled as an elastic joint, and the spectrum of natural frequencies is calculated for different positions and magnitudes of the elastic joint. Small sensors consisting of tungsten filaments coated with ZnO are embedded in the plate, and their output is modeled. The solution of the inverse problem depends on the position and extent of damage which can be uniquely solved if the system is not overdamped with respect to the primary frequency. Higher modes have a decreasing contribution to the signal output; when the primary mode is overdamped, only the secondary frequency can be detected reliably. The solution to the inverse problem is no longer unique; there are as many as three different solutions (damage position and extent of damage) all of which produce the same signal output.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
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