899 research outputs found

    Interaction of paraffin wax gels with random crystalline/amorphous hydrocarbon copolymers

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    The control mechanisms involved in the modification of wax crystal dimensions in crude oils and refined fuels are of joint scientific and practical interest. An understanding of these mechanisms allows strategies to be developed that lead to decreases in crude oil pour points or (for refined fuels) cold filter plugging points. The attainment of these goals involves the control and modification of wax crystals that spontaneously form in mixed hydrocarbon systems upon decreasing temperature. This work reports on the influence of random crystalline-amorphous block copolymers (ethylene-butene) upon the rheology of model oils. In a parallel fashion small-angle neutron scattering was exploited to gain microscopic insight as to how added poly(ethylene-butene) copolymers modify the wax crystal structures. The copolymers with different contents of polyethylene are highly selective with respect to wax crystal modification. Thus, the copolymer with the highest crystalline tendency is more efficient for the larger wax molecules while the less crystalline one is more efficient for the lower waxes

    Interaction of paraffin wax gels with ethylene/vinyl acetate copolymers

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    The commercial grades of ethylene/vinyl acetate (EVA) co-polymers have found application as pour point" depressants in refined fuels. This study focuses on their behavior as additives to crude oils, where the intent is to reduce the yield stress of the gels that can form when the oil exits the reservoir. The model crude oils consisted of 4 wt % wax in decane. At EVA dosage levels of similar to200 ppm, the reduction in yield stress is 3 orders of magnitude for the C-36 wax, whereas the reduction is 1 order of magnitude for C-32 and only 3-fold for the C-28 wax. This decrease in efficiency with decreasing wax carbon number indicates that the EVA materials would not provide an adequate reduction in yield stress to ensure against gelation in pipeline transport. Neutron scattering studies, as a function of temperature, of the self-assembly of the EVA co-polymers show dramatically different aggregated structures in decane. The EVA with the lowest ethylene content shows scattering that increases with a power-law exponent of similar to1.6. This scattering behavior is typical for weakly aggregating polymer gels. In contrast, the EVA with the higher ethylene content shows a transition from surface scattering (found for strongly segregated objects) to a plateau whose height is dependent on temperature. Micrographs of the wax crystal morphology indicate that the ethylene-poor EVA alters the wax crystal habit at higher concentrations more effectively than does its higher-ethylene-content counterpart, whereas the latter EVA grade seems to form more wax crystals at low concentrations

    On a classical spectral optimization problem in linear elasticity

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    We consider a classical shape optimization problem for the eigenvalues of elliptic operators with homogeneous boundary conditions on domains in the NN-dimensional Euclidean space. We survey recent results concerning the analytic dependence of the elementary symmetric functions of the eigenvalues upon domain perturbation and the role of balls as critical points of such functions subject to volume constraint. Our discussion concerns Dirichlet and buckling-type problems for polyharmonic operators, the Neumann and the intermediate problems for the biharmonic operator, the Lam\'{e} and the Reissner-Mindlin systems.Comment: To appear in the proceedings of the workshop `New Trends in Shape Optimization', Friedrich-Alexander Universit\"{a}t Erlangen-Nuremberg, 23-27 September 201

    Segue Between Favorable and Unfavorable Solvation

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    Solvation of small and large clusters are studied by simulation, considering a range of solvent-solute attractive energy strengths. Over a wide range of conditions, both for solvation in the Lennard-Jones liquid and in the SPC model of water, it is shown that the mean solvent density varies linearly with changes in solvent-solute adhesion or attractive energy strength. This behavior is understood from the perspective of Weeks' theory of solvation [Ann. Rev. Phys. Chem. 2002, 53, 533] and supports theories based upon that perspective.Comment: 8 pages, 7 figure

    Self Consistent Molecular Field Theory for Packing in Classical Liquids

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    Building on a quasi-chemical formulation of solution theory, this paper proposes a self consistent molecular field theory for packing problems in classical liquids, and tests the theoretical predictions for the excess chemical potential of the hard sphere fluid. Results are given for the self consistent molecular fields obtained, and for the probabilities of occupancy of a molecular observation volume. For this system, the excess chemical potential predicted is as accurate as the most accurate prior theories, particularly the scaled particle (Percus-Yevick compressibility) theory. It is argued that the present approach is particularly simple, and should provide a basis for a molecular-scale description of more complex solutions.Comment: 6 pages and 5 figure

    A Survey on the Krein-von Neumann Extension, the corresponding Abstract Buckling Problem, and Weyl-Type Spectral Asymptotics for Perturbed Krein Laplacians in Nonsmooth Domains

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    In the first (and abstract) part of this survey we prove the unitary equivalence of the inverse of the Krein--von Neumann extension (on the orthogonal complement of its kernel) of a densely defined, closed, strictly positive operator, S≥εIHS\geq \varepsilon I_{\mathcal{H}} for some ε>0\varepsilon >0 in a Hilbert space H\mathcal{H} to an abstract buckling problem operator. This establishes the Krein extension as a natural object in elasticity theory (in analogy to the Friedrichs extension, which found natural applications in quantum mechanics, elasticity, etc.). In the second, and principal part of this survey, we study spectral properties for HK,ΩH_{K,\Omega}, the Krein--von Neumann extension of the perturbed Laplacian −Δ+V-\Delta+V (in short, the perturbed Krein Laplacian) defined on C0∞(Ω)C^\infty_0(\Omega), where VV is measurable, bounded and nonnegative, in a bounded open set Ω⊂Rn\Omega\subset\mathbb{R}^n belonging to a class of nonsmooth domains which contains all convex domains, along with all domains of class C1,rC^{1,r}, r>1/2r>1/2.Comment: 68 pages. arXiv admin note: extreme text overlap with arXiv:0907.144
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