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  • 1
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 95 (1991), S. 6042-6049 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The molecular theory of nematic liquid crystals, proposed by Doi in 1981, exists in two versions: the original kinetic equation written in terms of the orientational distribution function and an averaged approximation of the original kinetic equation written in terms of the order parameter tensor. In this study, the two versions, as well as a third (hybrid) approach by Edwards and Beris (1989), are compared. Due to the complexity of the original kinetic equation, only uniaxial extensional flow in a homogeneous monodomain is considered. The solution of the original kinetic equation without simplifications is obtained for the first time—using a finite difference scheme with an iterative procedure for an integral equation. The solution of the kinetic equation written in terms of the order-parameter tensor (a nonlinear algebraic equation) is obtained by Newton's procedure. For the ordered phase, the order-parameter version provides acceptable approximation only in the low-concentration region, the extent of which decreases with increasing velocity gradient. The hybrid approach of Edwards and Beris (1989) provides no improvement over the order-parameter version; in the presence of a strong flow, it actually gives worse results at low concentrations.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 96 (1992), S. 4705-4717 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Doi's kinetic equation for the order-parameter tensor is utilized to study the molecular orientation, stability, stress, and pressure distributions in sink/source flows of solutions of rodlike polymers. In these flows, the velocity field can be determined without having to solve the kinetic equation simultaneously with the fluid-dynamical equation of motion. The steady state solution is obtained by Newton's procedure. The transient problem is solved by Runge–Kutta's method. All of the bifurcated solutions are tested for their dynamical stability, and the results reveal that the most stable distribution of molecular orientation is axisymmetric (or nearly axisymmetric), with the most probable orientation being the axis of symmetry. For solutions which can be nematic at equilibrium, the simulation also predicts a sudden drop in stress, followed by an immediate recovery, if the initial molecular orientation in sink flow is not in the principal direction of stretching.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 22 (1996), S. 11-27 
    ISSN: 0271-2091
    Keywords: finite elements ; liquid crystal ; nematic ; anisotropic ; electro rheological ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The orientation tensor L is introduced to construct a modified Leslie-Ericksen model for the viscous, incompressible flow of anisotropic suspensions (including electric field effects). This is then utilized to develop a weak variational formulation and finite element scheme for computing the flow and orientation fields. Numerical results are presented for exploratory test problems.
    Additional Material: 11 Ill.
    Type of Medium: Electronic Resource
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