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  • 1
    Electronic Resource
    Electronic Resource
    A hierarchical model for surface effects on chain conformation and rheology of polymer solutions. I. General formulation (1999)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 110 (1999), S. 616-627 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The flow behavior of polymer solutions near a solid surface (either neutral or adsorbing) is modeled through a new, hierarchical (macroscopic and microscopic) approach which enables the thermodynamically consistent extension of equilibrium (static) considerations to nonequilibrium (flow) conditions. The approach involves two steps: First, the set of primary, independent, variables defining the state of the system at the macroscopic level is chosen, and a complete set of transport and constitutive equations is constructed for them through a two fluid, Hamiltonian model. In the present work, the macroscopic variables include the polymer chain concentration, the macroscopic fluid velocity, and the conformation tensor (defined as the tensor of the second moment of the chain end-to-end vector). The governing equations involve the (extended) free energy or Hamiltonian of the system, H, and are valid both in the bulk of the fluid and in the interfacial region. Thus, to solve them one needs to specify H. This is done in a second step, by invoking a microscopic model, which consistently takes into account the simultaneous effect on chain conformations of both the solid boundary and the imposed flow field. Solid boundary effects are taken into account in the solution of a diffusion equation for the chain propagator G(r,n;r0) which represents the weighted probability that an n-segment long chain which starts at r0 will end at position r. Flow field effects are taken into account through the definition of a generalized propagator G′(r,n;r0,α), which further depends on the apparent strain tensor α, representing chain deformation effects due to flow. The present part of the paper describes the general formulation of the approach and its relevance with previous works. Results from applying the methodology to the case of a polymer solution flowing past a purely repulsive surface (a wall) are presented in the second part of this work. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.478119
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  • 2
    Electronic Resource
    Electronic Resource
    A hierarchical model for surface effects on chain conformation and rheology of polymer solutions. II. Application to a neutral surface (1999)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 110 (1999), S. 628-638 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: In this part, the general formulation described in Part I is applied to the modeling of the behavior of a dilute polymer solution near a purely repulsive, planar solid surface, i.e., near a noninteracting wall. The static equilibrium problem is considered first. The model equations here reduce to a minimization problem for the Helmholtz free energy of the system, which results into the well known equilibrium condition that the chemical potentials of all chain conformations in the interfacial area should be equal to each other. The numerical results show that the loss of polymer conformational entropy in the interfacial region gives rise to a strong polymer depletion which extends up to a distance about three times the equilibrium root-mean-square polymer end-to-end distance. Next, the problem of a polymer solution flowing past the wall is investigated. Here, the full model equations need to be considered; these are solved numerically with a spectral collocation technique. The numerical results show that the flow field enhances polymer depletion phenomena near the wall relative to those observed under equilibrium (static) conditions: By increasing the shear stress, the polymer concentration in the interfacial area decreases, in full agreement with available experimental data. Moreover, the flow field is found to affect significantly the chain conformations near the wall: The applied shear stress is seen to extend the chains along a primary direction, ξ, and to depress them in the transverse direction, η. The depletion of the interfacial region in polymer molecules is further seen to lead to the formation of a boundary layer close to the wall, where the macroscopic fluid velocity increases rapidly from its zero value exactly at the wall to its asymptotic bulk profile, resulting into an apparent macroscopic slip at the wall. The theoretically calculated slip coefficient is found to be of the same order of magnitude with the experimentally measured one, as reported in the literature for a dilute polymer solution of polymethylacrylate flowing near a glass surface [H. Mueller-Moehnssen et al., J. Rheol. 34, 223 (1990)]. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.478120
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  • 3
    Electronic Resource
    Electronic Resource
    Unified view of transport phenomena based on the generalized bracket formulation (1991)
    s.l. : American Chemical Society
    Industrial & engineering chemistry research 30 (1991), S. 873-881 
    Details
    ISSN: 1520-5045
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1021/ie00053a009
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  • 4
    Electronic Resource
    Electronic Resource
    Implementation of Model-Based Optimal Temperature Profiles for Autoclave Curing of Composites Using a Knowledge-Based System (1994)
    s.l. : American Chemical Society
    Industrial & engineering chemistry research 33 (1994), S. 2443-2452 
    Details
    ISSN: 1520-5045
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1021/ie00034a029
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  • 5
    Electronic Resource
    Electronic Resource
    Steady laminar flow of liquid–liquid jets at high Reynolds numbersf| (1993)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 5 (1993), S. 1703-1717 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The axisymmetric steady-state laminar flow of a Newtonian liquid jet injected vertically into another immiscible Newtonian liquid is investigated for various Reynolds numbers. The steady-state solution was calculated by solving the axisymmetric transient equations of motion and continuity using a numerical scheme based on the volume of fluid (VOF) method combined with the new continuum surface force (CSF) algorithm. The analysis takes into account pressure, viscous, inertial, gravitational, and surface tension forces. Comparison with previous experimental measurements, performed on a xylene/water system, under conditions where all of these forces are important, shows good agreement over the entire range of conditions studied. Comparisons of the present numerical method with the numerical results of previous boundary-layer methods help establish their range of validity.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.858847
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  • 6
    Electronic Resource
    Electronic Resource
    Direct numerical simulation of the turbulent channel flow of a polymer solution (1997)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 9 (1997), S. 743-755 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: In this work, we present from first principles a direct numerical simulation (DNS) of a fully turbulent channel flow of a dilute polymer solution. The polymer chains are modeled as finitely extensible and elastic dumbbells. The simulation algorithm is based on a semi-implicit, time-splitting technique which uses spectral approximations in the spatial coordinates. The computations are carried out on a CRAY T3D parallel computer. The simulations are carried out under fully turbulent conditions albeit, due to computational constraints, not at as high Reynolds number as that usually encountered in polymer-induced drag reduction experiments. In order to compensate for the lower Reynolds number, we simulate more elastic fluids than the ones encountered in drag reduction experiments resulting in Weissenberg numbers (a dimensionless number characterizing the flow elasticity) of similar magnitude. The simulations show that the polymer induces several changes in the turbulent flow characteristics, all of them consistent with available experimental results. In particular, we have observed, associated with drag reduction, a decrease in the streamwise vorticity fluctuations and an increase in the average spacing between the streamwise streaks of low speed fluid within the buffer layer. These findings suggest a partial inhibition of turbulence generating events within the buffer layer by the macromolecules after the onset of drag reduction. This inhibition is further shown to be associated with an enhanced effective viscosity attributed to the extensional thickening properties of polymer solutions, as proposed in the past by Metzner, Lumley and other investigators. Using the simulation results obtained for different sets of parameter values which modify the relaxational and extensional properties of the model, we propose a set of criteria for the onset of drag reduction. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.869229
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  • 7
    Electronic Resource
    Electronic Resource
    Drop formation in liquid–liquid systems before and after jetting (1995)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 7 (1995), S. 2617-2630 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The formation of drops resulting from the breakup of an axisymmetric Newtonian liquid jet injected vertically into another immiscible Newtonian liquid at various Reynolds numbers is investigated here. The full transient from startup to breakup into drops was simulated numerically by solving the time-dependent axisymmetric equations of motion and continuity using a combination of the volume-of-fluid (VOF) and continuous-surface-force (CSF) methods. The numerical simulation results compare well with previous experimental data and are significantly more accurate than previous simplified analyses based on drop formation before and after jetting over a wide range of conditions. © 1995 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.868710
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  • 8
    Electronic Resource
    Electronic Resource
    Dynamic breakup of liquid–liquid jets (1994)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 6 (1994), S. 2640-2655 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The axisymmetric, dynamic breakup of a Newtonian liquid jet injected vertically into another immiscible Newtonian liquid at various Reynolds numbers is investigated here. The full transient from jet start-up to breakup into drops was simulated numerically by solving the time-dependent axisymmetric equations of motion and continuity using an algorithm based on the Volume of Fluid (VOF) method that was previously proven successful in simulations of steady-state liquid jets (i.e., of the jet region close to the nozzle before breakup). The algorithm has been further refined here based on its performance on transient problems such as the solution of the free liquid–liquid capillary jet breakup problem. The comparison of the simulation results with previous experimental measurements of jet length under conditions where all forces, i.e., viscous, inertial, buoyancy, and surface tension, are important, can be judged satisfactory given the sensitive dependence of the results on details of the experimental setup that are not available. The comparison involves the jet length till breakup as well as the jet and drop shapes, often far from regular. In comparison with experiment, the results of the present numerical method show a greater sensitivity of the jet length to the Reynolds number than the best predictions previously available based on the linear stability analysis of the free liquid–liquid capillary jet breakup problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.868154
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  • 9
    Electronic Resource
    Electronic Resource
    Rotational Motion and Poisson Bracket Structures in Rigid Particle Systems and Anisotropic Fluid Theory (1998)
    Springer
    Open systems & information dynamics 5 (1998), S. 333-368 
    Details
    ISSN: 1573-1324
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Natural Sciences in General
    Notes: Abstract We explore the origins of rotational motion in anisotropic fluid theories from the most fundamental perspectives possible: collections of discrete entities or continuous spectra of fluid particles which are allowed to translate and rotate simultaneously. In either case, the starting point of our analysis is the principle of least action applied to rigid body systems involving both translation and rotation. Our methods of analyzing this problem are both very old and very recent, and we hope that the net result of these methods is an injection of much originality into an old problem. Hamiltonian mechanics of a system of discrete particles is considered where explicit accounting is made of both translational and rotational particle motion. The extended Poisson bracket is written down in terms of appropriate generalized coordinates and the Hamiltonian of the system. A similar treatment in terms of quasi-coordinates is also presented. An alternative formulation in terms of two orthogonal unit vectors is offered which simplifies the mathematical description of the system by working in an inertial reference frame with constant, diagonal inertia tensors. This methodology is transferred to a continuum material description in terms of functional relationships and Volterra differentiation. An analogous continuum bracket is derived, and ultimately transferred to a spatial description, along with the Hamiltonian. This results in a derivation of the most general form of the ideal anisotropic fluid equations in terms of the appropriate variables, an important subcase of which is the Leslie-Ericksen theory of liquid crystals. It extends and also provides insight into the molecular origins of the various constitutive relationships of continuum anisotropic fluid theories (such as the inertia tensor, body force, body couple, etc.). Our motivation is to provide, based on the Poisson bracket structure for all different descriptions of rigid particle rotation, an a priori derivation of the Poisson bracket structure corresponding to the rotational motion described in continuum anisotropic fluid theories which also leads to their consistent generalization.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1009691800395
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  • 10
    Electronic Resource
    Electronic Resource
    Evaluating all real roots of nonlinear equations using a global fixed-point homotopy method (1991)
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 37 (1991), S. 1749-1752 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/aic.690371122
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