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  • 1
    Electronic Resource
    Electronic Resource
    Kinetic theory and rheology of dilute, nonhomogeneous polymer solutions (1991)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 95 (1991), S. 2988-3000 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A phase-space kinetic theory of dilute polymer solutions is developed to account for the effects of nonhomogeneous velocity and stress fields. The theory allows the configuration distribution function to depend on spatial location and explicitly treats the polymer molecule as an extended object in space. Constitutive equations for the mass flux vector and stress tensor are derived that predict polymer migration induced by stress gradients and nonuniform velocity gradients. In addition, the constitutive equation for stress contains a diffusive term in stress, and hence the model does not fall within the class of simple fluids. Simple shear flow between parallel plates is solved to illustrate the features of the constitutive equations. Asymptotic analysis and numerical calculations show the formation of boundary layers in stress, velocity gradient, and polymer concentration that arise near solid walls as a result of preferential orientation of the polymer molecules there. The thickness of these layers scales as λHDtr/L2, where λH is the relaxation time of the macromolecule modeled as a Hookean dumbbell, Dtr is its translational diffusivity in solution, and L is the characteristic length scale of the macroscopic flow. The presence of these layers causes only a small change in the shear stress measured in typical rheometers, but can have a profound effect on the macroscale flow of polymer solutions in complex geometries by causing apparent fluid slip near solid boundaries.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.460900
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  • 2
    Electronic Resource
    Electronic Resource
    A large population of ‘Lyman-break’ galaxies in a protocluster at redshift z ≈ 4.1 (2004)
    [s.l.] : Macmillian Magazines Ltd.
    Nature 427 (2004), S. 47-50 
    Details
    ISSN: 1476-4687
    Source: Nature Archives 1869 - 2009
    Topics: Biology , Chemistry and Pharmacology , Medicine , Natural Sciences in General , Physics
    Notes: [Auszug] The most massive galaxies and the richest clusters are believed to have emerged from regions with the largest enhancements of mass density relative to the surrounding space. Distant radio galaxies may pinpoint the locations of the ancestors of rich clusters, because they are massive systems ...
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1038/nature02125
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  • 3
    Electronic Resource
    Electronic Resource
    Correlation of the electronic spectra and acidity of 5-substituted 2-nitroanilines with structure (1968)
    s.l. : American Chemical Society
    The @journal of organic chemistry 33 (1968), S. 1947-1949 
    Details
    ISSN: 1520-6904
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1021/jo01269a053
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  • 4
    Electronic Resource
    Electronic Resource
    The connection between hydrodynamic stability of gas flow in spin coating and coated film uniformity (1995)
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 77 (1995), S. 2297-2308 
    Details
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The thickness uniformity of a spin-cast film is governed by the air flow through the spin coater, particularly the boundary layer flow above the surface of the spinning wafer, which controls solvent evaporation from the dry film. Laser Doppler velocimetry (LDV) and hot wire anemometry (HWA) are used to map the flow field throughout an industrial spin coater and to study flow instabilities in the boundary layer for various combinations of wafer spin speed and exhaust flow rate. The flow field measured by LDV compares well with a numerical simulation of laminar, axisymmetric, and steady air flow throughout the coating bowl. However, Ekman spiral flow instabilities of both type I (positive spiral angle) and type II (negative spiral angle) were found by HWA in the boundary layer near the surface of the spinning wafer. The type-II spirals form at Reynolds number in the range 2000–2500 and the type-I spirals form at Reynolds number in the range 80 000–85 000. It is the type-II spirals that are responsible for disrupting the air flow in the boundary layer flow and that cause nonuniform drying of spin-cast films. © 1995 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.358751
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  • 5
    Electronic Resource
    Electronic Resource
    The effects of gas phase convection on mass transfer in spin coating (1993)
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 73 (1993), S. 585-600 
    Details
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The thickness uniformity of photoresist films deposited by spin coating critically influences the resolution of photolithography. This thickness uniformity depends on uniform evaporation from the film during drying. Simple scaling arguments demonstrate that, if the mass transfer coefficient at the surface of the wafer does not vary with radial position, then the dry coated resist film thickness will be independent of radial position. A model is presented for the compressible, laminar, steady-state, axisymmetric air flow in a spin coating apparatus for 6-in.-diam wafers. Flow fields computed by a finite-element–Newton method are used to evaluate the radial profile of the mass transfer coefficient at the surface of the rotating wafer, and to calculate the trajectories of particles that are generated as photoresist is flung from the edge of the spinning wafer. At a spin speed of 2000 revolutions/min and exhaust flow rate of 100 l/min through the coater, the calculations predict that the mass transfer coefficient should be independent of radius. Comparison with film contours measured from experiments at these conditions indicates radial nonuniformities in the film thickness and suggests the importance of hydrodynamic instabilities in the gas on the uniformity of the coating.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.353368
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  • 6
    Electronic Resource
    Electronic Resource
    Local similarity solutions for the stress field of an Oldroyd-B fluid in the partial-slip/slip flow (1997)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 9 (1997), S. 2191-2209 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Local similarity solutions are presented for the stress field of a fluid described by the Oldroyd-B viscoelastic constitutive equation near the singularity caused by the intersection of a planar free surface and a solid surface along which Navier's slip law holds, the partial-slip/slip problem. For the case where the velocity field is given by Newtonian kinematics, the elastic stress field is predicted to have a logarithmic singularity as the point of attachment of the free surface is approached. Asymptotic analysis for the fully-coupled flow, where the stress and flow fields are determined simultaneously, results in a local form for the flow and elastic stress fields that is similar in form to that for the decoupled case. For both the coupled and decoupled flow problems, the strength of the singularity depends on the dimensionless solvent viscosity and the slip coefficient, but not upon the Deborah number. The asymptotic results for the coupled flow differ from the predictions with Newtonian kinematics in that the strength of the singularity in the rate-of-strain and elastic stress fields scales with the inverse of the dimensionless solvent viscosity, and suggest that calculations with decreasing solvent viscosity become increasingly difficult. The fully-coupled analysis also suggests that the asymptotic behavior in the limit of vanishing solvent viscosity, the UCM limit, is qualitatively different from that for finite values of the solvent viscosity. The structure of the flow and stress fields for both the coupled and decoupled flow problems is reproduced by finite element calculations. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.869342
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  • 7
    Electronic Resource
    Electronic Resource
    The role of surface tension in the dominant balance in the die swell singularity (1995)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 7 (1995), S. 2328-2344 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The two-dimensional, free-surface flow of a Newtonian fluid exiting from a planar die is computed by finite element analysis using quasiorthogonal mesh generation and local mesh refinement with irregular, embedded elements to obtain extreme resolution of the velocity and pressure fields near the die edge, where the fluid sheet attaches to the solid boundary. Calculations for the limit of large surface tension, the stick-slip problem, reproduce the singular behavior near the die edge expected from asymptotic analysis using a self-similar form for the velocity field. Results for finite capillary number (Ca) predict that the meniscus separates from the die at a finite contact angle and suggest that the capillary force enters the dominant normal stress balance at the die edge through an infinite curvature, as previously suggested by Schultz and Gervasio. The size of this region with large positive curvature increases with increasing Ca, and the strength of the singularity is in good agreement with theoretical predictions for a straight meniscus attached to the die at the appropriate contact angle predicted by the simulations. The contact angle appears to be determined from matching of the inner solution structure valid near the singularity with the bulk flow, in agreement with arguments made by Ramalingam; increasing the Reynolds number decreases the contact angle, corroborating this effect. Introducing fluid slip along the surface of the die changes the structure of the singularity in the pressure and stresses, but does not alleviate the singular behavior. In fact, the calculations with slip coefficients small enough not to change the bulk solution are more difficult than calculations with the no-slip boundary condition. © 1995 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.868746
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  • 8
    Electronic Resource
    Electronic Resource
    A constitutive equation for concentrated suspensions that accounts for shear-induced particle migration (1992)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 4 (1992), S. 30-40 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A constitutive equation for computing particle concentration and velocity fields in concentrated monomodal suspensions is proposed that consists of two parts: a Newtonian constitutive equation in which the viscosity depends on the local particle volume fraction and a diffusion equation that accounts for shear-induced particle migration. Particle flux expressions used to obtain the diffusion equation are derived by simple scaling arguments. Predictions are made for the particle volume fraction and velocity fields for steady Couette and Poiseuille flow, and for transient start-up of steady shear flow in a Couette apparatus. Particle concentrations for a monomodal suspension of polymethyl methacrylate spheres in a Newtonian solvent are measured by nuclear magnetic resonance (NMR) imaging in the Couette geometry for two particle sizes and volume fractions. The predictions agree remarkably well with the measurements for both transient and steady-state experiments as well as for different particle sizes.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.858498
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  • 9
    Electronic Resource
    Electronic Resource
    Local similarity solutions in the presence of a slip boundary condition (1997)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 9 (1997), S. 1235-1247 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The local solution behavior near corners formed by the intersection of a slip surface with either a no-slip or a shear-free boundary is analyzed by finite element calculations of the two-dimensional flow of an inertialess Newtonian fluid in several model flow geometries; these flows are the flow in a tapered contraction, a sudden expansion and the extrudate swell from a planar die. Local finite element mesh refinement based on irregular, embedded elements is used to obtain extremely fine resolution of the velocity and pressure fields near the region where there is a sudden change in boundary condition. The calculations accurately reproduce the expected asymptotic behavior for a shear-free surface intersecting a no-slip boundary, where the solution is given by a self-similar form for the velocity and pressure fields. Replacing the shear-free condition with a slip condition yields a similar form for the local velocity and pressure fields and indicates that the slip boundary behaves, to leading order, as a shear-free surface. Calculations for a slip boundary intersecting a shear-free surface yield similar results, with the local behavior being given by asymptotic analysis for two shear-free surfaces intersecting to form a wedge. These results suggest that replacing the no-slip boundary condition in planar Newtonian die swell with a slip boundary condition can give rise to local behavior of velocity gradients and pressure which is more singular than the flow created with no-slip boundary conditions. This prediction is confirmed by calculations of Newtonian die swell with slip. These calculations also demonstrate that the local solution in Newtonian die swell is sensitive to the details of the numerical method. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.869263
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  • 10
    Electronic Resource
    Electronic Resource
    Traveling waves on vertical films: Numerical analysis using the finite element method (1994)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 6 (1994), S. 2202-2220 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Finite-amplitude waves propagating at constant speed down an inclined fluid layer are computed by finite element analysis of the Navier–Stokes equations written in a reference frame translating at the wave speed. The velocity and pressure fields, free-surface shape and wave speed are computed simultaneously as functions of the Reynolds number Re and the wave number μ. The finite element results are compared with predictions of long-wave, asymptotic theories and boundary-layer approximations for the form and nonlinear transitions of finite-amplitude waves that evolve from the flat film state. Comparisons between the finite element calculations and the long-wave predictions for fixed μ and increasing Re agree well for small-amplitude waves. However, for larger-amplitude waves the long-wave results diverge qualitatively from the finite element predictions; the long-wave theories predict limit points in the solution families that do not exist in the finite element solutions. Comparisons between the finite element predictions, previous numerical simulations and experimental results for the shape and speed of periodic and solitary-like waves are in good agreement. Nonlinear interactions are demonstrated between multiple waves in a periodic wave train that cause secondary bifurcations to families of waves that differ from those that evolve from the neutral stability curve. These predictions for fixed Re and decreasing μ are in quantitative agreement with the results of long-wave approximations for small-amplitude waves. Comparisons with the predictions of boundary-layer approximations show sensitivity of the solution structure to the value of the Weber number We.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.868222
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