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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. 2988-3000 
    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
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  • 2
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 73 (1993), S. 585-600 
    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
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  • 3
    Electronic Resource
    Electronic Resource
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 4 (1992), S. 30-40 
    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
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  • 4
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 6 (1994), S. 2202-2220 
    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
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  • 5
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 69 (1991), S. 3865-3877 
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A systematic theory is presented for the prediction of oxygen migration near a 60° dislocation and for the resulting retardation of dislocation motion. Quantitative predictions are based on the solution of the macroscopic equation for transport of oxygen in the elastic stress field created by the dislocation. The link between the microscopic dynamics of interstitial oxygen within the diamond lattice and macroscopic transport is established by a constitutive model for the dependence of the drift velocity band diffusivity of oxygen on the elastic interaction of oxygen atoms and dislocations and on temperature. The transport equation is solved numerically assuming that the dislocation core is fully saturated with oxygen. The drag force on the gliding dislocation caused by the surrounding oxygen is computed from linear elasticity theory, combined with the phenomenological model of Alexander and Haasen [Solid State Phys. 22, 27 (1968)] for the dependence on the applied stress of the velocity of a dislocation in pure silicon. The predicted dependence of the dislocation velocity on the applied stress at specific temperatures and oxygen concentrations is in qualitative agreement with the experimental data of Imai and Sumino [Philos. Mag. A 47, 599 (1983)].
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    Woodbury, NY : American Institute of Physics (AIP)
    Applied Physics Letters 62 (1993), S. 2584-2586 
    ISSN: 1077-3118
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Flow visualization in the gas above the surface of a rotating wafer in an industrial spin coating apparatus demonstrates the presence of an Ekman-like flow instability that adversely affects the uniformity of the dried film. Experiments performed with a 6-in.-diam wafer and typical operating conditions show 6–8 spiral vortices around the wafer oriented with negative angle, as is indicative of the type II flow instability predicted by linear stability analysis. The critical Reynolds number for onset is in reasonable agreement with the theory.
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    Woodbury, NY : American Institute of Physics (AIP)
    Applied Physics Letters 62 (1993), S. 172-174 
    ISSN: 1077-3118
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Formation and migration properties of self-interstitial atoms in silicon are calculated using systematic atomistic simulations based on the Stillinger–Weber interatomic potential [F. H. Stillinger and T. A. Weber, Phys. Rev. B 31, 5262 (1985)]. The lowest energy configuration of an interstitial atom is calculated to be an extended configuration with a formation energy that is 1.2 eV lower than the formation energy of the higher symmetry configuration with lowest energy. A mechanism for the interpretation of dopant diffusion data is proposed based on this result. The calculated lower bound for the diffusion coefficient of self-interstitials described by a simple migration path is in good agreement with experimental data over the temperature range 733 K〈T〈1473 K.
    Type of Medium: Electronic Resource
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  • 8
    Electronic Resource
    Electronic Resource
    Woodbury, NY : American Institute of Physics (AIP)
    Applied Physics Letters 58 (1991), S. 1842-1844 
    ISSN: 1077-3118
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Oxygen gettering to dislocations slows and stops dislocation motion caused by applied stress in silicon crystals. A model is presented that quantitatively describes the inhibition of dislocation motion by accounting for the drag caused by the oxygen atmosphere in the crystal around the dislocation and for oxygen aggregates inside the dislocation core. The oxygen distribution is computed by analysis of diffusion and stress-assisted migration in the crystalline lattice. The predictions of the model agree quantitatively with the experimental data of Imai and Sumino. Hysteresis is predicted in the dependence of the dislocation velocity on applied stress and explains the difference in the unlocking and locking stresses for dislocation motion.
    Type of Medium: Electronic Resource
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  • 9
    Electronic Resource
    Electronic Resource
    Woodbury, NY : American Institute of Physics (AIP)
    Applied Physics Letters 58 (1991), S. 1181-1183 
    ISSN: 1077-3118
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The leveling of a thin-liquid film on a substrate having a mesa-like feature is analyzed by finite element analysis and lubrication theory applied to the free-surface viscous flow problem. The height of the mesa is on the order of 1 μm and has a width on the order of 100 μm; the thin-liquid film is initially conformal to the substrate and has a thickness on the order of 1 μm. Capillarity is found to be the primary driving force for flow. The predicted leveling times from the numerical simulations compare favorably with an analytical solution developed from lubrication theory for the leveling of a thin film on a smooth substrate.
    Type of Medium: Electronic Resource
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