Bulletin of the American Physical Society
61st Annual Meeting of the APS Division of Fluid Dynamics
Volume 53, Number 15
Sunday–Tuesday, November 23–25, 2008; San Antonio, Texas
Session MU: Material Processing Flows |
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Chair: Bruce Murray, Binghamton University, State University of New York Room: 204B |
Tuesday, November 25, 2008 8:00AM - 8:13AM |
MU.00001: The Solidification of an Ideal Ternary Alloy in a Mushy Layer Daniel Anderson, Geoffrey McFadden, Sam Coriell, Bruce Murray We examine a model for the solidification of a ternary alloy in a mushy layer. Our model is of an isolated mushy layer, mathematically decoupled from any other liquid, mushy or solid layers. The effects of species transport are included along with heat transport in order to investigate the possibility of double-diffusive and other modes of convection in this system. In the ternary mushy layer system the liquidus constraint, which relates temperature to the concentrations of the two diffusing species, allows an additional degree of freedom not present in models for solidification of binary alloys in mushy layers. We investigate the properties of non-convecting base state solutions for this ternary system and then present linear stability results that reveal convective modes of instability. The base state and linear stability results are compared with previous work on binary and ternary alloy mushy layer solidification. [Preview Abstract] |
Tuesday, November 25, 2008 8:13AM - 8:26AM |
MU.00002: Linear stability analysis of a convecting ternary alloy undergoing solidification T.J. Flynn, Daniel Anderson We analyze the linear stability of a solidifying, aqueous ternary alloy cooled from below. During the solidification process, four layers are present. These include a completely liquid layer, two distinct mushy layers (primary and secondary) and a solid layer. Both diffusion of heat and solute as well as convection are treated by the model under study. After identifying a nonconvecting basic solution to the problem, infinitesimal linear perturbations are included to numerically determine the stability of the base state. A Chebyshev pseudospectral collocation method is used to compute the normal mode perturbations and their respective growth rates for various system parameter combinations. Marginal stability curves are presented along with the identification of critical Rayleigh numbers and wavenumber values. [Preview Abstract] |
Tuesday, November 25, 2008 8:26AM - 8:39AM |
MU.00003: Particle capture in binary solidification Justin Kao, Alexander Golovin, Stephen Davis We investigate the interaction of a spherical foreign particle and a propagating solidification front in a binary alloy: depending on material properties and the speed of the front, the particle may either be captured in the solid phase, or rejected and pushed ahead of the front. We employ numerical boundary integral and continuation methods to compute the critical speed for particle capture, and its scaling dependence on the system parameters. Our results reconcile differing predictions of previous theoretical works, and show that many typical systems may obey a new, intermediate, regime of the critical speed. We observe that the presence of solute \emph{decreases particle speeds} by an order of magnitude below those for a single-component system, but \emph{increases bubble speeds} as compared to the single-component system. [Preview Abstract] |
Tuesday, November 25, 2008 8:39AM - 8:52AM |
MU.00004: Comparison of Three Base Flow Representations for Modeling the Optically Heated Floating-Zone with the Full-Zone Han Li, Brent Houchens Three different base flow representations have been studied for the full-zone model of the optically heated floating-zone crystal growth process. The basic difference among the models is the variable groups that are used, and the resulting orders of differentiation in the governing equations. The models include: 1) a stream function-temperature representation, with 4th order derivatives in the biharmonic type governing momentum equation, 2) a vorticity transport-temperature representation, and 3) a primitive variable formulation. The last two involve 2nd order derivatives in the governing equations, as is typical. These three representations are presented and comparisons of computational performance and simulation precision are discussed. [Preview Abstract] |
Tuesday, November 25, 2008 8:52AM - 9:05AM |
MU.00005: High Resolution Numerical Model of Optically Heated Float-Zone Crystal Growth with Applied Magnetic Field Yue Huang, Brent Houchens During optically heated float-zone crystal growth processing, thermocapillary forces drive a flow in the melt. This steady, axisymmetric base flow is susceptible to instabilities, resulting in defects as the final crystal is solidified from the melt. To damp these instabilities, a magnetic field is employed. The stability of this flow, neglecting buoyancy, is studied with a full-zone model. The velocity and temperature fields are calculated by a spectral collocation method using Chebyshev polynomials as basis functions. Obtaining accurate base flows is crucial to the success of the subsequent stability analysis. A 2nd order vorticity transport representation is compared with a 4th order stream function representation. At low Hartmann numbers, the results are in good agreement. However, as resolution demands increase, the 2nd order vorticity transport formulation yields a better numerical representation by avoiding large computational errors caused by 4th and 3rd derivatives of Chebyshev terms in the 4th order stream function representation. This allows the stability analysis to be carried out at larger Hartmann numbers, where the critical thermocapillary Reynolds number is much greater. [Preview Abstract] |
Tuesday, November 25, 2008 9:05AM - 9:18AM |
MU.00006: Finite-amplitude dynamics of coupled cylindrical menisci Brenton Cox, Paul Steen In the planar-flow casting process where a thin ribbon is solidified as product, surface tension holds liquid metal in a ``puddle.'' A defect appearing in the ribbon motivates this study of the interfacial dynamics of coupled menisci, an idealization of the puddle region. In this idealization, a meniscus is pinned at either end of a rectangular slot and these interfaces communicate through the inviscid liquid in the slot between. Capillary forces are assumed dominant and the menisci are assumed circular in cross-section. The resulting model has a Hamiltonian structure, showing dynamical behavior like the Duffing-oscillator. The energy landscape has a single- and double-welled potential depending on the total liquid volume (a bifurcation parameter). The response to small and large disturbances is studied using linear and weakly-nonlinear stability analyses and simulations. For large enough disturbances, the interfaces are expected to break and predicting this ``blow-out'' event is of interest with possible relevance to the industrial process. [Preview Abstract] |
Tuesday, November 25, 2008 9:18AM - 9:31AM |
MU.00007: Thermocapillary Lithgraphy: Large Area Patterning of Nanoscale Polymer Films Mathias Dietzel, Sandra Troian Photolithographic patterning of semiconductor devices relies on optical projection techniques whose resolution limit is set by the Rayleigh diffraction criterion. While the ultimate resolution is of order 100 nm, photolithography is both costly and time consuming due to multiple step and repeat processes to deposit and strip photoresist layers and the limitation to small and flat areas. Alternative techniques, which are far less costly but offer submicron resolution, are of growing interest for a number of applications involving optoelectonic, photonic or biofluidic components. Here we discuss the novel use of thermocapillary lithography for large area patterning of nanoscale polymer films. We investigate geometries in which a supported fluid bilayer in the presence of a patterned upper substrate is subject to an ultrahigh transverse thermal gradient. Finite element simulations help identify the optimal range of parameter values for achieving minimal pitch and feature size. The simplicity of this technique, coupled with the flexibility in tuning the applied thermal distribution, inherent low cost, and extension to curved substrates, may provide an interesting new fabrication method for the manufacture of polymeric electronic and optical components. [Preview Abstract] |
Tuesday, November 25, 2008 9:31AM - 9:44AM |
MU.00008: Air--water gas exchange in wave--free environments Evan Variano, Edwin Cowen, David Ho, Victor Engel Field and laboratory experiments investigate the dynamics of gas exchange at natural water surfaces, focusing on those in which there is no surface shear due to wind. Laboratory results using quantitative imaging of both velocity fields and $CO_2$ concentration fields allow us to measure the conditional statistics of scalar flux due to subsurface--generated turbulence. Field measurements tracking a cloud of dissolved $SF_6$ gas through a patterned marshland allow us to determine the weekly--averaged interfacial gas transfer rate, which is dominated by thermal convection and rain--generated mixing. These results are used to evaluate potential models for predicting flux rates in such environments, which include many of the most ecologically productive habitats. Predicting these fluxes is an important foundation for ecological and biogeochemical research on these habitats. [Preview Abstract] |
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