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  • 1
    Electronic Resource
    Electronic Resource
    Convective stability in the Rayleigh–Bénard and directional solidification problems: High-frequency gravity modulation (1991)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 3 (1991), S. 2847-2858 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The effect of vertical, sinusoidal, time-dependent gravitational acceleration on the onset of solutal convection during directional solidification is analyzed in the limit of large modulation frequency Ω. When the unmodulated state is unstable, the modulation amplitude required to stabilize the system is determined by the method of averaging, and is O(Ω). Comparison of the results from the averaged equations with numerical solutions of the full linear stability equations (based on Floquet theory) show that the difference is O(Ω1/2). When the unmodulated state is stable, resonant modes of instability occur at large modulation amplitude. These are analyzed using matched asymptotic expansions to elucidate the boundary-layer structure for both the Rayleigh–Bénard and directional solidification configurations. The leading-order term for the modulation amplitude is of O(Ω2); the first-order correction of O(Ω3/2) is calculated, and the results are compared with numerical solutions of the full linear stability equations. Based on these analyses, a thorough examination of the dependence of the stability criteria on the unmodulated Rayleigh number, Schmidt number, and distribution coefficient, is carried out.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.857830
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  • 2
    Electronic Resource
    Electronic Resource
    The effect of gravity modulation on thermosolutal convection in an infinite layer of fluid (1992)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 4 (1992), S. 1176-1189 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The effect of time-periodic vertical gravity modulation on the onset of thermosolutal convection in an infinite horizontal layer with stress-free boundaries is investigated using Floquet theory for the linear stability analysis. Situations for which the fluid layer is stably stratified in either the fingering or diffusive regimes of double-diffusive convection are considered. Results are presented both with and without steady background acceleration. Modulation may stabilize an unstable base solution or destabilize a stable base solution. In addition to synchronous and subharmonic response to the modulation frequency, instability in the double-diffusive system can occur via a complex conjugate mode. In the diffusive regime, where oscillatory onset occurs in the unmodulated system, regions of resonant instability occur and exhibit strong coupling with the unmodulated oscillatory frequency. The response to modulation of the fundamental instability of the unmodulated system is described both analytically and numerically; in the double-diffusive system this mode persists under subcritical conditions as a high-frequency lobe.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.858236
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  • 3
    Electronic Resource
    Electronic Resource
    Bifurcation analysis of solutal convection during directional solidification (1991)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 3 (1991), S. 535-550 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Techniques of bifurcation theory are used to analyze the possible forms of steady, two-dimensional, buoyancy-driven flow present during the vertical directional solidification of a dilute binary mixture. Morphological instabilities of the crystal–melt interface are ignored and the interface is assumed to be planar. The focus of the study concerns the effect of lateral confinement on the flow patterns observable in this simple model system. The use of a time-dependent numerical scheme by McFadden and Coriell [Proceedings of the First National Fluid Dynamics Congress, Cincinnati (AIAA, Washington, DC, 1988), p. 1572] to investigate this same problem resulted in gaps in the bifurcation structure, because unstable steady states exist that cannot be computed by their method. The present work extends and completes the description of the possible steady states. In particular, the complex modal exchanges that occur as the separation between the lateral walls varies are elucidated, and stable flow regimes and the sensitivity of the results to the closure condition at the upper boundary are determined.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.858115
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  • 4
    Electronic Resource
    Electronic Resource
    THE EFFECT OF SOLUTAL CONVECTION ON THE MORPHOLOGICAL STABILITY OF A BINARY ALLOY (1983)
    Oxford, UK : Blackwell Publishing Ltd
    Annals of the New York Academy of Sciences 404 (1983), S. 0 
    Details
    ISSN: 1749-6632
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Natural Sciences in General
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1749-6632.1983.tb19479.x
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  • 5
    Electronic Resource
    Electronic Resource
    Cahn–Hoffman ξ-Vector and Its Relation to Diffuse Interface Models of Phase Transitions (1999)
    Springer
    Journal of statistical physics 95 (1999), S. 1245-1280 
    Details
    ISSN: 1572-9613
    Keywords: anisotropy ; surface energy ; diffuse interface model ; phase-field model ; stress tensor ; equilibrium shapes
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract In this paper we review two important theoretical areas to which J. W. Cahn has made major contributions: (i) The theory of the ξ-vector developed by Hoffman and Cahn, which provides an elegant setting for the description of the equilibrium shapes of sharp interfaces in the presence of anisotropic surface energy. (ii) Diffuse interface theories of phase transitions. We describe recent work which connects these two complementary facets of models of interfaces by the development of a generalized ξ-vector for diffuse interface models with anisotropic surface energy. We show that the generalized ξ-vector plays a central role in both the mathematical and physical aspects of a wide range of diffuse interface theories of interfaces with either anisotropic surface energy or attachment kinetics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1004575022280
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  • 6
    Electronic Resource
    Electronic Resource
    Transient phenomena in crystal growth systems (1980)
    Springer
    Journal of engineering mathematics 14 (1980), S. 161-176 
    Details
    ISSN: 1573-2703
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Technology
    Notes: Summary In a model of the Czochralski crystal growth system the crystal is represented by a solid rotating plane adjacent to a semi-infinite region occupied by the melt from which the crystal is grown. The melt itself may be subjected to rotation at large distances from the interface. In a co-ordinate system advancing with the interface the crystal growth is modelled by a ‘suction’ velocity at the interface. A transient analysis is performed following a discontinuous change of solute concentration in the bulk of the melt. Two cases are considered, namely (i) solid body rotation of crystal and melt and (ii) no melt rotation at large distances from the interface. The paper represents a re-examination and re-interpretation of earlier work by Burton, Prim and Slichter [1].
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00039313
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  • 7
    Electronic Resource
    Electronic Resource
    An orthogonal mapping technique for the computation of a viscous free-surface flow (1992)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 15 (1992), S. 1243-1258 
    Details
    ISSN: 0271-2091
    Keywords: Free surface ; Viscous flow ; Finite element method ; Orthogonal mappings ; 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: In this paper we describe finite element computations of the free-surface flow of a viscous fluid down an undulating inclined plane. The technique developed here employs an orthogonal mapping that is computed along with the velocity and pressure. This is allied to a technique to compute symbolically the Jacobian and other derivatives required for numerical continuation methods. The solutions obtained are compared with laboratory experiments and finite element computations reported by Pritchard and co-workers. The finite element computational method used by these authors employs spines to represent the free surface. An excellent agreement is shown to exist between the new computations and the laboratory experiments, and with the numerical solutions of Pritchard and co-workers.
    Additional Material: 11 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650151102
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  • 8
    Electronic Resource
    Electronic Resource
    On a finite element method for the calculation of steady cellular interfaces in the one-sided model of solidification (1989)
    New York, NY [u.a.] : Wiley-Blackwell
    Communications in Applied Numerical Methods 5 (1989), S. 309-320 
    Details
    ISSN: 0748-8025
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper we reconsider the work of Ungar and Brown.15 These authors reported calculations of the non-linear families of steady-state solutions of the one-sided model of unidirectional solidification of a binary alloy. They combined a finite element method with a Landau transformation13 to deal with the free boundary, and predicted the non-linear solutions using numerical continuation and bifurcation techniques. We show that the numerical scheme that they used to calculate these families is mesh-dependent when the solid-liquid interface becomes sufficiently deformed.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1630050504
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  • 9
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    Phase-field models for anisotropic interfaces (1993)
    American Physical Society
    Details
    Publication Date: 1993-09-01
    Print ISSN: 1063-651X
    Electronic ISSN: 1095-3787
    Topics: Physics
    Published by American Physical Society
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  • 10
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    Phase-field model of solute trapping during solidification (1993)
    American Physical Society
    Details
    Publication Date: 1993-03-01
    Print ISSN: 1063-651X
    Electronic ISSN: 1095-3787
    Topics: Physics
    Published by American Physical Society
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