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  • 1
    Electronic Resource
    Electronic Resource
    Asymptotic behavior of modulated Taylor–Couette flows with a crystalline inner cylinder (1993)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 5 (1993), S. 1891-1903 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The linear stability of a modulated Taylor–Couette system when the inner cylindrical boundary consists of a crystalline solid-liquid interface is considered. Both experimentally and in numerical calculations it is found that the two-phase system is significantly less stable than the analogous rigid-walled system for materials with moderately large Prandtl numbers. A numerical treatment based on Floquet theory is described, which gives results that are in good agreement with preliminary experimental findings. In addition, this instability is further examined by carrying out a formal asymptotic expansion of the solution in the limit of large Prandtl number. In this limit the Floquet analysis is considerably simplified, and the linear stability of the modulated system can be determined to leading order through a conventional stability analysis, without recourse to Floquet theory. The resulting simplified problem is then studied for both the narrow gap geometry and for the case of a finite gap. It is surprising that the determination of the linear stability of the two-phase system is considerably simpler than that of the rigid-walled system, despite the complications introduced by the presence of the crystal-melt interface.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.858815
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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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    Paper (German National Licenses)
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  • 3
    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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  • 4
    Electronic Resource
    Electronic Resource
    Stabilization of Taylor–Couette flow due to time-periodic outer cylinder oscillation (1990)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 2 (1990), S. 2147-2156 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The linear stability of circular Couette flow between concentric infinite cylinders is considered for the case when the inner cylinder is rotated at a constant angular velocity and the outer cylinder is driven sinusoidally in time with zero mean rotation. This configuration was studied experimentally by Walsh and Donnelly [Phys. Rev. Lett. 60, 700 (1988)]. The critical Reynolds numbers calculated from linear stability theory agree with the experimental values, except at large modulation amplitudes and small frequencies. The theoretical values are obtained using Floquet theory implemented in two distinct approaches: (1) a truncated Fourier series representation in time and (2) a fundamental solution matrix based on a Chebyshev-pseudospectral representation in space. For large-amplitude, low-frequency modulation, the linear eigenfunctions are temporally complex, consisting of a quiescent interval followed by rapid change in the perturbed flow velocities.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.857801
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  • 5
    Electronic Resource
    Electronic Resource
    Effect of a crystal–melt interface on Taylor-vortex flow (1990)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 2 (1990), S. 700-705 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The linear stability of circular Couette flow between concentric infinite cylinders is considered for the case that the stationary outer cylinder is a crystal–melt interface rather than a rigid surface. A radial temperature difference is maintained across the liquid gap, and equations for heat transport in the crystal and melt phases are included to extend the ordinary formulation of this problem. The stability of this two-phase system depends on the Prandtl number. For small Prandtl number the linear stability of the two-phase system is given by the classical results for a rigid-walled system. For increasing values of the Prandtl number, convective heat transport becomes significant and the system becomes increasingly less stable. Previous results in a narrow-gap approximation are extended to the case of a finite gap, and both axisymmetric and nonaxisymmetric disturbance modes are considered. The two-phase system becomes less stable as the finite gap tends to the narrow-gap limit. The two-phase system is more stable to nonaxisymmetric modes with azimuthal wavenumber n=1; the stability of these n=1 modes is sensitive to the latent heat of fusion.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.857723
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    Paper (German National Licenses)
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  • 6
    Electronic Resource
    Electronic Resource
    Lubrication theory for reactive spreading of a thin drop (1995)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 7 (1995), S. 1797-1810 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Solder drops spreading on metallic substrates are a reactive form of the wetting problem. A metallic component may diffuse in the liquid toward a metal substrate, where it is consumed by a reaction that forms a solid intermetallic phase. The resulting spatial variation in the composition of the drop may cause composition gradients along the free surface of the drop. Together with any thermal gradients along the free surface, Marangoni effects may, in turn, modify the bulk transport in the spreading drop. Motivated by this situation, we extend lubrication theory for the spreading of thin drops in the presence of gravity and thermocapillarity to include mass transport and solutocapillarity. We use an approximate solute profile in the drop to derive coupled evolution equations for the free surface shape and concentration field. Numerical solutions for the nonreactive (single component) drop agree well with previous theory. In the reactive case, we are only able to compute results for parameters outside of the range for solder materials. Including reactive effects in the model impacts the flow patterns and spreading rates at relatively early times; but by the end of the spreading, solutal effects have died out in the model. © 1995 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.868497
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