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Finite-sample-size effects on convection in mushy layers

Authors: Jin-Qiang Zhong; Anthony T. Fragoso; Andrew Wells; John S. Wettlaufer;

Finite-sample-size effects on convection in mushy layers

Abstract

AbstractWe report theoretical and experimental investigations of the flow instability responsible for mushy-layer convection with chimneys, drainage channels devoid of solid, during steady-state solidification of aqueous ammonium chloride. Under certain growth conditions a state of steady mushy-layer growth with no flow is unstable to the onset of convection, resulting in the formation of chimneys. We present regime diagrams to quantify the state of the flow as a function of the initial liquid concentration, the porous-medium Rayleigh number, and the sample width. For a given liquid concentration, increasing both the porous-medium Rayleigh number and the sample width drove a transition from a weakly convecting chimney free state to a state of mushy-layer convection with fully developed chimneys. Increasing the concentration ratio stabilized the system and suppressed the formation of chimneys. As the initial liquid concentration increased, onset of convection and formation of chimneys occurred at larger values of the porous-medium Rayleigh number, but the critical cell widths for chimney formation are far less sensitive to the liquid concentration. At the highest liquid concentration, the mushy-layer mode of convection did not occur in the experiment. The formation of multiple chimneys and the morphological transitions between these states are discussed. The experimental results are interpreted in terms of a previous theoretical analysis of finite amplitude convection with chimneys, with a single value of the mushy-layer permeability consistent with the liquid concentrations considered in this study.

Country
United Kingdom
Subjects by Vocabulary

Microsoft Academic Graph classification: Convection Materials science Aqueous solution Flow (psychology) Mechanics Rayleigh number Concentration ratio Fully developed Permeability (earth sciences) Chimney

arXiv: Physics::Fluid Dynamics

Keywords

Mechanical Engineering, Fluid Dynamics (physics.flu-dyn), FOS: Physical sciences, Physics - Fluid Dynamics, Condensed Matter Physics, Mechanics of Materials

42 references, page 1 of 5

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Anderson, D. M. & Worster, M. G. 1995 Weakly nonlinear analysis of convection in mushy layers during the solidification of binary alloys. J. Fluid Mech. 302, 307-331. [OpenAIRE]

Aussillous, P., Sederman, A. J., Gladden, L. F. & Huppert, H. E. amd Worster, M. G. 2006 Magnetic resonance imaging of structure and convection in solidifying mushy layers. J. Fluid Mech. 552, 99-125.

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Chen, C. F. & Chen, F. 1991 Experimental study of directional solidification of aqueous ammonium chloride solution. J. Fluid Mech. 227, 567-586.

Chen, F., Lu, J. W. & Yang, T. L. 1994 Convective instability in ammonium chloride solution directionally solidified from below. J. Fluid Mech. 276, 163-187.

Chung, C. A. & Worster, M. G. 2002 Steady-state chimneys in a mushy layer. J. Fluid Mech. 455, 387-411.

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  • citations
    This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    12
    popularity
    This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
    Top 10%
    influence
    This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    Average
    impulse
    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
    Average
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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
12
Top 10%
Average
Average
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