Convective instabilities during the solidification of an ideal ternary alloy in a mushy layer

2010 ◽  
Vol 647 ◽  
pp. 309-333 ◽  
Author(s):  
DANIEL M. ANDERSON ◽  
GEOFFREY B. McFADDEN ◽  
SAM R. CORIELL ◽  
BRUCE T. MURRAY
Keyword(s):  
Phase Diagram ◽  
Ternary Alloy ◽  
Liquidus Surface ◽  
Point Of View ◽  
Mushy Layer ◽  
Convective Instabilities ◽  
Diffusive Modes ◽  
Diffusion Convection ◽  
Static Point ◽  
Double Diffusive

We consider a model for the solidification of an ideal ternary alloy in a mushy layer that incorporates the effects of thermal and solutal diffusion, convection and solidification. Our results reveal that although the temperature and solute fields are constrained to the liquidus surface of the phase diagram, the system still admits double-diffusive modes of instability. Additionally, modes of instability exist even in situations in which the thermal and solute fields are each individually stable from a static point of view. We identify these instabilities for a general model in which the base-state solution and its linear stability are computed numerically. We then highlight these instabilities in a much simpler model that admits an analytical solution.

Economic Sociology: The Recursive Economic System of J. S. Mill

2005 ◽  
Vol 27 (3) ◽  
pp. 251-281 ◽  
Author(s):  
Amos Witztum
Keyword(s):  
Property Rights ◽  
Economic System ◽  
Income Tax ◽  
Economic Sociology ◽  
Evolutionary Change ◽  
Point Of View ◽  
Economic Variables ◽  
Statics And Dynamics ◽  
Internal Relationship ◽  
Static Point

In a recent paper, R. Ekelund and D. Walker (1996) argue that, “[i]ncentives, utilitarian principles, and the diffusion of property rights are the key to understanding Mill on the statics and dynamics of ‘equity and justice’”(p. 576). Their paper, which deals with John Stuart Mill's views on taxation, reads very much like a modern defense of popular capitalism. From the static point of view, it is imperative not to interfere with the internal relationship between economic variables and thus, distort incentives (proportional income tax). From the dynamic point of view, “inheritance taxes [are] the essential mechanism of an evolutionary change towards an efficiently functioning capitalism” (p. 578, italics added).

Respon ASEAN Terhadap Mundurnya India Dari Kerja Sama Regional Comprehensive Economic Partnership (RCEP)

2020 ◽  
pp. 183-202
Author(s):  
Raden Maisa Yudono ◽  
Wiwiek Rukmi Dwi Astuti ◽  
M. Chairil Akbar Setiawan
Keyword(s):  
Comparative Advantage ◽  
Economic Cooperation ◽  
Point Of View ◽  
Geographic Proximity ◽  
Strategic Partner ◽  
Business Interests ◽  
Political Conditions ◽  
Economic Partnership ◽  
Regional Comprehensive Economic Partnership ◽  
Static Point

Regional Comprehensive Economic Partnership (RCEP) is a cooperation framework formulated by ASEAN and 6 strategic partner countries and is the first proposal in ASEAN history to discuss comprehensive economic cooperation. RCEP is ASEAN's effort to strengthen its position as regional aktor in the Southeast Asian. RCEP negotiations underwent changes during India's decision to withdraw from the RCEP negotiations, which prompted ASEAN to respond to these developments. This study fokuses on response taken by ASEAN to India's decision to withdraw from the RCEP negotiations. The concept used is soft regionalism which emphasizes geographic proximity, historical relations and the comparative advantage of the region. Soft regionalism is driven by not only by economic and business interests, but also market interests that become the energy of soft regionalism in Asia. This concept is functioning well because it conforms to the pragmatic Asian political conditions. The findings of this study is that ASEAN cannot be separated from the concept of soft regionalism in which it has been running, and still sees all changes through static point of view. ASEAN needs to make new breakthroughs in realizing comprehensive cooperation in the region.

THE SYSTEM: BISMUTH–CADMIUM–MERCURY

1965 ◽  
Vol 43 (7) ◽  
pp. 1924-1928 ◽  
Author(s):  
A. N. Campbell ◽  
E. M. Kartzmark
Keyword(s):  
Binary System ◽  
Ternary Alloy ◽  
Room Temperature ◽  
Solid Phase ◽  
Liquidus Surface ◽  
Molar Volumes ◽  
X Ray

The liquidus surface of this ternary alloy has been determined, together with the nature of the solid phase separating from various melts. The densities and molar volumes of the binary system: Cd—Hg have been determined and it is shown that there is marked contraction when the α and β phases form from the components. X-ray powder photographs of various Cd—Hg alloys at room temperature have been made and the limits of homogeneity determined.

Modification of Al-Si Microstructure - The Al-Si-Sr Phase Diagram from 0–20 WT. % Si and 0–5.0 WT. % Sr

1982 ◽  
Vol 19 ◽  
Author(s):  
M. D. Hanna ◽  
A. Hellawell
Keyword(s):  
Thermal Analysis ◽  
Phase Diagram ◽  
Liquid Metal ◽  
Alkali Metal ◽  
Alkaline Earth ◽  
Liquidus Surface ◽  
Eutectic Silicon ◽  
Alkaline Earth Metals ◽  
Current Interest

ABSTRACTIt is well known that the morphology of primary and eutectic silicon resulting from solidification is sensitive to minor impurity additions: “modification” by alkali and alkaline earth metals is common foundry practice and the use of strontium is of recent and current interest because its effect is retained in liquid metal for relatively long times. The mechanism for modification remains obscure and is not necessarily the same from one elemental addition to the next, but it is essential to separate the equilibrium and kinetic influences if the phenomenon is to be better understood. Accordingly, the liquidus surface and eutectic reactions have been located in the relevant part of the Al-Si-Sr system by careful thermal analysis and the results correlated with the microstructure. Comparison is made with the parallel behavior of alkali metal additions.

Phase diagram and compounds of the Gd-Fe-Nb ternary alloy system in the Fe-rich corner

1998 ◽  
Vol 10 (40) ◽  
pp. 9183-9188 ◽  
Author(s):  
F Huang ◽  
J K Liang ◽  
Q L Liu ◽  
X L Chen ◽  
G Y Huo
Keyword(s):  
Phase Diagram ◽  
Ternary Alloy ◽  
Alloy System ◽  
Ternary Alloy System

A new oscillatory instability in a mushy layer during the solidification of binary alloys

1996 ◽  
Vol 307 ◽  
pp. 245-267 ◽  
Author(s):  
D. M. Anderson ◽  
M. Grae Worster
Keyword(s):  
Classical Case ◽  
Oscillatory Instability ◽  
Mushy Layer ◽  
Quiescent State ◽  
Specific Interest ◽  
Small Deviations ◽  
Stefan Number ◽  
Field Temperature ◽  
Diffusive Effects ◽  
Double Diffusive

We consider the solidification of a binary alloy in a mushy layer and analyse the linear stability of a quiescent state with specific interest in identifying an oscillatory convective instability. We employ a near-eutectic approximation and consider the limit of large far-field temperature. These asymptotic limits allow us to examine the dynamics of the mushy layer in the form of small deviations from the classical case of convection in a horizontal porous layer of uniform permeability. We consider also the limit of large Stefan number, which incorporates a key balance necessary for the existence of the oscillatory instability. The model we consider here contains no double-diffusive effects and no region in which a statically stable density gradient exists. The mechanism underlying the oscillatory instability we discover is instead associated with a complex interaction between heat transfer, convection and solidification.

Diffusive and phase change instabilities in a ternary mushy layer

2014 ◽  
Vol 760 ◽  
pp. 634-669 ◽  
Author(s):  
Peter Guba ◽  
Daniel M. Anderson
Keyword(s):  
Phase Change ◽  
Ternary Phase Diagram ◽  
Convective Transport ◽  
Solute Diffusion ◽  
Mushy Layer ◽  
Convective Instabilities ◽  
Stable Conditions ◽  
Thermodynamic Constraint ◽  
Small Growth ◽  
The Stability

AbstractWe analyse the stability of a mushy layer during the directional solidification of a ternary alloy. Our model includes diffusive and convective transport of heat and solutes, coupled by an equilibrium thermodynamic constraint of the ternary phase diagram. The model contains phase change effects due to latent-heat release, solute rejection and background solidification. We identify novel convective instabilities, both direct and oscillatory, which are present under statically stable conditions. We examine these instabilities asymptotically by simplifying to a thin mushy layer with small growth rates. We also discuss numerical results for the full problem, confirming the asymptotic predictions and providing the stability characteristics outside the small-growth-rate approximation. A physical explanation for these instabilities in terms of parcel arguments is proposed, indicating that the instability mechanisms generally involve different rates of solute diffusion, different rates of solute rejection and different background solute distributions induced by the initial alloy composition.

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