Solidification directional

The definition of directional solidification is a process in which the melt is being continuously supplied to solidification interface. This could almost apply to any solidification process in which the solidification front advances into the melt, but the operative word here is continuously, which implies some sort of a feed mechanism such as a continuous 

Schematic of a continuous casting process as an example of direction solidification. 

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An important example of an MMC in situ composite is one made by directional solidification of a eutectic alloy. The strength, (, of such an in situ metal-matrix composite is given by a relationship similar to the HaH-Petch relationship used for grain boundary strengthening of metals ... 

Siow withdrawai of mould from furnace Fig. 20.5. Directional Solidification (DS) of turbine blades. 

Directional solidification (see [121-123,125] and [126-129]) is the most frequent way in which a material changes its state from sohd to liquid. The necessary removal of the latent heat of freezing usually occurs in a direction prescribed by the location of heat sinks For a freezing lake it is the cold atmosphere above it in casting iron in a foundry it is the cold sand-form into which the heat flow is directed. 

A different problem of spacing, which is closely related to directional solidification but has some additional degrees of freedom, is electrocrystallization. We would like to mention at least one example of greater significance, namely the production of porous silicon [131], which is still not very well understood today. 

In our treatment of directional solidification above, only one diffusion field was treated explicitly, namely the compositional diffusion. If a simple material grows dendritically (thermal diffusion) one may worry about small amounts of impurities. This was reconsidered [132], confirming a qualitative previous result [133] that impurities may increase the dendritic growth rate. Recently some direct simulation results have been obtained with two coupled diffusion fields, one for heat and one for matter, but due to long computing times they are not yet in the state of standard applications [120,134]. 

I. Durand, K. Kassner, C. Misbah, H. Muller-Krumbhaar. Strong coupling between diffusive and elastic instabilities in directional solidification. Phys Rev Lett 76 10X1, 1996 I. Cantat, K. Kassner, C. Misbah, H. Muller-Krumbhaar, Directional solidification under stress. Phys Rev E 58 6011, 1998. 

A. Classen, C. Misbah, H. Miiller-Krumbhaar, Y. Saito. Kinetics in directional solidification. Phys Rev A 45 6920, 1991. 

K. Kassner, J.-M. Debierre, B. Billia, N. Noel, H. Jamgotchian. Cellular structures in three-dimensional directional solidification simulation and analysis. Phys Rev E 57 2849, 1998. 

L. Biihler, S. H. Davis. Flow induced changes of the morphological stability in directional solidification localized morphologies. J Crystal Growth 756 629, 1998 Y.-J. Chen, S. H. Davis, Directional solidification of a binary alloy into a cellular convective flow (unpublished). Applied Math Technical Report No. 9708, Northwestern University, Evanston, IL 60208. 

J. A. Warren, J. S. Langer. Prediction of dendritic spacings in a directional solidification experiment. Phys Rev E 47 2102, 1993. 

Arav, A., Granut, R., Shturman, H., Rubinsky, B. (1993). Cryopreservation of bovine semen with directional solidification. Cryobiol. 30,632-633 (abstract). 

Ishiguro, H. Rubinsky, B. (1994). Mechanical interactions between ice crystals and red blood cells during directional solidification. Crybiol. 31.483-500,... 

Meiron (12) and Kessler et al. (13) have shown that numerical studies for small surface energy give indications of the loss-of-existence of the steady-state solutions. In these analyses numerical approximations to boundary integral forms of the freeboundary problem that are spliced to the parabolic shape far from the tip don t satisfy the symmetry condition at the cell tip when small values of the surface energy are introduced. The computed shapes near the tip show oscillations reminiscent of the eigensolution seen in the asymptotic analyses. Karma (14) has extended this analysis to a model for directional solidification in the absence of a temperature gradient. 

The presentation in this paper concentrates on the use of large-scale numerical simulation in unraveling these questions for models of two-dimensional directional solidification in an imposed temperature gradient. The simplest models for transport and interfacial physics in these processes are presented in Section 2 along with a summary of the analytical results for the onset of the cellular instability. The finite-element analyses used in the numerical calculations are described in Section 3. Steady-state and time-dependent results for shallow cell near the onset of the instability are presented in Section 4. The issue of the presence of a fundamental mechanism for wavelength selection for deep cells is discussed in Section 5 in the context of calculations with varying spatial wavelength. 

Progressive freezing, sometimes called normal freezing, is the slow, directional solidification of a melt. Basically, this involves slow solidification at the bottom or sides of a vessel or tube by indirect cooling. The impurity is rejected into the liquid phase by the advancing solid... 

Fig. 3.25.2. Porous structure of collagen sponge produced by directional solidification accord-t-UfT- to the. Power- hVxw tx. rxxeJbocI- atlcL...

Fig. 3.25.3. Magnification of the defined and homogeneous porous structure of a collage sponge produced by directional solidification according to the Power-Down method and subsequent freeze drying (scanning electron microscope, white bar = 0.1 mm) (from [3.67]).

The problem of morphological instability was solved theoretically by Mullins and Sekerka [20], who proposed a linear theory demonstrating that the morphology of a spherical crystal growing in supercooled melt is destabilized due to thermal diffusion the theory dealt quantitatively with and gave linear analysis of the interface instability in one-directional solidification. 

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