Morphological instability induced by the interaction of a particle with a solid-liquid interface

European Physical Journal B

Volumn 37, Issue 1, 2004, Pages 85-89

  Hadji, L ^a  

^a UNIVERSITY OF ALABAMA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

HEAT CONDUCTION; HEAT FLUX; INTERFACIAL ENERGY; SOLIDIFICATION; SUPERCONDUCTING MATERIALS; THERMAL CONDUCTIVITY; THERMAL GRADIENTS; THRESHOLD VOLTAGE; ZONE MELTING;

BIOLOGICAL CELL SUSPENSIONS; CRYOPRESERVATION; LIQUID SUSPENSIONS; METALLIC POLLUTANTS;

INTERFACES (MATERIALS);

EID: 2542483408     PISSN: 14346028     EISSN: None     Source Type: Journal    
DOI: 10.1140/epjb/e2004-00032-2     Document Type: Article

References (20)

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11. The directional solidification of an alloy is subject to a morphological Mullins-Sekerka instability when the growth rate V exceeds some critical value (W.W. Mullins, R.F. Sekerka [J. Appl. Phys. 34, 323 (1963)]). The planar interface undergoes a bifurcation to a cellular state whose wavelength is determined from a competition between the destabilizing diffusion length scale and the stabilizing capillary length scale. The wavelength varies roughly between 10 and 100 μm. (I. Durand, K. Kassner, C. Misbah, H. Müller-Krumbhaar, Phys. Rev. Lett. 76, 3013 (1996)). This wavelength is of the same order of magnitude as the size of the inclusions that are used in PMMC and found in other processes. In this paper, the mere presence of the particle in the melt provides the length scale. Furthermore, the growth rates considered here are so low (ε ≪ 1) that the Mullins-Sekerka instability does not arise
12. The directional solidification of an alloy is subject to a morphological Mullins-Sekerka instability when the growth rate V exceeds some critical value (W.W. Mullins, R.F. Sekerka [J. Appl. Phys. 34, 323 (1963)]). The planar interface undergoes a bifurcation to a cellular state whose wavelength is determined from a competition between the destabilizing diffusion length scale and the stabilizing capillary length scale. The wavelength varies roughly between 10 and 100 μm. (I. Durand, K. Kassner, C. Misbah, H. Müller-Krumbhaar, Phys. Rev. Lett. 76, 3013 (1996)). This wavelength is of the same order of magnitude as the size of the inclusions that are used in PMMC and found in other processes. In this paper, the mere presence of the particle in the melt provides the length scale. Furthermore, the growth rates considered here are so low (ε ≪ 1) that the Mullins-Sekerka instability does not arise
13. -5. We assume that the perturbation to the interface profile is of order (e). The case of a pure substance with zero growth rate has been analyzed by L. Hadji, Scripta Materialia 48, 665 (2003)
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18. A.D. Poularikas, The Transforms and Applications Handbook, 2nd edn. (CRC Press, Boca Raton, Florida, 1999). The interaction of a single particle with the interface sets up a perturbation in the interface due to the difference in thermal conductivities (α ≠ 1). In case the instability sets in. this disturbance travels radially in all directions, decreasing in magnitude as it goes. Far away from the particle, at r = l, the particle's effect vanishes. In our calculations, we have arbitrarily chosen l = 10
19. S. Ahuja, Ph.D. Dissertation, The University of Alabama, p. 100 (1992)
20. J.A. Sekhar, R. Trivedi, Mater. Sci. Eng. A 147, 9 (1991). This paper investigates the morphological stability of a solidifying interface in the presence of large number of particles