Abstract
Results of the directional solidification (DS) experiments on particle engulfment and pushing by solidifying interfaces (PEP), conducted on the space shuttle Columbia during the Life and Microgravity Science (LMS) Mission, are reported. Two pure aluminum (99.999 pct) 9 mm cylindrical rods, loaded with about 2 vol pct 500µm-diameter zirconia particles, were melted and resolidified in the microgravity (µg) environment of the shuttle. One sample was processed at a stepwise increased solidification velocity and the other at a stepwise decreased velocity. It was found that a pushing/engulfment transition (PET) occurred in the velocity range of 0.5 to 1 µm/s. This is smaller than the ground PET velocity of 1.9 to 2.4 µm/s. This demonstrates that natural convection increases the critical velocity. A previously proposed analytical model for PEP was further developed. A major effort to identify and produce data for the surface energy of various interfaces required for calculation was undertaken. The predicted critical velocity for PET was 0.775 µm/s.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
Abbreviations
- a :
-
coefficient (0 for no contact and 1 for perfect contact)
- a O :
-
atomic diameter
- A :
-
Hammaker constant
- B :
-
constant defining the disjoining pressure (CTM model)
- d :
-
equilibrium distance
- d cr :
-
critical distance
- D :
-
liquid diffusivity
- E vdW :
-
van der Waals energy
- F g :
-
gravity force
- F D :
-
drag force
- F L :
-
life force
- F vdW :
-
van der Waals force
- F γσ :
-
interaction force between the particle and the SL interface
- G :
-
temperature gradient in the liquid (CTM model)
- ΔH f :
-
latent heat of fusion
- ΔH vap :
-
heat of sublimation
- kB :
-
Boltzman’s constant
- K O :
-
material constant
- K*:
-
ratio between the thermal conductivity of the particle (K P) and of the liquid (K L)
- n :
-
exponent between 2 and 7 (UCJ and SAS models)
- R :
-
particle radius
- ΔS f :
-
entropy of fusion
- T :
-
temperature
- V :
-
velocity
- V cr :
-
critical velocity
- V L :
-
fluid velocity at the SL interface parallel to the interface
- V SL :
-
solidification velocity
- W ad :
-
work of adhesion
- γ :
-
surface energy
- η :
-
liquid viscosity
- ϑ :
-
contact angle
- σ :
-
surface tension
- Δσ O :
-
surface tension difference
- Δγ0 :
-
surface energy difference
- Θ:
-
atomic volume
- Ω (∞):
-
function with value of 0.34
- L :
-
liquid (matrix)
- P :
-
particle
- S :
-
solid (matrix)
References
S. Sen, B.K. Dhindaw, D.M. Stefanescu, A. Catalina, and P.A. Curreri: J. Cryst. Growth, 1997, vol. 173, pp. 574–84.
A.A. Chernov, D.E. Temkin, and A.M. Mel’nikova: Sov. Phys. Crystallogr., 1977, vol. 22 (6), pp. 656–58.
A.A. Chernov, D.E. Temkin, and A.M. Mel’nikova: Sov. Phys. Crystallogr., 1976, vol. 21 (4), pp. 369–74.
G.F. Bolling and J.A. Cissé: J. Cryst. Growth, 1971, vol. 10, pp. 56–66.
D.M. Stefanescu, B.K. Dhindaw, S.A. Kacar, and A. Moitra: Metall. Trans. A, 1988, vol. 19A, pp. 2847–55.
D.K. Shangguan, S. Ahuja, and D.M. Stefanescu: Metall. Trans. A, 1992, vol. 23A, pp. 669–80.
C. Körber, G. Rau, M.D. Causman, and E.G. Cravalho: J. Cryst. Growth, 1985, vol. 27, pp. 649–62.
J. Pötschke and V. Rogge: J. Cryst. Growth, 1989, vol. 94, pp. 726–38.
Q. Han and J.D. Hunt: Iron Steel Inst. Jpn. Int., 1995, vol. 35 (6), pp. 693–94.
R.B. Fedich and W.R. Wilcox: Sep. Sci. Technol., 1980, vol. 15 (1), pp. 31–38.
R.H. Nunn: Intermediate Fluid Mechanics, Hemisphere Publishing Co., New York, NY, 1989, pp. 51–55.
D.R. Uhlmann, B. Chalmers, and K.A. Jackson: J. Appl. Phys., 1964, vol. 35, pp. 2986–93.
A. Cottrell: Introduction to the Modern Theory of Metals, The Institute of Metals, London, 1988.
P.K. Rohatgi, S. Ray, R. Asthana, and C.S. Narendranath: Mater. Sci. Eng., 1993, vol. A162, pp. 163–74.
A.W. Neumann, R.J. Good, C.J. Hope, and M. Sejpal: J. Colloid Interface Sci., 1974, vol. 69 (2), pp. 291–302.
S.N. Omenyi, A.W. Neumann, and C.J. Van Oss: J. Appl. Phys., 1981, vol. 52 (2) pp. 789–95.
A.W. Adamson: Physical Chemistry of Surfaces, John Wiley & Sons, Inc., New York, NY, 1982.
D.T. Livey and P. Murray: J. Am. Ceramic Soc., 1956, vol. 39 (11), pp. 363–72.
W.D. Kingery: J. Am. Ceramic Soc., 1954, vol. 37 (2), pp. 42–45.
S.H. Overbury, P.A. Bertrand, and G.A. Somorjai: Chem. Rev., 1975, vol. 75 (5), pp. 547–57.
L.R. Murr: Interfacial Phenomena in Metals and Alloys, Addison-Wesley, Reading, MA, 1975.
A.A. Chernov: private communication, University Space Research Association, Huntsville, AL, 1997.
J.G. Li: Ceram. Int., 1994, vol. 20, pp. 391–412.
CRC Handbook of Chemistry and Physics, 67th ed., R.C. Weast, ed., CRC Press Inc., Boca Raton, FL, 1986.
T. lida and R.I.L. Guthrie: The Physical Properties of Liquid Metals, Clarendon Press, Oxford, United Kingdom, 1988.
ASM Handbook, ASM INTERNATIONAL, Materials Park, OH, 1990, vol. 2, pp. 1099–1201.
Thermophysical Properties of High Temperature Solid Materials, Y.S. Touloukian, ed., The Macmillan Company, New York, NY, vol. 4.
Y.S. Touloukian, R.W. Powell, C.Y. Ho, and P.G. Klemens: Thermophysical Properties of Matter, IFI/Plenum, New York, NY, 1970, vol. 1.
G. Kaptay: Mater. Sci. Forum, 1994, vol. 20, pp. 467–74.
D.J. Shaw: Introduction to Colloid and Surface Chemistry, Butterworth and Co., London, 1980.
D. Langebin: in Intermolecular Forces, B. Pullman, ed., Reidel, Dordrecht, Netherlands, 1981, p. 547.
S.N. Omenyi and A.W. Neumann: J. Appl. Phy., 1976, vol. 47, p. 3956.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Stefanescu, D.M., Juretzko, F.R., Catalina, A. et al. Particle engulfment and pushing by solidifying interfaces: Part II. Microgravity experiments and theoretical analysis. Metall Mater Trans A 29, 1697–1706 (1998). https://doi.org/10.1007/s11661-998-0092-3
Received:
Issue Date:
DOI: https://doi.org/10.1007/s11661-998-0092-3