Abstract
A population balance model is presented for the coarsening of the dispersed phase of liquid-liquid two-phase mixtures in microgravity due to gravity sedimentation and Marangoni migration, which lead to the collision and coalescence of droplets. The model is used to predict the evolution of the size distribution of the dispersed phase in a liquid-phase miscibility gap system, Zn-Bi, which has been used in a number of experimental microgravity processing studies in which significant phase segregation has been observed. The analysis shows that increasing the temperature gradient, gravity level, volume fraction of the dispersed phase, initial average drop radius, initial standard deviation of droplet radii, or the temperature coefficient of the interfacial tension leads to an increase in the rate of droplet growth due to collision and coalescence. Comparison of the distribution evolutions for unimodal and bimodal initial distributions shows that the latter yield significantly more rapid droplet growth. Finally, it is shown that droplet growth can be dramatically reduced with antiparallel orientation of the gravity vector and the temperature gradient, provided that the relative magnitude of these two vectors is properly chosen.
Similar content being viewed by others
References
H.U. Walter:ESA Spec. Publ. 219, 1984, pp. 47–64.
B. Predel, L. Ratke, and H. Fredriksson: inFluid Sciences and Materials Science in Space: A European Perspective, H.U. Walter, ed., Springer-Verlag, New York, NY, 1987, pp. 517–65.
H.U. Walter: inMaterials Sciences in Space, B. Feuerbacher, H. Hamacher, and R.J. Naumann, eds., Springer-Verlag, New York, NY, 1986, pp. 343–78.
J.M. Reger: Interim Report on NASA Contract NAS8-28267, TRW Systems Group, Redondo Beach, CA, May 1973.
H. Ahlborn and K. Lohberg:17th AIAA Conference, New Orleans, LA, 1974, Paper No. 74–208.
L.L. Lacy and G.H. Otto:AIAA J., 1975, vol. 13, pp. 219–20.
T. Carlberg and H. Fredriksson:Metall. Trans. A, 1980, vol. 11 A, pp. 1665–76.
H. Fredriksson:ESA Spec. Publ. 219, 1984, pp. 25–34.
A. Kneissel, P. Pfefferkorn, and H. Fischmeister:ESA Spec. Publ. 191, 1983, pp. 55–62.
S.H. Gelles, A.J. Markworth, and C.E. Mobley:ESA Spec. Publ. 191, 1983, pp. 307–12.
I.M. Lifshitz and V.V. Slyozov:J. Phys. Chem. Solids, 1961, vol. 19, pp. 35–51.
J.S. Langer and A.J. Schwartz:Phys. Rev. A, 1980, vol. 21, pp. 948–58.
H. Lamb:Hydrodynamics, 6th ed., Dover, New York, NY, 1932, p. 601.
N.O. Young, J.S. Goldstein, and M.J. Block:J. Fluid Mech., 1959, vol. 6, pp. 350–56.
ESA Spec. Publ. 219, 1984, pp. v–ix.
A. Bergman and H. Fredriksson: inMaterials Processing in the Reduced Gravity Environment of Space, G. Rindone, ed., North Holland, New York, NY, 1982, pp. 564–78.
B.C. Allen: inLiquid Metals: Physics and Chemistry, S. Beer, ed., Marcel Dekker, Inc., New York, NY, 1972, pp. 161–204.
L. Ratke:J. Colloid Interface Sci., 1987, vol. 119, pp. 391–97.
R.H. Davis:J. Fluid Mech., 1984, vol. 145, pp. 179–99.
X.E. Berry:J. Atmos. Sci., 1967, vol. 24, pp. 688–701.
X.E. Berry and R.L. Reinhardt:J. Atmos. Sci., 1974, vol. 31, pp. 1814–31.
W.K. Witherow and B.R. Facemire:J. Colloid Interface Sci., 1985, vol. 104, pp. 185–92.
D. Langbein:ESA Spec. Publ. 219, 1984, pp. 3–12.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Rogers, J.R., Davis, R.H. Modeling of collision and coalescence of droplets during microgravity processing of Zn-Bi immiscible alloys. Metall Trans A 21, 59–68 (1990). https://doi.org/10.1007/BF02656424
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02656424