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the effect of fluid flow due to the crystal-melt density change on the growth of a parabolic isothermal dendriteThe Ivantsov (1947) analysis of an isolated isothermal dendrite (with zero surface tension) growing into a supercooled liquid is extended to include the effects of the fluid flow due to volume contraction or expansion upon solidification. For an axisymmetric paraboloidal dendrite, an analytic solution to the Navier-Stokes equations is obtained. The magnitude of the flow is proportional to the relative density change epsilon, and the flow becomes negligible far from the surface of the dendrite. The temperature field consistent with this flow can also be found explicitly. The well-known expression that relates the dimensionless supercooling to the Peclet number in the absence of fluid flow is modified for nonzero epsilon, but the effect is of order epsilon and hence is seen to be minor for most values of epsilon and dimensionless supercooling that occur in practice.
Document ID
Document Type
Reprint (Version printed in journal)
Mcfadden, G. B.
(National Bureau of Standards Gaithersburg, MD, United States)
Coriell, S. R.
(NBS Gaithersburg, MD, United States)
Date Acquired
August 12, 2013
Publication Date
April 1, 1986
Publication Information
Publication: Journal of Crystal Growth
Volume: 74
ISSN: 0022-0248
Subject Category
Distribution Limits